Document YjK4jJZE7Xr3yYZoq1djz2EJE

PLAINTIFF'S EXHIBIT American Writer Works Association ANSI/AWWA C403-78 (First Edition) AWWA STANDARD PRACTICE for THE SELECTION OF ASBESTOS-CEMENT TRANSMISSION AND FEEDER MAIN PIPE, SIZES 18 IN. THROUGH 42 IN. ilCAN NATIONAL] SSTANDARDS* Approved by .1 IVWA Board of Directors Jan. 28, 1978. Approved by American .National Standards Institute. Inc., Jut. 17, 1978. AMERICAN WATER WORKS ASSOCIATION 6666 West Quincy Avenue, Denver, Colorado 80235 CTD000727 Committee Personnel [ he Standards Committee on Asbestos-Cement Pressure Pipe that reviewed and approved this standard had the following personnel at the tin e of approval: R. S. Bryant, Chairman J. L. Warden, Vice-Chairman T. R. Gillen, Secretary Consumer Members S. C. Baker, Nat al Facilities Engineering Command, Alexandria, VA L. C. Bradley, Fort Worth Water Department, Forth Worth, TX R. S. Bryant, Department of Water and Power, Los Angeles, CA F. (Denson, Works and Operations Department, Winnepeg, Manitoba R. Graff, Water l tilities, San Diego, CA J. E. Johnson,* l S Bureau of Reclamation, Denver, CO R. A. Mari hand, Water Department, Warren, OH J. L. Warden, l S Bureau of Reclamation, Denver, CO (NAYFAC) (AWWA) (ASCE) (AWWA) (AWWA) (BLREC) (AWWA) (BLREC) General Interest Members G. C. Anderson. Insurance Services Office, New York, NY R. A. Barrows, C. E. Maguire, Inc., Waltham, MA Y. R. Bivkkl, Department of Environmental Health, Albuquerque, N'M S. L. Bishop,* Metcalf X Eddy, Boston, MA C. L. Frick,* Insurance Services Office, New York, NY R. S. Holxigren Jr., James M. Montgomery, La Jolla, CA F. A. Obert, Metcalf X Eddy, Boston, MA J. S. Slicer, Factory Mutual Research, Norwood, MA M. R. Slchomel, L'nderwriters Laboratories, Northbrook, IL W. Taggart, Wright-McLaughlin Engineering, Denver, CO (ISO) (NEWWA) (APWA) (N EW'W'A) (ISO) (AWWA) (WTCF) (FMR) (LL) (ASCE) Producer Members A. E. Alpine, Cement Asbestos Products Co., Birmingham, AL T. R. Gillen, Johns-Manville Sales Corp., Denver, CO J. C. J.u kson, Asbestos-Cement Pipe Producers Association, Washington, DC E. J. Lawless. CertainTeed Products Corp., Yalley Forge, PA 11. L. Olmin,* Johns-Manville Sales Corp., Denver, CO (AWAYA) (AWWA) (ACPI'Aj (AWWA) (AWWA) y Alternate Copyright 1978 by American Water Works Assn. Printed in US ii CTD000728 Table of Contents SEC. UAt 'U Foreword I. History ofStandard............................... v II. i ............................................ vi Standard 1 General............................................ 1.1 Scope .................................................... 1 I 2 GeneralDesign ............................... 2.1 Strength .uul DcAgu Factors 2.2 Combined Loading Theory. . 2..i Three-Edge Bearing Load........... 2 4 .1 External Loads....................................... 4.1 Introduction............................................. 4.2 Earth Loads............................................. 4.3 Superimposed Loads............................. 4 4 4 20 SEC. L'AttU 4 impact Factors......... ... 21 5 V alues of Load Coefficients C, for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit................. 21 6 Concentrated Superimposed (Wheel) Load on Asbestos-Cement "Transmission Pipe--Single Wheel = 16 000 lb (H-20) ... . 7 Design Internal Pressure and Design External Load Intercepts for L se With Selection Curves ... 25 8 Minimum Safety Factors for Lse With Asbestos-Cement Transmission-Pipe Selection.......... 25 Cl Present Worth of an Income of SI a Year for the Next n Years............. C5,9 4 Hydrostatic Pressure............................ 4.1 Introduction............................................ 4.2 Operating Pressure ......................... 4.3 Surge Pressure........................................ 22 22 24 24 5 Pipe Selection......................................... 5.1 Combined Loading Curves............... 5.2 Safety Factors ....................................... 5.4 Lse of Selection Charts for Economical Design........................... 5.4 Illustrative Problem on Pipe Selection................................................ 24 24 24 24 25 Appendices A Friction Loss of Head Chart............. A1 B Surge Pressure Analysis....................... B1 B.l Water Hammer or Surge......... B1 B.2 Water Hammer Analysis......... B2 B.3 Valve Closure............................... B2 B.4 Pumped Systems......................... B4 B.5 Methods of Control.................... B5 B.6 Surge Calculation Example. . . B6 B.7 Air in Pipelines............................ B7 C Frictional Power Requirements........ Cl Tables 1 Correlation of Bedding Conditions, Pipe Size, and Bedding Load Factors ................................................ 2 Earth Loads fib/Lin ft)........................ 4 Recommended Safe Design Values of c for Tunnel Conditions ............. 4 7 18 Figures 1 Bedding Conditions............................ 2 2 Load Pressure Curve.................................... 1 3 Crushing Test Assembly................... 4 4 Classification of Construction Techniques...................................... 5 5 Values of C,i for "Trench Conditions. 6 6 Embankment Conditions.................. 12 7 Values of Cc for Positive Projecting Pipe........................................................ 13 8 Values of BJBi at Which the Trench and Positive Projecting Pipe Equations Give Equal Loads . . 14 9 Values for C,, for Negative Projecting Pipe and Imperfect Ditch Conditions............................................ 16 10 Projection Ratio ip) for the Negative Projecting Pipe Embankment Condition.............................................. 11 Projection Ratio (/>) for the Imperfect Trench Embankment Condition........................................... 17 18 12 Values of Cr for Tunnel Conditions. 19 13 Superimposed Loads........................... 20 14 Combined Loading Curves for Pipe Sizes 18 In. Through 42 In. . . . 2 7, 46 B1 Time (Te) = Effective for Full Cut Off L'niformly at Maximum Rate B4 Cl Yearly Power Cost to Compensate for Friction Loss of Head _.C2,3 in CTD000729 # Foreword This foreword is for information only and is not a part of .1 IVIVA C403 I. History of Standard A new pipe material consisting of an intimate mixture of portland cement and asbestos fibers was intro duced to the North American market in 1931 following several years of usage in other countries, particularly 1taly. In the ensuing years, this type of pipe gained popularity, and in 1949 AWVYA established a committee on standard specifications for asbestoscement pipe under the chairmanship of S. M. Clark of (ireeley and Hanson, Chicago. 1'he committee developed a stan dard for asbestos-cement water pipe 'which was approved by the AWWA Board of Directors as tentative, A\Y\YA C400-53T, May 15, 1953. In 1958, the committee was reacti vated as Committee 8340D on Asbes tos-Cement Pipe under the chairman ship of Roy H. Ritter, Whitman, Requardt and Assocs., Baltimore, to review several suggested changes and to recommend revisions to the stan dard. The committee produced a revised tentative standard adopted as A\Y\YA C400-64T, Jan. 27, 1964. It was advanced to standard without revision Jul. 2, 1965 and designated as AWAYA C400-65. The committee concluded that an installation guide was desirable to bring to the attention of users certain important requirements on the inspec tion, handling, installation, and field testing of asbestos-cement pressure kpipe. The committee submitted its "final draft in 1963, and it received approval as tentative, AWWA C603- 64T, Jan. 27, 1964. It was advanced to standard without revision Aug. 9, 1965 and designated as AWWA C603-65. In early 1968, the committee was reactivated as the Standards Com mittee on Asbestos-Cement Pipe to review and revise all AWWA stan dards on asbestos-cement pipe. The committee produced a revised stan dard approved by the AWWA Board of Directors Jan. 31, 1972, designated as AWWA C400-72, "Standard for Asbestos-Cement Pressure Pipe for Water and Other Liquids." AWWA C401-64, "Standard Prac tice for the Selection of AsbestosCement Water Pipe" (originally des ignated Handbook H 2), was first approved by the AWWA Board of Directors Jan. 27, 1964. Although it covered pipe sizes up to and including 36 in., it was primarily intended for use with asbestos-cement pipe in smaller distribution sizes (4 through 16 in.). In the winter of 1972-1973 the committee was reorganized and en larged to include representatives of national organizations having an in terest in the scope of the committee and wishing to participate in the work. The reorganized committee reaffirmed AWAYA C400-72 without revision so that it could be presented to the American National Standards Institute for designation as an Ameri can National Standard. In 1975 the committee produced a revised standard that was approved by the AWWA Board of Directors Jan. 26, 1975, and designated AWWA V 1 CTD000730 FOREWORD C400-75, "Standard for AsbestosCement Pressure Pipe, 4 in. Through 24 in., for Water and Other Liquids." The asbestos-cement pipe manufac turers have developed a new series of large pipe classifications, designed to give greater freedom of selection to design engineers. 'Phis is of particular significance for large diameter pipeline projects where the savings in material cost can exceed the increased cost of more detailed design, better control of methods of installation, and pro vision of surge controls when justified. To provide the user with a ready reference and specification for this type of pipe, known as transmission pipe, the committee produced and the AWWA Board of Directors approved AWWA C402-75, "Standard for As bestos-Cement Transmission Pipe, 18 in. Through 42 in., for Water and Other Liquids." The possibility of confusion between the two 1975 standards, AWWA C400 and C402, was carefully reviewed by the committee. The results were AW WA C402-77, which covers sizes 18 through 42 in., and AWWA (7400-77, which covers sizes 4 through 16 in. There is now no overlap of sizes. Consequently, it was desirable to revise AWWA C401-64 so that it would be directly compatible with AWWA C400-77, and to develop a new pipe selection standard to be directly compatible with AWWA C402-77. ' AWWA C401-77 and this new standard, AWWA C403, "Stan dard Practice for the Selection of Asbestos-Cement Transmission and Feeder Wain Pipe, Sizes 18 in. Through 42 in.," are the result. II. Discussion The effect of water hammer gener ated by the opening and closing of fire hydrants can be of significant magni tude in small distribution pipe sizes due to the high velocities generated by open hydrant How conditions. Furthermore, it is difficult to accu rately evaluate the magnitude of these surges; and, if calculated, con trol through the use of surge tanks or other devices is impractical. Rather than employ a rule-of-thumb allow ance for surge based upon an assumed velocity change, to compensate for undetermined surge pressures AWAV'A C400-77 (covering sizes 4 through 16 in.) incorporates a large fixed safety factor for each asbestos-cement pres sure class. In large transmission and feeder main pipe sizes the effect of surge pres sures generated by the opening and closing of fire hydrants connected to smaller diameter distribution pipelines is of significantly lower magnitude. For example, the surge pressure gener ated by hard closure of a hydrant connee ted to a 6-in. distribution line would be nine times greater than that which would occur in an 18-in. feeder main supplying a 6-in. distribution line. Major surge pressures in large transmission or feeder main pipelines, caused by stopping and starting pumps and similar components, are more readily calculated. It also is more economically practical to control these surges by incorporating into the system design a variety of devices which will reduce anticipated surge pressures to lower levels. This stan dard is based on individually evaluat ing all stress loadings placed on a pipe and on applying adequate safety fac tors commensurate with a complete review of all design criteria. CTD000731 I * ANSI/AWWA C403-78 (First Edition) AWWA Standard Practice for The Selection of Asbestos-Cement Transmission and Feeder Main Pipe, Sizes 18 in. Through 42 in. Section 1--General Sec. 1.1 Scope This standard has been prepared so that design engineers may quickly determine the correct strength classifi cation of asbestos-cement transmis sion pipe to use under various com binations of internal pressure (static, operating, and surge) and external load (earth and superimposed live loads). Combined loading curves de picting the relationship between hy drostatic loading and external loading capabilities are included to expedite the selection of the correct pipe strength classification. Note: Information to assist the engineer in selecting the most eco nomical size of pipe is in the ap pendices. Appendix A contains a friction loss of head chart based on the Hazen and Williams formula. Appendix B is a detailed analysis of surge pressure factors. Appendix C includes tables to assist the engineer in determining the yearly power costs to overcome friction loss of head. The appendices are for information only and are not part of AWWA C403. 1.1.1 Pipe classifications. The pipe strength classifications of 30, 35, 40, 45, 50, 60, 70, 80, and 90 refer to the similarly numbered classifications specified in AWWA C402, "Standard for Asbestos-Cement Transmission Pipe, 18 In. Through 42 In., for Water and Other Liquids." 1.1.2 Installation. Detailed cover age of the installation of asbestoscement pipe can be found in AWWA C603, "Standard for the Installation of Asbestos-Cement Pressure Pipe." CTD000732 1 1 A-C TRANSMISSION' AND REF.DISK MAIN PIPE Section 2--General Design Sec. 2.1 Strength and Design Factors The strength of asbestos-cement transmission pipe must be sufficient to withstand the com!lined forces of all types of internal pressures (static, operating, and surge) and externa! loadings (earth, live, and impact). Sound engineering practice also re quires that adequate safety factors he applied to strength requirements to ensure performance under other than ideal or calculated loading conditions. The magnitude of these safety factors is inversely proportional to the confifidence that the designer lias in engineering estimates of actual operat ing conditions. Suggested safety fac tors based on experience are in cluded under specific design factor subheadings. 2.1.1 Bedding conditions. The bed ding conditions described in Fig. 1 have been selected as representative of typical installation conditions en countered in the field. Descriptions of bedding conditions are as follows: Class A--Gravel or sand base, back fill compacted. (Approximately cS()r) Standard Proctor, AASHTO T-W.) Class B--Same as A, but backfill not compacted. Class C--Pipe laid on earth mounds or pipe barrel on flat trench bottom with excavated coupling holes, back fill compacted. (Approximately b()(, Standard Proctor, AASHTO T-0.) Class D--Pipe barrel on flat trench bottom with excavated coupling holes, backfill not compacted. Sec. 2.2 Combined Loading Theory Fig. 1. Bedding Conditions Class .1 bedding conditions are slw.cn in (</) and (b). Class C conditions are sltoun in (<) and (d). In all four diagrams, the lightly shaded area represents approved backfill, not frozen and free from lumps, large stones, boulders, or other unsuitable substances. The heavily shaded areas represent approved backfill, carefully compacted in 4-in. layers. In (a), a minimum of 2 in. of sand is placed in a shaped bottom under the pipe. In (hi, the pipe is bedded in a gravel base. In in, the pipe barrel rests on earth mounds and then the backfill between the earth mounds is com pacted. In (d), the pipe barrel is resting on the fiat bottom of the trench. Class B condition is the same as Class .4, and Class D is the same as Class C except that the backfill is not compacted in B or D. indicate that there is a relationship between the combined loads at the point of pipe fracture. This relation ship can be represented by a parabolic curve as shown in Fig. 2. The equa tion for the load pressure parabolic curve, which is known as the Schlick formula, may be expressed as : Tests of asbestos-cement pipe under various combinations of internal pres sure and external crush load applied in three-edge bearing (see Sec. 2.3) in u Inch, P is the internal pressure, in pounds CTD000733 SECTION 2 3 Fig. 3. Crushing Test Assembly P represents the internal pressure; \V the external load. per square inch, that will hurst the pipe when no external load exists. \V is the external load, in pounds per lineal foot of pipe in the three-edge bearing test, that will crush the pipe when no internal pressure exists. pr is the internal pressure, in pounds per square inch which, in combination w ith some external load u't applied in three-edge bearing, will fracture the pipe. wT is the external load, in pounds per lineal foot of pipe applied in threeedge bearing which, in combination with some internal pressure pr, will fracture the pipe. The diagram at the left shows a side view of the test assembly; that at the right, an end view. P represents load; R, approximately 0.5 in.--the radius of the bearings; D, the nominal diameter of the pipe; and C, the clear space between sup ports. C should be approximately 1 in. ft of internal pipe diameter but in no case less than l in. it is necessary to apply a bedding load factor to the laboratory threeedge bearing loads to correlate them to the actual field loads. Since the external load equals the bedding fac tor times the three-edge bearing load, the bedding factor equals the external load divided by the three-edge bearing load. Table 1 shows bedding factors to be applied for each of the bedding conditions described in P'ig. 1. TABLE 1 Sec. 2.3 Three-Edge Bearing Load Correlation of Bedding Conditions, Pipe Size, and Bedding Load Factors The combined loading curve shown in Fig. 2 is calculated on the basis of crush strengths determined by labora tory tests employing the three-edge bearing test method, which utilizes hardwood test blocks (Fig. 3). Be cause the field supporting strength of a pipe is influenced by the bedding conditions and by the lateral pressure acting against the sides of the pipe, Bedding Class A B C D Pipe bize in. 18-20 24-42 18-42 18-20 24-42 18-42 Bedding Load Factor 1.8 2.0 1.5 1.4 1.5 1.1 CTD000734 L 4 \-L TRANSMISSION' AND FEEDER MAIN I'lI'E Section 3--External Loads Sec. 3.1 Introduction For the design of asbestos-cement transmission pipe external loads (te7-) are defined by die following equation : in which, u'r = the total external load in pounds per linear fool of pipe applied in three-edge bearing that, in com bination with some internal pressure, pr, will fracture the pipe. zc/,' = the total earth load in pounds per linear foot of pipe to which the pipe is subjected. The magnitude of this load is a direct function of the burial conditions encountered or specified (trench, embankment, tun nel, etc.). w.s = the total superimposed load, in pounds per linear foot of pipe, transmitted through the burial en vironment to the pipe by factors other than the earth loads. These loads can be static, dynamic, or a combination of both. B.F. = the bedding load factor, which is a load factor correlating three-edge bearing test loads to field loads associated with specific bedding conditions. (For a more explicit explanation see Sec. 2.3.) S.F. = the design safety factor specified by the design engineer. Safety factors are based on judgment, past experience, and sound engineer ing principles. For asbestos-cement transmission pipe, a design minimum safetv factor of 1.5 is recommended tor external loads. Sec. 3.2 Earth Loads Earth loads (zur) to which pipe is subjected are a function of the soil density, pipe diameter, depth of cover, and construction techniques employed in laying the pipeline. They depend on the interplay between the weight of the prism of earth directly o\er the pipe, called the interior prism, and the frictional shearing forces, plus or minus, transferred to that interior prism by the adjacent outside prisms of earth. The magnitude of earth loads caries with the construction technique employed. There tire two major construction techniques nor mally encountered: trench and em bankment. Another technique, the tunnel condition, is not normally found, but nevertheless has unique design methods which make its in clusion in this discussion necessary. Fig. 4 shows these three construction tech nit]ties. 3.2.1 Murston's equation. For as 9 bestos-cement transmission pipe de sign, earth loads are calculated by the general form of Marston's equation: in which, Ur -- Cu.\B- Kq 3 zcr = the total earth load trans mitted to the pipe in pounds per linear foot of pipe. U'c = the soil density in pounds per cubic foot. Soil densities range in value from 100 to 135 lb/cu ft. In the absence of accurate soil density information, a value of 120 lb/cu ft is recommended for asbestos-cement transmission pipe design. B = the trench width or pipe diam eter measured in feet. The value chosen depends on the installation conditions employed in laving the pipe. C = a coefficient that is dependent upon CTD000735 SECTION' 3 5 Fig. 4. Classification of Construction Techniques Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. 1.. Ratio of the height of fill to the width of trench or pipe diameter. , 2. Shearing forces between the interior and adjacent earth prisms. 3. Direction and amount of rela tive settlement between in terior and adjacent earth prisms for embankment con ditions. The calculations used to find the value of the coefficient will depend on the installation conditions employed in laying the pipe. Values for B and C must be deter mined to calculate earth loads by Eq. 3 for the trench, embankment, and tunnel construction techniques. The following subsections describe the different conditions and explain the methods for finding the values needed to use Marston's equation for soil loading. 3.2.2 Trench condition. A trench condition is defined as that in which the pipe is installed in a narrow trench, generally less than two to three diameters in width, cut in un disturbed ground and backfilled to the original ground surface, as illus trated in Fig. 4. For this condition, Eq 3 is rewritten as: we = CdWeB<r Eq 4 in which, Bd = the trench width in feet, measured at the top of the pipe. Cd = the load coefficient which is a function of the ratio H/Bd, where H is the height of the backfill in feet, measured to the top of the pipe, and Bd is the trench width as previouslydefined. 3.2.2.1 The values of Cd are ob tained from Fig. 5, in which curves A, B, C, D, and E take into account the CTD000736 6 A-C TRANSMISSION AND FEEDER MAIN PIPE Fig. 5. Values of Cd for Trench Conditions Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers." WPCF and ASCE. 1966. friction coefficient between the back fill and the sides of the trench for the various soil compositions likely to be encountered. Curve A is for granular materials without cohesions. Curve B is for sand and gravel. Curve C is for saturated top soil. Curve D is for clay. Curve E is for saturated clay. Table 2 contains a series of earth load selection tables and is included as a convenience. 3.2.3 Embankment condition. An embankment condition is defined as either that condition where the pipe is installed in a trench that is w ider than two to three pipe diameters and that is cut in undisturbed ground, or that condition where the pipe is CTD000737 i SECTION 7 TABLE 2 Earth Loads (lb/lineal ft) Note: Values are for clay (part D of Fig. 9. K/* = K#*' = 0.130) with weight of earth taken as 120 Ib'cu ft. Correction for other earth weights may be made by simple direct proportions. For corrections for other types of soils, reier. to formulas in Sec. 3. Boldface figures indicate maximum earth load for depth of trench. Pipe size 18 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 2.5 490 640 810 1 000 I 200 1 350 1 500 1 600 1 725 1 850 2 050 2 200 2 300 2 400 2 500 2.75 640 835 i no 1 320 1 520 1 690 1 850 2 000 2 120 2 360 2 570 2 720 2 840 3 000 3.0 1 240 l 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 4.0 4.5 5.0 5.5 1 640 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 2 825 3 230 3 550 4 000 4 400 4 800 5 100 5 350 3 635 4 440 5 220 5 640 6 040 6 400 6 040 6 830 7 450 7 620 Width 2 ft 5 in. 2 ft 8 in. 2 ft 10 in. 3 ft 8 in. 3 ft 10 in. 4 ft 0 in. 4 ft 1 in. 4 ft 3 in. 4 ft 5 in. 4 ft 7 in. 4 ft 9 in. 5 ft 0 in. 5 ft 2 in. Pipe size 20 in. ID Trench Width--ft 2.7S 545 705 870 1 110 1 320 1 520 1 690 1 850 2 000 2 120 2 380 2 570 2 720 2 840 3 000 3.0 890 1 250 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 1 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 3.75 4.0 4.5 5.0 5.5 1 750 2 050 2 500 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 1 770 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 2 220 2 655 3 000 3 300 3 650 4 000 4 400 4 800 5 100 5 350 3 095 3 545 3 980 4 660 5 200 5 640 6 040 6 400 4 310 5 760 6 450 7 060 7 450 6 640 7 500 8 410 Width 2 ft 8 in. 2 ft 10 in. 3 ft 0 in. 3 ft 4 in. 3 ft 8 in. 3 ft 11 in. 4 ft 1 in. 4 ft 3 in. A ft 5 in. 4 ft 6 in. 4 ft 10 in. 5 ft 1 in. 5 ft 2 in. 5 ft 4 in. S ft 7 in. l CTD000738 L 8 A-C TRANSMISSION AND FEEDER MAIN PIPE TABLE 2--Continued Pipe size 21 in. ID Trench ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width --ft 2.75 570 745 870 1 110 l 320 1 520 l 690 l 850 2 000 2 120 2 360 2 570 2 720 2 340 3 000 3.0 730 915 l 250 1 450 1 700 l 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 I 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 1 380 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 3.75 1 360 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 880 4.0 2 325 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 2 795 3 250 3 725 4 140 4 660 5 200 5 540 6 040 6 400 5.0 4 210 5 160 6 000 6 450 7 050 7 450 5.5 6 100 7 020 7 950 8 460 6.0 8 920 Willi li 1 it 9 in. 2 it 11 in. 3 ft 2 in. 3 it 6 in. 3 ft 10 in. 4 ft 6 in. 4 ft ! in. 4 it 9 in. 5 tt 0 in. 5 it 3 in. 5 it 6 in. 5 It 8 in. Pipe size 24 in. ID Trench C v 11 ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 3.0 630 805 955 1 250 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 810 l 010 1 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 1 010 l 400 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 3.75 1 490 l 940 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 4.0 2 030 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 2 550 3 080 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 3 620 4 130 4 660 5 400 6 000 6 450 7 050 7 450 5.5 4 660 5 740 6 750 7 410 8 000 8 460 6.0 6.5 6 800 7 850 8 910 9 600 10 000 Width 3 it 1 in. 3 it 3 m. 3 it 5 in. 3 it 9 in. 4 ft 1 in. 4 ft 5 in. 4 it 8 in. 4 it 10 in. 5 it 0 in. 5 it 2 in. 5 it 5 in. 5 it H in. 5 it 11 in. 6 it l in. 6 it 2 in. CTD000739 SECTION i 9 TABLE 2--Continued Pipe size 27 in. ID Trench Cover ft 2 2.5 3 4 5 7 8 9 10 12 14 16 18 20 Trench Width--ft 3.25 710 895 1 040 1 330 1 010 I K65 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 905 1 095 1 400 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 000 3 900 4 150 4 350 3.75 1 540 1 940 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 4.0 1 600 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 2 200 2 735 3 110 3 480 3 790 4 140 4 660 5 200 5 840 6 040 6 400 5.0 3 385 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 5.5 3 980 4 590 5 190 6 060 6 750 7 410 8 000 8 460 6.0 6 390 7 550 8 300 9 000 9 600 6.5 7.0 7 560 8 800 9 960 10 890 10 000 11 180 Transition Width 3 it 5 in. 3 ft 6 in. 3 ft 8 in. 4 ft in. 4 tL 6 in. 5 ft 1 in. 5 ft 3 in. 6 ft 0 in. 6 ft 3 in. 6 ft 6 in. 6 ft 8 in. 6 ft 10 in. Pipe size 30 in. ID Trench u 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 3.5 755 965 1 150 1 400 l 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 4.0 1 185 1 675 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 1 680 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 2 340 3 005 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 5.5 6.0 6.5 7.0 7.5 3 665 4 320 4 840 5 260 6 060 6 750 7 410 8 000 8 460 4 980 5 660 6 800 7 550 8 300 9 000 9 600 6 990 8 320 9 210 9 960 10 890 8 320 9 610 10 980 11 890 10 980 12 300 Width 3 ft 7 in. 3 ft 10 in. 3 ft ll in. 4 ft 5 in. 4 ft 8 in. 5 ft 0 in. 5 ft 5 in. 5 ft 7 in. 5 ft 10 in. 6 ft in. 6 ft 5 in. 6 ft 9. in. 7 ft 0 in. 7 ft 3 in. 7 ft 5 in. CTD000740 10 A-C TRANSMISSION AND FEEDER MAIN PIPE TABLE 2--Continued Pipe size 33 in. ID Trench Cover ft 2 1.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 3.75 810 1 050 1 220 1 540 1 940 2 210 2 515 2 705 3 040 3 240 3 660 4 050 4 350 4 620 4 860 4.0 1 060 l 290 l 675 2 050 2 400 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 5 575 4.5 1 815 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 2 445 3 050 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 5.5 3 205 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 6.0 6.5 7.0 7.5 8.0 3 925 4 640 5 400 5 000 6 800 7 550 8 300 9 000 9 600 5 610 6 070 7 450 8 350 9 210 9 960 10 890 7 550 9 030 10 110 It 060 11 890 10 470 12 120 13 020 13 390 Transition Width 3 ft 10 in. 4 ft 6 in. 6 ft 10 in. 7 ft 11 in. Pipe size 36 in. ID Trench Cover ft 2.5 3 4 5 6 7 8 y 10 12 14 16 18 20 Trench Width--/ 4.0 920 t 130 1 325 l 675 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 925 1 145 1 550 1 950 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 I 950 2 555 3 050 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 5.5 2 555 3 340 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 6.0 3 340 4 160 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 6.5 7.0 7.5 8.0 8.5 4 950 5 760 6 430 7 450 8 350 9 210 9 960 10 890 5 760 6 540 8 150 9 170 10 110 11 060 11 890 8 150 9 750 11 000 12 150 13 020 9 750 11 330 12 900 14 140 12 900 14 510 Width 4 ft 3 in. 4 ft 4 in. 4 ft 11 in. 5 ft 3 in. 6 ft 10 in. 7 ft 4 in. 7 ft 8 in. 7 ft 11 in. 8 ft 2 in. 8 ft 6 in. CTD000741 SECTION 3 11 TABLE 2--Continued Pipe size 39 in. ID Trench ft 2 2.5 3 -1 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 4.5 990 l 290 l 520 1 950 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 1 580 2 220 2 555 3 050 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 5.5 2 340 2 980 J J40 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 6.0 3 680 4 320 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 6.5 7.0 7.5 8.0 8.5 9.0 4 500 5 360 5 760 6 430 7 450 8 350 9 210 9 960 10 890 6 430 7 170 8 150 9 170 10 110 11 060 11 890 7 440 8 980 9 750 11 000 12 150 13 021 9 310 11 090 11 980 12 900 14 140 12 830 14 330 IS 260 16 130 Width 4 ft 5 in. 4 ft 7 in. 4 ft 9 in. 5 ft 2 in. 5 ft 6 in. 5 ft 10 in. 6 ft 3 in. 6 ft 7 in. 6 ft 11 in. 7 ft 3 in. 7 ft 8 in. 8 ft t in. 8 ft 5 in. 8 ft 8 in. 8 ft 11 in. Pipe size 42 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 1 060 1 390 1 700 2 220 2 555 3 050 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 2 350 3 080 3 340 3 920 4 460 4 840 S 260 6 060 6 750 7 410 8 000 8 460 3 930 4 320 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 4 690 5 600 5 760 6 430 7 450 8 350 9 210 9 960 10 880 6 630 7 170 8 150 9 170 10 110 11 060 11 890 7 730 8 980 9 750 11 000 12 150 13 020 9 830 10 940 11 980 12 900 14 140 11 550 13 580 14 390 15 260 15 250 16 430 16 830 Transition Width 4 ft 8 in 4 ft 10 in. S ft 0 in. 5 ft 4 in. 5 ft 8 in. 6 ft 1 in. 6 ft 5 in. 6 ft 10 in. 7 ft 2 in. 7 ft 6 in. 8 ft 0 in. 8 ft 5 in. 8 ft 10 in. 9 ft 1 in. 9 ft 4 in. CTD000742 12 A-C TRANSMISSION AND FEEDER MAIN PIPE Fig. 6. Embankment Conditions aa and bb The trench width is less than the transition width; earth loads are computed by the trench equation (Eq 4). cc The trench width is the transition width; earth loads are computed by either Eq 4 or Eq 5. dd and ee The trench width is greater than the transition width; earth loads are computed by the positive projecting pipe embankment equation (Eq. 5). For a given depth of cover the earth loads resulting from trench widths cc, dd, and ee are equal. covered with fill above the original ground surface. Embankment con ditions are further subdivided into positive and negative projecting pipe categories, depending on the location of the top of the pipe relative to the original undisturbed ground. A special case where compressible ma terial is used as part of the backfill, called an imperfect trench, also is classified as an embankment con dition. The various embankment conditions are illustrated in Fig. 6. 3.2.4 Positive projecting pipe em bankment condition. A positive pro jecting pipe condition is defined as either that condition where the pipe is installed in a trench cut in un disturbed ground that is wider than two to three pipe diameters, or that condition where the top of the pipe is above the adjacent original ground surface and covered with fill above the original ground surface. For this condition, Eq 3 is rewritten as: in which, Ws = CcW.Be* Eq 5 .Bc = the pipe outside diameter in feet. Cc = the load coefficient, which is a function of the ratio H/Bc, the projection ratio p, and the settlement ratio r,i- 3.2.4.1 The values of Cc are ob tained from Fig. 7. Cc also may be obtained from Eq 6 when the follow ing conditions exist simultaneously: 1. The ratio H/Bc is greater than 1.3. 2. The product p(r.d) = 0.7. Cc = 1.892H/Bc - 0.96 Eq 6 3.2.4.2 The projection ratio p is defined as the ratio of the distance that the top of the pipe projects above the original ground surface to the pipe outside diameter. The recommended value for the settlement ratio r,d is +0.7 for asbestos-cement transmis sion pipe design. 3.2.5 Transition width. It will be noted from the preceding discussion that under construction conditions where a trench is cut in undisturbed ground two methods of computing the earth load are available: (1) the trench condition, and (2) the positive projecting pipe embankment con dition. The method chosen is de- CTD000743 4 SECTION' 3 13 Fig. 7. Values of Cc for Positive Projecting Pipe Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. pendent on the ratio of the trench width to the pipe diameter. As pre viously stated, when the trench width is less than two to three times the pipe diameter, earth loads are computed by the trench condition equation (Eq 4). The width of trench at which both methods of computation give equal loads is called the transition width. The earth load computed at the transition width is theoretically the maximum external earth load that can be transmitted to the pipe for any given depth of cover. For all trench widths greater than the transition width, earth loads are computed by the positive projecting pipe embank ment condition equation (Eq 5). In this latter case and for a given depth of cover, the earth loads are equal to the load that results at the transition width and that is computed by the trench condition equation (Eq 4). [See Fig. 6.] 3.2.5.1 The transition width is determined from Fig. 8 by multiplying 1 CTD000744 14 A-C TRANSMISSION' AND FEEDER MAIN FIFE CTD000745 0.1924 SECTION 3 15 the applicable ratio Bd/Br by the applicable pipe outside diameter (B,.). The applicable ratio of trench width to pipe outside diameter (Bd/Bc) can be obtained from Fig. 8 for any given ratio of backfill height to pipe outside diameter (FI/Br). 3.2.6 Negative projecting pipe em bankment condition. A negative pro jecting pipe condition is defined as that condition where the pipe is installed in a relatively shallow trench wherein the top of the pipe is at some elevation below the original ground surface. The trench is then backfilled and compacted, and embankment is constructed thereon to finished grade (Fig. 4). For this condition, Eq 3 is rewritten as tVE = Cn'&'Bd1 Eq 7 in which, Bd = the trench width in feet, mea sured at the top of the pipe. C,, = the load coefficient which is a function of the ratio H/Bd, the pro jection ratio p, and the settlement ratio rsd. negative projecting pipes. However, as the trench width increases and the ratio Bd/B,. becomes greater than that given in Fig. 8, the earth load should be determined from Eq 5 for positive projecting pipes. Adherence to the preceding rule will result in the most realistic earth loads for design purposes. 3.2.7 Imperfect trench embankment condition. The imperfect trench em bankment condition occurs rather in frequently and is included for general information. The imperfect trench embankment condition refers to that construction technique wherein the pipe is first installed as a positive projecting pipe. A portion of the embankment is then built up to some elevation above the pipe top and thoroughly compacted as it is placed. A trench the same width as the pipe is then excavated directly over the pipe down to or near to its top and subsequently backfilled with loose compressible material. The remainder of the embankment is then built up to final elevation (Fig. 11). For this condition, Eq 3 is rewritten as 3.2.6.1 The various values of Cn are obtained from Fig. 9. The pro jection ratio p is defined as the ratio of the vertical distance from the original ground surface down to the pipe top to the trench width, Bd. (See Fig. 10.) For asbestos-cement transmission pipe design the recom mended value for the settlement ratio rid is zero. 3.2.6.2 When calculating earth loads under negative projecting pipe embankment conditions, considera tion must be given to the transition width as defined in paragraph 3.2.5. For values of the ratio Bd/Br less than those given in Fig. 8, the load on a pipe is determined from Eq 7 for ke = CnV.Bp Eq 8 in which, Bc = the pipe outside diameter in feet. C,, = the load coefficient which is a function of the ratio H;BC, the pro jection ratio p, and the settlement ratio rsd. 3.2.7.1 The various values of C,, are obtained from Fig. 9. The pro jection ratio p is defined as the ratio of the vertical distance from the top of the excavated trench down to the pipe top to the pipe diameter (Fig. 11). For asbestos-cement transmis sion pipe design the recommended CTD000746 16 A-C TRANSMISSION AND FEEDER MAIN PIPE Coefficient C,, Fig. 9. Values of C,, for Negative Projecting Pipe and Imperfect Ditch Conditions Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers." WPCF and ASCE. 1966. value for the settlement ratio rsii is equal to --0.3. 3.2.8 Tunnel conditions. There are two types of tunnel construction en countered in normal pipe laying operation. 3.2.8.1. The first type is the most frequently encountered and occurs when a sleeve of a larger diameter than the specified pipe is first jacked through an embankment. The pipe is then placed into the sleeve without CTD000747 SECTION' 3 Top of embankment / Projection ratio = 17 Top of natural ground Fig. 10. Projection Ratio p for the Negative Projecting Pipe Embankment Condition becoming an integral part of the tunnel construction. In this example the sleeve supports the entire earth load and the pipe contained therein is not subjected to crushing loads. When selecting the required pipe classification for this condition, only the internal pressure needs to be con sidered for design. 3.2.8.2. The second type of tunnel condition is rarely encountered in transmission work but is discussed here for completeness. It occurs when the pipe itself must carry the entire load. The area through which the pipeline must pass is bored and braced with the necessary supports. The pipe then is placed in the tunnel and the void between the pipe and tunnel braces is backfilled with compacted earth, grout, or concrete. Once this operation is completed, the earth load automatically transfers from the tun nel supports to the pipe itself. For this condition, Eq 3 is rewritten as we = CtBt{w,Bt -- 2c) Eq 9 in which, Bt = the maximum width of the tunnel excavation in feet. c = the coefficient of cohesion in pounds per square foot. Ct = the load coefficient which is a function of the coefficient of internal fraction for the material of the tunnel and of the ratio H/BT, where H is the distance from the ground surface to the top of the tunnel in feet and Br equals the width of the tunnel ex cavation in feet. CTD000748 18 A-C TRANSMISSION AND FEEDER MAIN PIPE Top of embankment / Projection ratio = ' Compressible backfill Top of stage construction compacted fill / Trench dug in compacted fill Natural ground / $% Fig. 11. Projection Ratio p for the Imperfect Trench Embankment Condition 3.2.8.3 Values of Ct for different types of soil are obtained from Fig. 12. If the value for the coefficient of cohesion is not available from labora tory tests, then the recommended safe design values in Table 3 are to be used. TABLE 3 Recommended. Safe Design Values of c for Tunnel Conditions Material Clay, very soft Clay, medium Clay, hard Sand, loose dry Sand, silty Sand, dense Top soil, saturated Values of c 40 250 1000 0 100 300 100 3.2.8.4 When, in tunnel construc tion, the excavation becomes exces sive, or when the void surrounding the pipe or tunnel lining is not carefully filled, or when the cohesion of the undisturbed material above the tunnel construction is destroyed by soil saturation or vibration, the earth load should be calculated by Eq 4 for trench conditions. Since it can be exceedingly difficult to either predict or assess whether the tunnel excava tion is excessive, it is recommended that Eq 4 be used for most in stallations for safe asbestos-cement transmission pipe design. 3.2.8.5 It should be noted that the preceding discussion is based on the premise that the tunnel would be constructed in homogenenous soils that do not create unusual pressures and stresses. If the tunnel is con structed through materials that tend to squeeze or swell, such as some types of clay or shale, or through blocky and seamy rock, then methods other than tunnel construction must CTD000749 SECTION" 3 19 Values of coefficient Cj Fig. 12. Values of Ct for Tunnel Conditions Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. CTD000750 L 20 A-C TRANSMISSION' AND FEEDER MAIN PIPE Concentrated superimposed toad, wsi, vertically centered over pipe. Distributed superimposed load, wsj. vertically centered over pipe. Fig. 13. Superimposed Loads be utilized. The method of instal lation that is used is the responsibility of the engineer who is in charge of construction. Sec. 3.3 Superimposed Loads Superimposed loads ws are ex ternal loads other than the normal earth loads transmitted to the pipe. There are two types of superimposed loads as illustrated in Fig. 13: (1) concentrated wsi, and (2) distributed ws2- Superimposed loads are fre quently referred to as live loads. 3.3.1 Concentrated loads. A con centrated load is a load caused by a single force which may be either static or dynamic in nature. In normal pipe design, vehicular wheel loads are the most frequently encountered con centrated loads. The magnitude of the load produced by concentrated superimposed forces is determined by in which ws\ = the load on a pipe caused by a concentrated superimposed force in pounds per linear foot of pipe. (For convenience, concentrated superim posed loads resulting from a 16,000-lb wheel force are presented in Table 6.) P, = the concentrated force in pounds. The American Association of State Highway and Transportation Officials (AASHTO) design manual gives loads for various sizes and types of vehicles. F = the impact factor. American Association of State Highway and Transportation Officials (AASHTO) vehicular wheel loads are shown in Table 4. Impact factors vary from one locale to another and values that are consistent with local, state, and federal specifications should be chosen. L = the effective pipe length in feet. For pipe less than three feet, the actual length of the section should be used. For all other pipe lengths an effective length of three feet should be used. CTD000751 SECTION' S 21 TABLE 4 Impact Factors Dept 11 of Cover /( 1.0-2.0 2.0--3.0 3.0 or greater Impact Factor F 1.2 1.1 1.0 C, = the load coefficient, which is a function of the depth of cover to the top of the pipe and the nominal inside diameter of the pipe. Values of Cs are obtained from Table 5. 3.3.2 Distributed load. A distri buted load is a load caused by a uniform force distributed equally over a given area. The load may be either static or dynamic in nature. The magnitude of the load produced by distributed forces is determined by in which, K's: = C>P<F Bc Fq 11 li's-i = the load on a pipe caused by distributed superimposed force in pounds per linear foot of pipe. Ps = the intensity of the distri buted force in pounds per square foot. F = the impact factor as explained in paragraph 3.3.1. Bc = the pipe diameter in feet. C, -- the load coefficient, which is a function of the depth of cover to the top of the pipe and the nominal inside diameter of the pipe. Values of C are obtained from Table 5. 3.3.3. Illustrative problem. An 18in. asbestos-cement transmission pipe is to be installed in a 3-ft wide trench under 8 ft of cover. The backfill is ordinary clay with a weight of 120 lb/cu ft. Determine the earth load on the pipe. :Solution The load must be com puted two ways using the Marston equations for the trench condition and for the projecting pipe condition. a. Trench condition Eq 4: wE = t>, (#.,)2 g IL - - = 2.7 (approximately 3) B, ~ Cd = 1.9 ^from Fig. 5 and -- ^ wf. = (1.9)(120)(3)2 = 2100 Ih/ft TABLE 5 Values of Load Coefficients C. for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit Pipe size. Depth of Cover ft 2 2} 4 5 6 8 10 12 16 20 18 0.391 0.289 0.221 0.136 0.092 0.066 0.038 0.025 0.017 0.010 0.006 20 0.422 0.316 0.241 0.150 0.102 0.073 0.042 0.027 0.019 0.011 0.007 21 0.436 0.327 0.251 0.157 0.107 0.077 0.044 0.029 0.020 0.012 0.007 24 0.478 0.362 0.280 0.177 0.120 0.087 0.050 0.033 0.022 0.013 0.008 27 0.510 0.392 0.306 0.195 0.133 0.096 0.056 0.037 0.025 0.014 0.008 30 0.543 0.423 0.332 0.213 0.147 0.106 0.062 0.041 0.029 0.016 0.010 33 0.563 0.446 0.353 0.230 0.159 0.115 0.067 0.045 0.032 0.018 0.011 36 0.590 0.470 0.375 0.248 0.171 0.124 0.073 0.049 0.035 0.020 0.012 39 0.615 0.502 0.404 0.272 0.191 0.140 0.083 0.054 0.041 0.026 0.015 42 0.619 0.516 0.422 0.286 0.202 0.147 0.089 0.063 0.043 0.030 0.017 Note: For convenience, concentrated superimposed loads resulting from a 16,000-lb wheel force are presented in Table 6. CTD000752 22 A-C TRANSMISSION' AND FEEDER MAIN I'll'E TABLE 6 "'SI Concentrated Superimposed (Wheel) Load on Asbestos-Cement Transmission Pipe Single Wheel -- 16,000 ib (11-20 Wheel Load) % Cover Over Top of Pipe 1 ft IX 20 } 208.1* 2251 -> I2 1541 1682 2 1178 1286 4 725 800 5 490 544 6 852 489 8 204 224 10 144 144 12 91 100 16 58 59 20 52 37 21 2464 1728 1444 857 570 410 254 154 105 64 40 24 2545 1949 1494 944 640 464 267 176 117 69 45 Pipe Diameter m. 27 2720 2091 1652 1040 710 512 299 197 155 75 45 40 2896 2256 1724 1146 784 566 580 219 155 85 55 44 2992 2568 1878 1224 845 611 457 240 170 96 60 46 4149 2510 2000 1521 912 662 490 261 187 107 63 46 4280 2677 2154 1450 1018 747 445 288 219 189 80 4401 2752 2250 1525 1077 784 475 456 229 , 160 91 * Values shown are in pounds per linear foot of pipe. Xote: Table is based on impact factor of one. If different impact is to be used, simply multiply value from table times desired impact factor. 1). Projecting pipe condition Eq 5: to.- = Ccse,(Bc)- B= 18 in. pipe OD = 1.7 ft Cc = 1.892 (11/Be) - 0.96 = 1.892(8/1.7) - 0.96 = 8 = (82(120/(1.7)- = 2800 Ib/ft c. The engineer, knowing the job | ^ conditions and degree of inspec tion, should decide which load applies. Section 4--Hydrostatic Pressure Sec. 4.1 Introduction For the design of asbestos-cement transmission pipe, the internal hydro static pressure pr is defined by pT = (P,, + PAS.F. Kq 12 in which, pr = the total internal pressure in pounds per square inch which, in combination with some external load w'7- applied in three-edge bearing, will fracture the pipe. Po = the static or operating pres sure in pounds per square inch de fined by the design criteria. Ps = the surge pressure in pounds per square inch resulting from either water hammer or other incremental pressures over and above the norma! operating pressure. S.F. = the design safety factor specified by the purchaser. Safety factors are based on judgment, past experiences, and sound engineering principles. For asbestos-cement trans 0 CTD000753 L SECTION' 4 23 mission pipe design, a minimum safetyfactor of 2.0 is recommended. For simplicity in design and selec tion of asbestos-cement transmission pipe, the internal pressure may be separated into two components: (1) operating pressure, and (2) water hammer or surge pressure. Each will be determined separately. Sec. 4.2 Operating Pressure The operating pressure Pa is that pressure which exists under normal or steady conditions of operation. The pressure may be induced by pumps, gravity (such as the head created by a reservoir or elevated water tank), or a combination of both pumps and gravity, Under a 100 percent gravity situation, the pressure in the line at a given point is somewhat higher when there is no flow and conditions are static. Under static conditions the pressure at a given point, measured in feet of head, is equal to the difference between the elevation of that point and the water surface level at the reservoir. Under flowing conditions the pressure at a given point is re duced by the amount of friction and other energy losses resulting from the flow of water from the reservoir to that point. The magnitude of this head loss may be found by using the Hazen and Williams chart in Ap pendix A. In piping systems that have long runs with relatively few fittings and accessories, the recom mended value of C (coefficient of flow) is 140. Sec. 4.3 Surge Pressure Surge pressures P, are of a transient nature and are caused by unsteady or changing conditions in the pipeline. The terms "water hammer,1' "surge,'' or "transient pressure" are often used interchangeably to refer to these pres sures, which are of brief duration but often of considerable magnitude. A variety of conditions may cause surge pressures. These include a valve opening or closing, sudden movement of air in a line, or a pump starting or stopping. Transient pressures are often a controlling factor in the selection of pipe strength. For this reason, a pipe system should always be analyzed for surge pressure deter minations and the results should be used in pipe selection. 4.3.1. Surge control. There are numerous methods for control of surge pressures in the line. Con: sideration should be given to use of these methods to limit pressures to an acceptable level. Economics plays a major role in this area. Various designs may have to be balanced, depending on the complexity of the system, to yield an economical and efficient design. 4.3.1.1 Appendix B presents a dis cussion of water hammer with em phasis on how it may be analyzed and controlled. Although the subject is discussed in some detail, and an illustrative problem is included that involves controlling surge pressure by timing a valve closure, the subject is too complex to be thoroughly covered in this standard. It is suggested that control of surge for any transmission system be discussed with surge control equipment manufacturers or con sultants in this particular field. The effects of surge in a pipeline, however, should not be ignored, as neglect of this factor may result in severe dam age to the system. Also, because of the number of variables invoked in creating water hammer pressures, and because of the ability to regulate their magnitude with proper controls, it is CTD000754 24 A-C TRANSMISSION AND FEEDER MAIN PIPE not recommended that fixed water hammer allowances based on assumed velocitv changes or some other single criterion be used for the larger diam eter transmission and feeder main lines. Section 5--Pipe Selection Sec. 5.1 Combined Loading Curves As discussed previously, it has been demonstrated satisfactorily by tests that asbestos-cement transmis sion pipe conforms generally to the Schlick formula for combined loading (Sec. 2.2). Numerous tests have established values for P, internal hy drostatic design pressure with no crush load applied, and for If', ex ternal crush design load with no internal pressure applied, for all diam eters and strength classifications. These values represent the end points on the combined loading curves; the intermediate points on the curves are computed by use of the Schlick formula. (It should be noted fhat all values used for P and W represent a conservative interpretation of the test data.) On the curves, each intermediate point--wr, pr--repre sents a combination of crush loading and internal pressure that the pipe will withstand when the loads are applied simultaneously. 5.1.1 Selection curves. Selection curves in Fig. 14a-14j are presented for each size of pipe from 18 through 42 in. On the graph for each pipe diameter, a combined loading curve is drawn for each strength classification of that pipe size. The vertical axis represents the internal hydrostatic design pressure P, and the horizontal axis represents the external three-edge bearing crush design load W. Table 7 lists the values of P and IT for the strength classifications of each pipe size. In Sec. 5.3, Use of Selection Charts for Fconomical Design, the method for pipe selection is outlined. Sec. 5.2 Safety Factors Safety factors are normally applied by the engineer to his computed de sign values of crush- and internal pressure that are to be resisted by the pipe in service. These factors protect against unforeseen loads that may be placed on the line at some time in the future, and against other contin gencies such as improper construction. It is the engineer's prerogative to select which safety factors he feels should apply to a given system. Con siderable field experience as well as extensive laboratory work has yielded a wealth of information on the be havior of asbestos-cement transmis sion pipe. For this reason, suggestions for minimum safety factors are made in Table 8. Note that, since the com bined loading principle is applicable, the safety factors will be applied to both hydro and crush simultaneously. Note also that water hammer and live load, which are both transient load conditions, are considered as acting simultaneously for design purposes here. Since the likelihood of both occurring at the same time is minimal, an additional conservative element is introduced into the design. Sec. 5.3 Use of Selection Charts for Economical Design After all loads on the pipe have been computed (operating pressure, water CTD000755 SECTION' 5 25 TABLE 7 Design Internal Pressure* and Design External Load\ Intercepts far i'se With Selection Curves for the Following Pipe Classifications 30 35 40 45 50 60 70 80 90 Pipe Size in. P* = 300 P = 350 P = 400 P = 450 P = 500 P = 600 P = 700 P = 800 l> = 900 Ht IV ir ir it" ir If ir ir 18 2 500 3 000 4 000 5 000 6 500 8 500 11 000 14 000 18 000 20 2 500 3 500 4 500 5 500 7 100 9 500 12 000 15 000 20 000 21 2 500 3 500 4 500 5 800 7 300 9 700 12 500 16 000 21 000 24 2 800 3 800 5 000 6 200 8 100 11 000 15 000 19 000 24 000 27 3 500 4 200 5 506 7 000 8 800 12 500 16 500 20 500 27 000 30 3 500 4 500 6 000 7 500 9 700 13 500 18 000 22 500 30 000 33 3 500 5 000 6 500 8 000 10 500 14 500 19 500 24 500 33 000 36 4 000 5 000 7 000 9 000 11 200 16 000 21 000 26 000 36 000 39 4 200 5 300 7 500 9 700 12 000 17 200 22 500 28 000 39 000 42 4 300 5 700 8 000 10 500 13 000 18 500 24 000 30 000 42 000 * P-psi. t W--lb/lin ft. hammer, earth load, and live load), the most economical strength of pipe to meet the service conditions should be selected. The applicable selection procedure using the suggested safety factors is: 1. Add operating pressure and water hammer, P0 -f Ps (Sec. 4). 2. Add earth load and live load, wE + ws (Sec. 3). 3. Enter the combined loading graph for the appropriate pipe diam eter. Plot the values from Steps 1 and 2 above as one point. When using the left-hand scales, be sure to multiply the operating pressure plus water hammer by the suggested safety factor of 2.0. When using the bottom scale, be sure to multiply the earth load plus live load by the suggested safety factor of 1.5, and then to divide it by the bedding factor (Sec. 2.3). 4. The point plotted will lie be tween the curves for two pipe TABLE 8 Minimum Safety Factors for Use With Asbestos-Cement Transmission Pipe Selection Type of Load Safety Factor Hydro Crush Operating pressure plus water hammer, combined with earth load plus live load 2.0 1.5 strengths. Select the higher strength of the two. This represents the most economical selec tion consistent with engineering requirements. Sec. 5.4 Illustrative Problem on Pipe Selection A 24-in. asbestos-cement transmis sion line is to be installed in a 4-ft wide trench with 5 ft of cover. The operating pressure will be 100 psi. Surge pressures will be limited to a CTD000756 26 A-C TRANSMISSION AND FEEDER MAIN PIPE maximum of 50 psi. A 16,000-lb wheel load is to lie assumed, with an impact factor = 1. Class C bedding will be used. Select the proper strength of pipe to be used with safety factors of 2.0 in hydro (P,, P,) and 1.5 in crush (tc>; tc.s). Solution : Following instructions for use of selection charts with safety factors as described in Sec. 5.3 gives 1. Pu + P, = 100 + 50 = 150 psi 2. tcn T- n's = 2030 640 = 2670 lb/'ft 3. (P,, + P,)(S.F.) = 150 X 2.0 = 300 psi , (- + vs){S.F.) (2670) (1.5) 4- B.F. ~ ~ ~ 1.5 = 2670 lb/ft 5. Consult the combined loading chart for 24-in. pipe, using the left hand and bottom scales. Plot the two loads as a single point on the chart. The point falls between T-40 and T-45. Cse T-45. CTD000757 O <0 >. i 1 3 CO Ocl Oao) SECTION' 5 27 a> a c g> T(<D/D) T3 x>:. 03 C 5 c 0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 External crush load 3-edge bearing i--WMb/fti J Safety factor WT ~ earth load + live load Bedding factor Fig. 14a. Combined Loading Curves for 18-in. Transmission Pipe i CTD000758 28 A-C TRANSMISSION' AND FEEDER MAIN' PIPE I Internal hydrostatic design pressure--P t psn 'Operating pressure t water hammer' safety factor 2000 4000 6000 8000 10.000 12.000 14.000 External crush load '3-edge bearing -- W-1b/ft Safety factor Wr = earth load + live load Bedding factor 16.000 Tig. 14b. 20-in. Transmission Pipe CTD000759 SECTION 29 CCOl K. a. D to t<oD a c gi tQOo> o m sXcow>zDo. c aj c 0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 External crush load 3-edge bearing --WMb/ft' Safety factor WT = earth load + live load -B--e--d-d--i-n-g---f-a--c-t-o--r- Fig. 14c. 21-in. Transmission Pipe i CTD000760 <> 30 A-C TR \XSM ISSION \\[) FEEDER MAIN' PIPE safety factor 'Operating pressure + water hammer - ' psi pressure--P j design hydrostatic Internal I *' 2000 4000 6000 8000 10,000 12,000 External crush toad < 3-edge bearing i--Wilb/fti Safety factor H/r = iearth load + live load Bedding factor 14,000 16,000 Fig. 14d. 24-in. Transmission Pipe CTD000761  SECTION' 5 31 Internal hydrostatic design pressure--P j .psC - 'O perating pressure t water hammer safety factor 0 2000 4000 6000 8000 10.000 12,000 14.000 16.000 External crush load '3-edge bearing -- IViIb/ft Safety factor Wr = earth load + live load ----------------------Bedding factor Fig. 14e. 27-in. Transmission Pipe # CTD000762 4 External crush load i3-edge bearing > -- Wlb/ft Safety factor WT ='earth load + live load > Bedding factor Fig. 14f. 30-in. Transmission Pipe J CTD000763 SECTION' 5 33 Internal hydrostatic design pressure--P j 'psh -- iOperating pressure i- water ham m er' safety factor 0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 External crush load 3-edge bearing. -- W' Ib/ft i W Safety factor earth load + live load Bedding factor Fig. 14g. 33-in. Transmission Pipe I CTD000764 34 A-C TRANSMISSION' AND FEEDER MAIN PIPE Internal hydrostatic design pressure--P j ipsi. - 'Operating pressure i water hammer' safety factor I 0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 External crush load (3-edge bearingi--WiIb/ft> W Safety factor earth load + live load Bedding factor Fig. 14h. 36-in. Transmission Pipe CTD000765 SECTION' 5 35 Internal hydrostatic design pressure--P j ipsti - (operating pressure + water hammeri safety factor 4000 8000 12,000 16,000 20,000 External crush load 3-edge bearing. -- Wr Ib/ft Safety factor Wr = earth load + live load i--------------------Bedding factor Fig. 14i. 39-in. Transmission Pipe 24,000 I CTD000766 36 A-C TRANSMISSION' AND FEEDER MAIN PIPE Internal hydrostatic design pressure--P j ipsii = (operating pressure + water hammer: safety factor 0 4000 8000 12,000 16,000 20,000 24.000 External crush load i3-edge bearing , -- Wi Ib/ft Safety factor Wr = iearth load + live load Bedding factor Fig. 14j--42-in. Transmission Pipe CTD000767 Derived from the Hazen and Williams formula: V = 1.318 CK0 S0M" Loss of Head in Feet per Thousand Feet of Length Appendix A Friction Loss of Head Chart-Coefficient of Flow, C = 140 This appendix is for information only and is not a part of A WU'A C403. E i A1 CTD000768 CTD000769 NOTE: Loss of head values derived from this chart are for coefficient of flow C = 140. They may be converted to loss of head for other coefficients 1.15forC = 130 1.34 for C = 120 1.57forC = 110 1.86 forC = 100 2.26 for C = 90 NOTE: Diameters derived from this chart are for coefficient of flow C = 140. These may be converted to diameters for other 1.033 for C =130 1.063 for C =120 1.100 for C = 110 1.142 for C =100 1.185 for C = 90 Appendix B Surge Pressure Analysis This appendix is for information only and is not a part of WIVA C403. B.l Water Hammer or Surge The slowing down or stopping of any moving mass requires a force or forces to counterbalance the kinetic energy that keeps the mass in motion. The faster a mass is decelerated and brought to a halt, the greater the force that is required. B.1.1 Forces involved. It is some what of an oversimplification, but water hammer, or surge, can be de fined in these terms: The shutting of a valve or the stopping of a pump causes a moving column of water in a pipeline to slow down and stop. The forces that bring about' this deceleration are exerted radially on the moving water column by the pipeline walls. Conversely, the water exerts added pressure on the pipe, and the hoop stresses in the pipe walls thus increase over the normal operat ing pressure values. The faster the column of water is brought to a halt, the higher these stresses rise. B.1.2 Rate of velocity fluctuation. The pipe wall stresses are thus de veloped by, and increase in direct proportion to, the internal pressure that builds up as the column of water decelerates. The slower the de celeration, the less the pressure builds up, and the less the pipe wall stresses increase. It is, therefore, of impor tance to the pipe designer to know how to control the rate of velocity fluctu ation, since by controlling this rate he controls the magnitude of the pressure variations during the transi tional periods. By such control he can keep the pipe wall stresses during surge to a predetermined value that will allow an economical installation. B.l.3 Wave motion. Water, being liquid, will act in a fairly complex manner when undegoing acceleration or deceleration. Pressure waves are set up which move along the pipeline at a rate of 2500--4500 ft/sec, the rate depending on the pipe wall material. The waves will continue until they encounter a boundary con dition, such as a reservoir, a closed valve, or a change in pipe diameter, at which point they will reflect back in the opposite direction. The wave motion will oscillate back and forth in the pipe until it is dampened out by the friction effects of the pipe walls. B.l.4 Causes. The two major causes of water hammer or surge are 1. The closing or opening, fully or partially, of a valve in a pipeline system. The valve may be in the line for one of a number of purposes. It could be a gate valve, float valve, pressure reducing valve, or serve some other function. 2. The starting up or shutting down of a pump (switch or power failure). It can be seen that both of these occurrences cause changes in the velocity, and consequently in the quantity, of w^ater flowing in the pipeline. B.l.5. Effects. Ignoring the effects of surge in the pipeline can lead to difficulties after the line is in operu- CTD000770 B2 APPENDIX B tion. Surge can result in damaged equipment and seriously reduced capacity. B.2 Water Hammer Analysis The elastic wave theory for surge analysis has been empirically estab lished to be correct by many ex periments, the first of which were performed as early as 1890. Its application to pipeline problems will yield results which are accurate and which may be relied upon for adequate analysis. B.2.1 Wave velocity. Water ham mer pressures are a function of the maximum rate of change of How. When a valve is closed or a pump stops, a pressure wave is propagated along a pipeline. The velocity of the wave is the same as the velocity of sound in water, modified by physi cal characteristics of the pipeline; it is given by the following equation: in which, 4660 a = /--------------- Vl + kd/Ee Eq III 4 a -- pressure wave velocity, in feet per second k = modulus of compression of water, 300,000 psi d = internal diameter of pipe, in inches E = modulus of elasticity of as bestos-cement pipe, 3,400,000 psi e = wall thickness, in inches 4660 = velocity of sound in water in feet per second B. 2. 2. Maximum pressure. If the pressure wave is reflected back from a boundary condition, such as a reservoir, and returns to its initial position after the flow in the line is completely stopped, then maximum water hammer pressure for those conditions will result. Stopping of the flow may be effected by closing a valve or by a pump stoppage. The magnitude of that maximum pressure is given In ti r h =-- Eq B2 in which, h = surge pressure, in feet of water V = velocity of water in the pipe line during normal conditions, in feet per second a = velocity of pressure wave, in . ft/sec g = acceleration due to gravity, 32.2 ft/sec2 B.2.3 Critical time. The longest elapsed time before final flow stoppage that will still permit this maximum pressure to occur is called the critical time; it is simply the total length that the pressure wave travels in one cycle, divided by the velocity of the wave. It is given by the following equation: in which, U = --a Eq B3 U = the critical time, in seconds L = distance within the pipeline that the pressure wave moves before it is reflected back by a boundary condition, in feet a = velocity of the pressure wave in the line, in feet per second B.3 Valve Closure A valve in a water line may be of several different varieties, including gate, cone, and globe valves. When closing a valve, the area of the cross section of the pipeline that is pro gressively cut off is not generally proportional to the reduction in flow. In Fig. Bl, Graph 1 presents a plot CTD000771 Percent of hmax (Instantaneous Closure) Percent Full Flow SECTION' B.J B3 Time --(TE) = Effective For Full Cut Off Uniformly at Maximum Rate Full Area Gate. 4-------- Te = 39.2%Tt--------- >1 Reduced Area Globe, -Te = 51.7% Tt- 14-Full Area Cone, TE = 48.6% Tt->( Open Percent Time of Valve Stem Travel - Tr Closed 0 10 20 30 40 50 60 70 80 90 100 90 80 70 60 50 40 30 20 10 0 "N" = (Te) Effective Closing Time -- in Units of 2 L/a Seconds Fig. Bl. Time (TV) = Effective for Full Cut Off Uniformly at Maximum Bate Reprinted by permission of the Johns--ManvilleSales Corporation. of stem travel versus flow in the line for three types of valves. Note that the first 30-40 percent of stem travel has little effect on the flow in the pipeline. B.3.1 Effective time. As stated previously, water hammer pressure is a function of the maximum rate of change of flow. Therefore, if tangents to the curves in Fig. Bl are drawn at the fastest rate of change (or steepest slope), the effective time of closure Te is obtained. (See the curves in fig. Bl with tangents plotted and values of TE determined.) This effec tive time, Te, is the time that is used in water hammer calculations. In most cases, it is about one half of the actual valve closing time. This indicates that if the critical time of a certain installed valve is calculated from Eq B3 and found to be x seconds, then the actual time for complete valve closure which will cause maxi mum pressure to occur will be ap proximately 2x seconds. B.3.2 Relation to surge control. In the design of a water system one of the major considerations in the selec tion of a pipe is the design internal CTD000772 B4 APPENDIX B pressure that the pipe will be required to carry in service. The design internal pressure is the operating pressure plus the water hammer pres sure. In order to keep the water hammer or surge pressures at a con trolled level, calculations must be made to determine the-valve closure times that will be required to stay within the design pressure level. B.3.3 Determining effective time. Figure Bl presents a convenient three-step method for determining effective valve closure times for a given percentage of the maximum pressure (surge pressure when valve is closed in less than the critical time). 1. Determine the pipeline constant K given by in which, K = pipeline constant a = velocity of the pressure wave in the line, in feet per second V = velocity of water in the flow line under normal conditions, in feet per second g = acceleration due to gravity, 32.2 ft/sechu -- operating pressure in the line under normal conditions, in feet of water 2. Determine the maximum head that might be developed from the surge by employing the formula h max & ^ /jj* 3. Determine the percentage of hmux and find the corresponding effec tive closing time shown on the horizontal axis. This is given in units of 2L/a, which represents the critical time for the pipeline. Note that the time determined is the effective closing time and the actual time of valve stem travel is about twice as long. The reason for this is that the first half of the closing of the valve has little effect on the stoppage of the flow. It is the closing of the final half of the valve stem travel which closes off the flow. The second half is the effective closing time. There fore, two times the effective closing time is the actual time of the valve stem travel. B.4 Pumped Systems In relation to water hammer and surge, the most important elements in a system are pumps and valves. In a gravity system only valves have to be considered. Both pumps and valves must be considered in a pumped system. B.3.1 Complexity. The surge analy sis of a pumped system is more com plex than in a 100 percent gravity system because 1. In a pumped system, the prob lem begins in the slowing down of the rising water column when the pump is shut off (because of power failure or otherwise). Con sideration must be given to the time required for the pump to stop and for the flow to come to a halt. This involves the inertia of the motor and any flywheel in the assembly. Provisions nor mally should be made for slow opening and closing of pump control valves on pump systems. In a gravity system the hydraulic problem consists only of stopping the descending water column. 2. In a pumped system, the pipeline profile is usually irregular, with successive high and low points and with variable slopes. These conditions may give rise to water CTD000773 SECTION B.5 B5 column separation, causing se vere surges and operational troubles. Surges from water column separation do not follow a standard pattern and they have been measured at many times the calculated values. B.4.2 Alternative layouts. The de sign of a pumped system may involve the consideration of alternative lay outs to keep surges and the consequent operational difficulties to a minimum. This work should be directed toward reducing the magnitude of surges and toward reducing the risk of water column separation that may be caused by the shutdown of a pump. B.4.3 Water column separation. Water column separation can be serious due to the large magnitude of the surges developed when the water column rejoins. It can occur 1. At pump locations at the start of a steep main. 2. When the pressure at a high point falls below atmospheric and air enters the line through air valves that may be located at a high point. 3. When the pressure falls to below the vapor pressure of water. B.4.4 Entrapped air. Water col umn separation can cause difficulties, not only because of the before-men tioned surges set up by the rejoining of the water column, but because of the difficulties in getting air out of the line on subsequent start-up, even with air valves. Entrapped air can cause flow fluctuations and can seri ously reduce the capacity of the system. B.5 Methods of Control The two types of surge to be con trolled are negative surge and positive surge. The type is determined, of course, by whether the surge pressures developed are below or above the normal static level. B.5.1 Negative surges. Negative surges in themselves are usually not dangerous, except when they cause water column separation. If this occurs, extremely high positive surges result when the cavity closes, and this frequently causes serious prob lems. The control of both negative and positive surges should be given consideration. B.5.2 Surge control devices. Limit ing negative and positive surges is accomplished by several types of surge control devices, as follows: 1. Controlled valves. This is one of the most effective means for controlling positive surges. As explained previously, the rate of opening and closing of a valve can be calculated to allow an acceptable level of surge. 2. Flywheel on pump motor. In the event of a power outage the inertia of the flywheel will keep the pump running for a period of time, during which it will gradually slow to a stop. This means that the water column in the pipeline will also be brought to a gradual stop, thus reducing the risk of water column separation. 3. Standpipe. This is generally a tank with the surface of the water at atmospheric pressure. It is, therefore, only practical at low heads. At a pump stoppage and consequent re duced pressure, the reserve of water in the tank flows into the pipe and reduces the risk of water column separation. For positive surge control the tank CTD000774 B6 APPENDIX B provides an outlet for the built-up pressure in the system. 4. Air vessel or surge tank. This is an enclosed vessel containing air and water. It functions similarly to a standpipe, with water reentering the line during negative surge and leaving dur ing positive surge. The major difference is that the air in the vessel is under pressure and much higher heads can be em ployed in the pipe system. 5. One-way surge tank. This is an adaptation of the surge tank. It contains a check valve that permits water to enter the line during negative surge, but will ' not permit water to leave during positive surge. It is, therefore, only for control of negative surges and is very effective. 6. Reservoir of water. This is similar to the one way surge tank, but provides some control of positive surge by permitting the slow entrance of water into the reservoir during a positive surge. 7. Suction pipe. This is a bypass around the pump from the suction side. It contains a check valve to prevent backflow into the reservoir. 11 effec tively reduces negative pressure adjacent to the pump. 8. Surge relief valve. This is used for controlling positive and negative surges. The valve opens at a certain pressure and discharges water to relieve a surge; positive or negative. It must be carefully designed and controlled in order to be effective. 9. Nonreturn valve. This is a check, strategically placed in a line, that can bring a small mea sure of relief to positive pres sure. I lowever, unless properly placed, it can lead to higher rather than lower surge. 10. Reversal of pump. At pump stoppage the column of water reverses itself. If the pump will not run backwards to permit water to flow back through it, then positive surges will be developed by the sudden slop ping of the backflowing column of water. The pump should be designed to run reversed with out damage to itself. Design of pumps that can run reversed without damage is a significant problem. Other measures may have to be taken. B.5.3 Economic considerations. From an economic standpoint it is usually worthwhile to properly evalu ate the surge potential in a system under design. The cost of control devices may be balanced against the added strength of pipe, valves, and other equipment that will be needed if surges are not controlled, and the most advantageous conclusion reached. Manufacturers of surge con trol equipment or consultants in this field should be sought for advice in complex situations. B.6 Surge Calculation Example The following example problem illustrates the calculation that may be followed to determine valve closing time for the control of surge within prescribed limits. A 24-in. gravity transmission line is to operate at a pressure of 100 psi. Velocity in the line is to be 5 ft/sec. A waive is to be included in the line at a distance of 5000 ft from the reservoir. If positive surge pressure CTD000775 SECTION' B.7 B7 is to We controlled within 50 psi, determine the minimum time for valve closure. Assume that the effective closing lime is one half of the actual valve stem travel time. {E for as bestos-cement pipe = 3.4 X 106, wall thickness is 1.5 in., k for water = 3 X 105) actual valve stem travel time would be twice this amount, or 17.4 sec. This calculated time (17.4 sec.), therefore, represents the fastest allowable time the valve can be closed in order to keep the surge pressure below the desired control level of 50 psi. SOLUTION 1. Determine surge wave velocity 4660 a 4660 V 3 X 10s X 24 .5.4 X 106 X 1.5 = .5000 ft/sec. 2. Determine maximum surge pres sure if the valve closes within the critical time a l' .5000 X 5 T = 32.2 = 465 ft of water (200 psi) 3. Determine the critical time 1 X 5000 = 3.33 sec a 3000 4. Determine Constant K for tise in Craph 2 (Fig. Bl) aY 3000 X 5 ~ 2gh,, ~ 2 X 32.2 X 231 " ' 5. Determine percent of maximum surge pressure that should not be exceeded in the system. 50 ----- X 100 = 25 percent 6. Enter Graph 2 (Fig. Bl) with percent of hmnz (25 percent). Go horizontally to the curves where K = 1.0. Read the effective clos ing time along the horizontal axis. This value is 2.6 and is given in units of 2L;a seconds. The effective closing time in seconds would be 2L;a X 2.6 = 3.33 X 2.6 = 8.7 sec. The B.7 Air in Pipelines Air in pipelines can cause serious operational difficulties, including re duction in capacity because of re duced cross-sectional area, and fluctu ation in flow caused by expanding and contracting air in the line. These fluctuations in flow cause sudden movements of the air from one loca tion to another, followed by slugs of water, and this can cause serious surges. B.7.1 Entrance oj air. Air can enter a pipeline in many ways. It may enter at the intake. Entry may be caused by release of air from water due to temperature and pressure variation, or it may be caused by draining the line, or by draining parts of the line during normal shut-down. Negative surges may cause air to enter at air valves. Air should be prevented from entering the line in the first place. This is very important in order to reduce operational diffi culties. Suggested solutions for con trol are as follows: 1. Intake. Correct design pro cedures, provide low water-level pump cut-off. 2. Release of air. Air is entrained in the water at intake and its release cannot be prevented. However, the quantities are not large and provisions for exhaust ing can be made by means of air valves. There are various types of air valves with different CTD000776 B8 APPENDIX B functions, and the selection of the proper type and location for installation is essential. 3. Draining the line. Air cannot be prevented from entering the line on draining, of course. Large orifice air valves should L t pro vided for exhausting the air during refilling. Draining and then refilling does not often oc cur; therefore, long tilling times may be satisfactory. 4. Drainage during shut down. This can be a serious problem. Open standpipes can be pro vided for air entry and exhaust. Sweeping air out using high velocities is also a method. 5. Negative surges. The best way to prevent air from entering under these conditions is to de sign out the possibility of water column separation. Large vol umes of air may be involved here and can cause serious problems. Any one of the negative surge control devices described in para graph B.5.2 will normally be adequate. B.7.2. Recommendations to combat air entrapment. Colorado State Uni versity has conducted studies to determine the effect of air entrapment in pipelines. The result of the studies proved that suddenly released en trapped air, under apparently static conditions, creates a situation similar to that of classic water hammer. Pressures are generated which may be on the order of fifteen times the pipeline test pressure. Any pipeline material is seriously affected by this rapid magnitude of load increase. Hydrostatic failure due to defective pipe may in all probability be traced to suddenly released entrapped air. The initial filling and testing of a pipeline is often the most critical period of its service life. Recom mendations to combat air entrapment were made as follows: 1. Pipeline should be laid to grade wherever possible. 2. Automatic continual acting air release valves should be used at all high points. 3. Air should be bled from pipeline slowly. 4. Limit filling velocity in the pipe line to one foot per second or less. 5. Use d/D = 1/10 to 1/100. d = diameter of air release valve D -- pipe diameter The results of this study, together with the recommendations, have been found to be most useful to contractors in performing pipeline tests. Such rec ommendations also have been found to be useful to engineers from the standpoint of designing pipelines to minimize air problems. CTD000777 Appendix C Frictional Power Requirements This appendix is for information only and is not a part of AWWA C700. The chart shown in Fig. Cl permits rapid calculations of the yearly power costs to overcome friction loss of head. This chart is based on continuous pumping operation (24 hours per day and 365 days per year), a power cost of $0.01 per kwlir, and a motor-pump efficiency of 100 percent. For actual operating conditions and local power costs, appropriate factors must be ap plied to the values shown in the chart. By calculating power costs to over come friction in two pipe sizes, or for two different types of pipe having different flow coefficients, an annual power cost savings can be determined. Economic justification for going to a larger pipe diameter with lower annual power costs can be determined by establishing the present worth of the annual savings using Table Cl, which is based on the discounted cash flow method. If the present worth of the annual savings based on established interest rates exceeds the added costs for the installation of a different size or type of material, then economic justification exists for the added capital expenditure. Nomograph values for Fig. Cl are based on the following: Cost per 1000 ft of pipe per year--in dollars Power cost--l<f per kilowatt hour Motor-pump efficiency (combined)--100 percent Friction coefficient C = 140 Continuous operation Note : Yearly power cost values derived in Fig. Cl are for coefficient of flow C = 140. They may be con verted to yearly power cost values for other coefficients of flow by means of the following multiplying factors: 1.15 for C = 130 1.34 for C = 120 1.57 for C = 110 1.86 for C = 100 2.26 for C = 90 2.83 for C = 80 4.82 for C -= 60 Diameters derived from Fig. Cl are for coefficient of flow C = 140. These may be converted to other diameters for other coefficients of flow by means of the following multiplying factors: 1.033 for C = 130 1.063 for C = 120 1.100 for C = 110 1.142 for C = 100 1.185 for C = 90 1.261 for C = 80 1.365 for C = 60 Cl CHJOOO778 C2 APPENDIX C CfDOOOT79 1 FIGURE Cl CTD000780 Reprinted by permission of the Johns--Manville Sales Corporation. C3 C4 APPENDIX C Table Cl * Apply the following formula to Table Cl, Present Worth of an Income of $1.00 per Year for the Next N Years: (1 + r) ~ 1 r(l + r)N where r -- rate of yield in percent N = number of years from present Example: When using a 10 percent rate of yield, an income of $1.00 occurring each year for the next 5 years has a* * This table is reprinted by permission of the Johns-Manville Sales Corporation from their publication, "Discounted Cash Flow Method of Investment Appraisal." present worth of S3.791 ; for the next 7 years, $4,868; for the next 10 years, $6.145; etc. The present worth {PW) of a regular pattern of savings in the future is found as follows : Total years of operation--25 Amount of annual savings-- $5000.00 PW factor at 10 percent--9.077 Total present worth {PW)-- $45,385.00 When expenditure, cash income, and life are known, and income is the same each year, the PW factor can be computed by dividing expenditure by annual cash income. Yield can then be determined by looking for the factor on the line or known life in Table Cl. CTD000781 TABLE Cl C5 TABLE Cl Present Worth of an Income of $1.00 per Year for the Next N Years r. .3* UK LJ* 2.0* lit 3.0* 3.9* 4.0* 4.9* 5.0* Twrt l .995 .990 .985 .980 .976 2 1.985 1.970 1.956 1.912 1.927 3 2.970 2.9a 2.912 2.881 2.856 1* 3.950 3.902 3.851 3.808 3.762 5 1.926 1.053 1.783 1.713 1.616 .971 1.913 2.829 3.717 1.560 .966 1.900 2.802 3.673 1.515 .962 1.886 2.775 3.630 1.152 .957 1.873 2.719 3.588 1.390 .952 1.859 2.723 3.516 1.329 1 2 3 1 5 6 5.096 5.795 5.697 5.601 5.508 7 6.062 6.728 6.598 6.172 6.319 8 7.023 7.652 7.186 7.325 7.170 9 8.779 8.566 8.361 8062 7.971 10 9.730 9.171 9.222 8.983 8.752 5.a? 6.230 7.020 7.786 8.530 5.329 6.115 6.871 7.608 8.317 5.2a 6.002 6.733 7.135 8.111 5.158 5.893 6.596 7.269 7.913 5.076 5.786 6.163 7.108 7.722 6 7 8 9 10 11 10.66 10.37 10.07 9.787 9.511 12 11.62 11.26 10.91 10.58 10.26 13 12.56 12.13 11.73 11.35 10.98 11* 13.19 13.00 12.51 12.11 11.69 15 11.12 13.87 13.31 12.85 12.38 9.253 9.951 10.61 11.30 11.91 9.002 9.663 10.30 10.92 11.52 8.760 9.385 9.986 10.56 11.12 8.529 9.119 9.683 10.22 10.71 8.306 8.863 9.391 9.899 10.38 11 12 13 u 15 16 15.31 11.72 11.13 13-58 13.06 17 16.26 15.56 11.91 11.29 13.71 18 17.17 16.10 15.67 11.99 11.35 19 18.08 17.23 16.13 15.68 11.98 20 18.99 18.05 17.17 16.35 15.59 12.56 13.17 13.75 11.32 11.88 12.09 12.65 13.19 13.71 11.21 11.65 12.17 12.66 13.a 13.59 11.23 11.71 12.16 12.59 13.01 10.61 11.27 11.69 12.09 12.16 16 17 18 19 20 21 19.09 18.86 17.90 17.01 16.19 22 20.78 19.66 18.62 17.66 16.77 23 21.68 20.16 19.33 18.29 17.33 21* 22.56 21.21 20.03 18.91 17.89 25 23.15 22.02 20.72 19.52 18.12 15.12 15.91 16.11 16.91 17 .a 11.70 15.17 15.62 16.06 16.18 11.03 U.15 11.86 15.25 15.62 a.a 13.78 11.15 11.50 U. 83 12.82 13.16 a.a 13.80 11.09 21 22 23 2U 25 26 21.32 22.80 21.10 20.12 18.95 27 25.20 23.56 22.07 20.71 19.16 28 26.07 21.31 22.73 21.28 19.97 29 26.93 25.07 23.38 21.81 20.15 30 27.79 25.81 21.02 22.10 20.93 31 28.65 26.51 21.65 22.91 21.10 32 29.50 27.27 25.27 23.17 21.85 33 30.35 27.99 25.68 23.99 22.29 31* 31.20 28.70 26.18 21.50 22.72 35 32.01 29.U 27.08 25.00 23.15 36 32.87 30.11 27.66 25.19 23.56 37 33.70 30.80 28.21 25.97 23.96 36 31.53 31.19 28.81 26.11 21.35 39 35.35 32.16 29.37 26.90 21.73 l*o 36.17 32.81 29.92 27.36 25.10 a 36.99 33.50 30.u6 27.30 25.17 1*2 37.80 31.16 30.99 28.21 25.82 13 36.61 31.81 31.52 28.66 26.17 1*1* 39.a 35.16 32.01 29.08 26.50 15 10.21 36.09 32.55 29.19 26.83 16 a.00 36.73 33.06 29.89 27.15 17 a.79 37.35 33.55 30.29 27.17 18 12.58 37.97 31.01 30.67 27.77 19 13.36 38.59 31.53 31.05 28.07 50 UU.lii 39.20 35.00 31.12 28.36 17.88 18.33 18.76 19.19 19.60 16.89 17.29 17.67 18.01 18.39 15.98 16.33 16.66 16.98 17.29 15.15 15.15 15.71 16.02 16.29 11.36 11.61 11.90 15.11 15.37 26 27 28 29 30 20.00 20.39 20.77 21.13 21.19 18.71 19.07 19.39 19.70 20.00 17.59 17.87 18.15 ie.a 18.67 16.51 16.79 17.02 17.25 17.16 15.59 15.80 16.00 16.19 16.37 31 32 33 31* 35 21.83 22.17 22.19 22.81 23.12 20.29 20.57 20.81 21 ao 21.36 18.91 19.11 19.37 19.58 19.79 17.67 17.86 18.05 18.23 18.10 16.55 16.71 16.87 17.02 17.16 36 37 38 39 1*0 23 .a 23.70 23.98 21.25 21.52 21.60 21.81 22.06 22.28 22.50 19.99 20.19 20.37 20.55 20.72 18.57 18.72 18.87 19.02 19.16 17.29 i7.a 17.55 17.66 17.77 a a 1*3 u* 1*5 21.78 25.03 25.27 25.50 25.73 22.70 22.90 23.09 23.28 23.16 20.89 21.01 21.20 21.31 21.18 19.29 i9.a 19.51 19.65 19.76 17.88 17.98 18.08 18.17 18.26 1*6 1*7 1*8 1*9 50 CTD000782 C6 TABLE Cl TABLE Cl (continued) Yaor* 5.3* 6.0* 6.5* 7.0* 7.5* 8.0* 8.5* 9.0* 9.3% 10.0* Yaori 1 .918 .913 .939 935 .930 .926 .922 .917 913 .909 1 2 i 1.816 1.833 1.821 1.808 1.796 1-783 1.7a 1.759 1.717 1.736 2.696 2.673 2.618 2.621 2.6C1 2.577 2.551 2.531 2.509 2.187 2 3 u 3.505 3.165 3.126 3.387 3.319 3.312 3.276 3.210 3.2Q1 3.170 1 1.270 1.212 1.156 1.100 1.016 3.993 3.911 3.890 3.810 3.791 5 6 1.996 1.917 : 1.767 1.691 1.623 1.551 1.186 1.120 1.355 6 7 5.683 5.562 5.185 5.389 5.297 5.206 5.119 5.033 1.950 1.868 7 8 6.335 6.ao 6.089 5.971 5.857 5.717 5.639 5.535 5.133 5.335 8 9 10 6.952 6.802 6.656 6.515 6.379 6.217 6.119 5.995 5.875 5.759 9 7.538 7.360 7.189 .7.021 6.861 6.710 6.561 6.118 6.279 6.115 10 11 8.093 7.887 7.689 7.199 7.315 7.139 6.969 6.805 6.617 6.195 11 12 8.619 8.381 8.159 7.913 7.735 7.536 7.315 7.161 6.981 6.811 12 13 H 9.117 6.853 8.600 8.358 8.126 9.590 9.295 9.011 8.715 8.189 7.901 7.691 7.187 7.291 7.103 8.2U 8.010 7.786 7.572 7.367 13 11 15 io. oa 9.712 9.103 9.108 8.827 8.559 8.301 8.061 7.828 7.606 15 16 10.16 10.n 9.768 9.117 9.112 8.851 8.575 8.313 8.062 7.821 16 17 10.87 10.18 10.11 9.763 9.131 9.122 8.825 8.511 8.276 8.022 17 18 11.25 10.83 10.13 10.06 9.706 9.372 9.055 8.756 8.1a 8.201 18 19 11.61 11.16 10.71 10.31 9.959 9.601 9.268 8.950 8.650 8.365 19 20 11.95 11.17 11.02 10.59 10.19 9.a8 9.163 9.129 8.812 8.5U 20 a 12.28 11.76 11.29 10.81 10.11 10.02 9.611 9.292 8.961 8.619 21 22 12.58 12.01 U.51 11.06 10.62 10.20 9.ao 9.112 9.097 8.772 22 23 12.88 12.30 11.77 11.27 io.a 10.37 9.963 9.580 9.2a 8.883 23 21 13.15 12.55 11.99 11.17 10.98 10.53 10.10 9.707 9.331 8.985 21 25 13 .11 12.78 12.20 11.65 11.15 10.68 10.23 9.823 9.138 9.077 25 26 13.66 13.00 12.39 11.83 11.30 io.a 10.35 9.929 9.532 9.161 26 27 28 13.90 13.21 12.58 11.99 11.11 10.91 10.17 10.03 9.618 9.237 27 11.12 13.11 12.75 12.11 11.57 11.05 10.57 10.12 9.697 9.307 28 29 30 lii.33 13.59 12.91 12.28 11.70 11.16 10.66 10.20 9.769 9.370 29 11.53 13.77 13.06 12.11 ii.a 11.26 10.75 10.27 9.835 9.127 30 ! 31 11.72 13.93 13.20 12.53 11.92 11.35 10.83 10.31 9.895 9.179 31 t 32 33 31 11.90 11.06 13.33 12.65 12.02 15.08 11.23 13.16 12.75 12.11 15.21 11.37 13.58 12.85 12.19 11.11 10.90 10.11 9.950 9.526 11.51 10.97 10.16 10.00 9.569 11.59 11.03 10.52 10.05 9.609 32 33 31 35 15.39 11.50 13.69 12.95 12.27 11.66 11.09 10.57 10.09 9.611 35 36 15.51 11.62 13.79 13.01 12.35 11.72 11.11 10.61 10.13 9.677 36 37 38 15.67 11.71 13.89 13.12 12.12 15.81 11.85 13.98 13.19 12.18 11.78 11.19 10.65 10.16 9.706 11.83 11.21 10.69 10.19 9.733 37 38 39 10 15.93 11.95 11.07 13.27 12.51 11.88 11.28 10.73 10.22 9.757 39 16.05 15.05 11.15 13.33 12.59 11.93 11.32 10.76 10.25 9.779 10 11 12 13 oil 15 16.16 16.26 16.36 16.16 16.55 15.11 15.23 15.31 15.38 15.16 U.22 11.29 11.36 11.12 11.18 13.39 13.15 13.51 13.56 13.61 12.65 12.69 12.71 12.78 12.82 11.97 12.01 12.01 12.08 12.11 11.35 11.38 ll.ll ll.H 11.17 10.79 io.a 10.81 10.86 10.88 10.27 10.29 10.31 10.33 10.35 9.799 9. a? 9.831 9.819 9.863 11 12 13 11 15 16 17 ItS 19 50 16.63 16.71 16.79 16.86 16.93 15.52 15.59 15.65 15. a 15.76 11.51 U.59 11.61 11-68 11.73 13.65 13.69 13.73 13.77 13.80 12.86 12.89 12.92 12.95 12.98 12.11 12.16 12.19 12. a 12.23 11.19 ll.5i 11.53 11.55 11.57 10.90 10.92 10.93 10.95 10.96 10.36 10.38 10.39 10.10 10.11 9.875 9.887 9.897 9.906 9.915 16 17 18 19 50 CTD000783 TABLE Cl 7 TABLE Cl (continued) Yar 10.5* 11.0* 11.5* 120* 115* 13.0* 13.5* M.O* 14.5* 15.0* Yar* 1 .905 .901 .697 .893 .889 2 1.721* 1.713 1.701 1.690 1.679 3 2.1*65 2.1*l*i* 2.1*23 2.1*02 2.381 1* 3.136 3.102 3.070 3.037 3.006 5 3.71*3 3.696 3.650 3.605 3.561 6 1*.292 1*. 231 U.170 i*.m 1*.051* 7 1*.789 1*. 712 1*. 637 1*. 561* 1*.1*92 8 5.239 5.11*6 5.056 1*.968 1*. 882 9 5.61*6 5.537 5.1*31 5.328 5.228 10 6.015 5.889 5.768 5.650 5.536 11 6.31*8 6.207 6.070 5.938 5.810 12 6.650 6.1*92 6.3U. 6.191* 6.053 13 6.923 6.750 6.583 6.1*21* 6.270 u* 7.170 6.982 6.801 6.628 6.1*62 15 7.391* 7.191 6.997 6.811 6.633 16 7.596 7.379 7.172 6.971* 6.785 17 7.779 7.51*9 7.329 7.120 6.920 18 7.91*5 7.702 7.1*70 7.250 7.01*0 19 8.095 7.839 7.596 7.366 7.11*7 20 8.231 7.963 7.710 7.1*69 7.2L1 21 8.351* 6.075 7.811 7.562 7.326 22 6.1*65 8.176 7.903 7.61*5 7.1*01 23 8.566 8.266 7.981* 7.718 7.1*67 21* 8.657 6.31*8 8.058 7.781* 7.526 25 8.739 8.1*22 8.121* 7.81*3 7.579 .8C5 1.668 2.361 2.971* 3.517 .881 1.657 2.3L1 2.91*1* 3.1*75 .877 1.61*7 2.322 2.911* 3.1*33 .873 1.636 2.302 2.881* 3.392 .870 1.626 2.283 2.855 3.352 3.998 l* .1*23 1*.799 5.132 5.1*26 3.91*3 L.355 li.7l8 5.038 5.320 3.889 1*.288 ii.639 1* .91*6 5.216 3.836 1* .221* 1* .562 1*. 856 5.116 3.781* 1*.160 1*. 1*87 L.772 5.019 5.687 5.918 6.122 6.302 6.1*62 5.568 5.787 5.979 6.11*9 6.299 5.U53 5.660 5.81*2 6.002 6.11*2 5.3ia 5.538 5.710 5.861 5.992 5.231* 5.1*21 5.583 5.721* 5.81*7 6.601* 6.729 6.81*0 6.938 7.025 6.1*31 6.51*7 6.61*9 6.739 6.819 6.265 6.373 6.1*67 6.550 6.623 6.106 6.206 6.291* 6.370 6.1*37 5.951* 6.01*7 6.128 6.198 6.259 7.102 7.170 7.230 7.283 7.330 6.889 6.951 7.005 7.053 7.095 6.687 6.71*3 6.792 6.835 6.873 6.1*95 6.51*6 6.590 6.629 6.663 6.312 6.359 o.399 6.1*31* 6.1*61* 1 2 3 1* 5 6' 7 8 9 10 11 12 13 11* 15 16 17 18 19 20 21 22 23 21* 25 26 8.811* 8.1*88 6.183 7.896 7.626 27 8.881 8.51*8 8.236 7.91*3 7.667 28 8.91*2 3.602 8.283 7.981* 7.701* 29 8.997 8.650 8.326 6.022 7.737 30 9.01*7 8.691* 8.361* 8.055 7.766 31 9.093 6.733 6.398 8.085 7.792 32 9.131* 8.769 8.1*29 8.112 7.815 33 9.171 8.801 8.1*56 8.135 7.636 31* 9.201* 8.829 8.1*81 3.157 7.851* 35 9.235 8.855 8.503 8.176 7.870 36 9.262 8.879 8.523 8.192 7.835 37 9.287 8.900 8.51*1 8.208 7.898 38 9.309 8.919 8.557 8.221 7.909 39 9.330 8.936 8.571 8.233 7.919 1*0 9.31*8 8.951 5.531* 8.21*1* 7.928 la 9.365 8.965 8.595 8.253 7.936 U2 9.380 8.977 8.606 6.262 7.91*3 1*3 9.391* 8.989 8.615 8.270 7.91*9 iiil 9.1*06 8.999 8.623 8.276 7.955 1*5 9.1*17 9.008 8.631 8.283 7.960 1*6 9.1*27 9.016 8.637 8.288 7.965 1*7 9.1*37 9.021* 8.61*3 8.293 7.968 1*8 9.1*1*5 9.030 8.61*9 8.297 7.972 1*9 5o 9.1*52 9.036 8.651* 3.301 7.975 9.1*59 9.01*2 8.658 8.301* 7.978 7.372 7.1*09 7.1*la 7.1*70 7.1*96 7.132 7.165 7.191* 7.219 7.21*2 6.906 6.935 6.961 6.983 7.003 6.693 6.718 6.71*1 6.761 6.778 6.1*91 6.511* 6.531* 6.551 6.566 7.516 7.538 7.556 7.572 7.586 7.261 7.279 7.291* 7.307 7.319 7.020 7.035 7.01*8 7.060 7.070 6.793 6.806 6.817 6.827 6.836 6.579 6.591 6.600 6.609 6.617 7.598 7.609 7.618 7.627 7.631* 7.330 7.339 7.31*7 7.351* 7.361 7.079 7.087 7.091* 7.100 7.105 6.81*1* 6.851 6.856 6.861 6.866 6.623 6.629 6.631* 6.638 6.61*2 7.61a 7.61*7 7.652 7.657 7.661 7.366 7.371 7.375 7.379 7.383 7.110 7.111* 7.117 7.120 7.123 6.870 6.873 6.876 6.879 6.881 6.61*5 6.61*8 6.650 6.652 6.651* 7.661* 7.668 7.671 7.673 7.675 7J86 7.388 7.390 7.392 7.391* 7.126 7.128 7.130 7.131 7.133 6.883 6.885 6.836 6.887 6.889 6.656 6.657 6.659 6.660 6.661 26 27 28 29 30 31 32 33 31* 35 36 37 38 39 1*0 la 1*2 1*3 1*1* 1*5 1*6 1*7 1*8 1*9 50 CTD000784 C8 AIM'EXDIX C TABLE Cl (continued) Year* 15.3% 16.0* 16.5% 17.0% 17.5% 18 0% 18.5% 19.0% 19.4% 20.0% Ym 1 .866 .o62 .858 .655 .851 2 1.615 1.605 1.595 1.585 1.575 } 2.261* 2.21*6 2.228 2.210 2.192 U 2.826 2.798 2.770 2.71*3 2.716 5 3.313 3.271* 3.236 3.199 3.163 6 3.731* 3.685 3.636 3.589 3.51*3 7 1*.099 1*. 039 3.980 3.922 3.866 8 1*.1*15 U.3UU 1*. 271* i*.207 !*.U*2 9 U.688 1*.607 U.527 1*.1*51 it.376 10 U.925 1*. 833 l*.7l*5 1*. 659 1*.575 11 5.130 5.029 1* .931 U.836 1*.71*5 12 5.307 5.197 5.091 1*.988 U.889 13 5.1*61 5.31*2 5.228 5.118 5.012 Ik 5.591* 5.1*68 5.31*6 5.229 5.117 15 5.709 5.575 5.1*1*7 5.321* 5.206 16 5.808 17 5.895 18 5.969 19 6.031* 20 6.090 5.668 5.71*9 5.818 5-877 5.929 5.531* 5.609 5.673 5.728 5.775 5.1*05 5.1*75 5.531* 5.581* 5.628 5.281 5.32*6 5.1*oi 5.1*1*7 5.1*87 21 6.139 5.973 5.815 5.665 5.521 22 6.181 6.011 5.850 5.696 5.550 23 6.217 6.01*1* 5.880 5.723 5.571* 2U 6.21*9 6.073 5.905 5.71*6 5.595 25 6.276 6.097 5.927 5.766 5.613 .81*7 1.566 2.171* 2.690 3.127 .81*1* 1.556 2.157 2.661* 3.092 .81*0 1.51*7 2.11*0 2.639 3.058 .837 1.537 2.123 2.613 3.021* .833 1.528 2.106 2.589 2.991 3.1*98 3.812 1*.078 1*. 303 l*.2*9l* 3.1*53 3.758 U.015 lt.232 u.a5 3.ao 3.706 3.951* U.163 1*.339 3.367 3.655 3.895 U.0?6 U.265 3.326 3.605 3.837 U.031 U.192 U.656 1*. 793 i*.910 5.008 5.092 U.570 1*.700 a 810 U.903 U.982 !*.1*86 l*.6ll U.715 It.802 1*.876 !*.i*06 U.523 U.622 1*.705 It. 771* U.327 U.U39 U.533 U.611 U.675 5.162 5.222 5.273 5.316 5.353 5.01*8 5.101* 5.151 5.191 5.221* U.938 U.990 5.033 5.070 5.101 U.932 U.880 U.921 l*.95l* U.983 U.730 1*.775 1*.812 It.81*3 U.870 5.381* 5.1*10 5.1*32 5.1*51 5.1*67 5.252 5.276 5.296 5.313 5.328 5.127 5.11*9 5.167 5.182 5.195 5.007 5.026 5.01*3 5.057 5.069 U.891 U.909 U.925 lx.937 l*.9l*8 1 2 3 u 5 6 7 8 9 10 U 12 13 li* 15 16 17 18 19 20 21 22 23 2U 25 26 6.299 6.118 5.91*6 5.783 5.628 27 6.320 6.136 5.962 5.798 5.6a 28 6.337 6.152 5.976 5.810 5.652 29 6.353 6.166 5.988 5.820 5.661 30 6.366 6.177 5.999 5.829 5.669 31 6.378 6.187 6.007 5.837 5.676 32 6.387 6.196 6.015 5.81*1* 5.681 33 6.396 6.203 6.021 5.81*9 5.686 3k 6.1*01* 6.210 6.027 5.851* 5.691 35 6.1*10 6.215 6.032 5.858 5.691* 36 6.1*16 6.220 6.036 5.862 5.697 37 6.1*20 6.221* 6.039 5.865 5.700 38 6.1*25 6.228 6.01*2 5.867 5.702 39 6.1*28 6.231 6.01*5 5.869 5.701* U0 6.1*31 6.233 6.01*7 5.871 5.705 a 6.1*31* 6.236 6.01*9 5.873 5.707 1*2 6.1*36 6.238 6.051 5.871* 5.708 U3 6.1*38 6.239 6.052 5.875 5.709 1*1 6.1*1*0 6.21*1 6.053 5.876 5.710 U5 6.1*1*2 6.21*2 6.051* 5.877 5.710 1*6 6.1*1*3 6.21*3 6.055 5.878 5.711 1*7 6.1*2*1* 6.21*1* 6.056 5.879 5-711 1*8 6.1*1*5 6.21*5 6.057 5.879 5.712 1*9 6.1*1*6 6.21*6 6.057 5.880 5.712 50 6.1*1*7 6.21*6 6.058 5.880 5.712 5.1*80 5.1*92 5.502 5.510 5.517 5.31*0 5.350 5.359 5.366 5.372 5.206 5.215 5.223 5.229 5.235 5.078 5.086 5.093 5.099 5.101* 1*.956 lt.961* U.970 1*.975 U.979 26 27 28 29 30 5.523 5.528 5.532 5.536 5.539 5.377 5.382 5.365 5.389 5.391 5.239 5.21*3 5.21*6 5.21*9 5.251 5.108 5.111 5.111* 5.116 5.118 U.982 U.985 U.9B8 U.990 U.992 31 32 33 3U 35 5.5a 5.51*3 5.51*5 5.51*7 5.51*8 5.393 5.395 5.397 5.398 5.399 5.253 5.255 5.256 5.257 5.258 5.120 5.121 5.122 5.123 5.121* U.993 U.99U U.995 U.996 U.997 36 37 38 39 Uo 5.51*9 5.550 5.551 5.552 5.552 5.1*00 5.1*01 5-1*02 5.1*02 5.1*03 5.259 5.260 5.260 5.261 5.261 5.125 5.125 5.126 5.126 5.127 U.997 U.998 U.998 U.998 U.999 a a a u* U5 5.553 5.553 5.551* 5.551* 5.551* 5.1*03 5.1*ol* 5.1*01* 5.1*01* 5.1*01* 5.261 5.262 5.262 5.262 5.262 5.127 5.127 5.127 5.127 5.128 U.999 U.999 U.999 U.999 U.999 U6 U7 U8 U9 50 CTD000785 TABLE Cl C9 TABLE Cl {continued) Vm 21% 22% 23% 24% 25% 26% 27% 28% 27% 30% Ym 1 .826 .620 .813 .806 .800 2 1.509 1.1*92 l.u7U 1.U57 1.UU0 3 2.07e 2.01*2 2.011 1.981 1.952 u 2.5UO 2.U9U 2.UUB 2.U0U 2.362 5 2.526 2.86U 2.803 2.7U5 2.689 6 3.2US 3.167 3.092 3.020 2.951 7 3.508 3.L16 3.327 3.2U2 3.1-1 8 3.726 3.619 3.518 3.1*21 3.329 9 3.905 3.786 3.673 3.566 3.U63 10 U.05U 3-923 3.799 3.682 3.571 11 U.177 U.035 3.902 3.776 3.656 12 U.278 U.127 3.985 3.851 3.725 13 U.362 U.203 U.053 3.912 3.780 u U.U32 U.265 U.1O0 3.962 3.82U IS U.U89 U.315 U.153 U.001 3.859 16 U.536 U.357 U.189 U.033 3.887 17 U.576 U.391 U.219 U.059 3.910 18 U.606 L.L19 U.2U3 u.oao 3.928 19 U.63S U.1*1*2 U.263 U.097 3.91*2 20 U.657 U.U60 U.279 U.UO 3.95U 21 U.675 U.U76 U.292 U.121 3.963 22 U.690 U.U88 U.302 U.UO 3.970 23 U.703 U.U99 U.311 U.U7 3.976 2L U.713 U.507 U.318 U.1U3 3.981 25 U.721 U.SlU U.323 U.1U7 3.985 79U 1.U2U 1.923 2.320 2.635 .787 1.U07 1.896 2.260 2.583 .781 1.392 1.868 2.21*1 2.532 .775 1.376 1.81*2 2.203 2.U83 .769 1.361 1.816 2.166 2.1*36 2.885 3.083 3.2U1 3.366 3.U65 2.821 3.009 3.156 3.273 3.36L 2.759 2.937 3.076 3.18U 3.269 2.700 2.868 2.999 3.100 3.178 2.61(3 2.802 2.925 3.019 3.092 3.51*3 3.606 3.656 3.695 3.726 3.1*37 3.1*93 3.538 3.573 3.601 3.335 3.387 3.U27 3.U59 3.U83 3.239 3.286 3.322 3.351 3.373 3.11*7 3.190 3.223 3-.2L9 3.268 3.751 3.771 3.786 3.799 3.808 3.623 3.6UO 3.65U 3.66U 3.673 3.503 3.518 3.529 3.539 3.51*6 3.390 3.1*03 3.U13 3.U21 3.1*27 3.283 3.295 3.301* 3.311 3.316 3.816 3.822 3.827 3.831 3.83U 3.679 3.68U 3.609 3.692 3.69U 3.551 3.556 3.559 3.562 3.56U 3.1*32 3.1*36 3.1*38 3.1*1*1 3.UU2 3.320 3.323 3.325 3.327 3.329 1 2 3 U 5 6 7 8 9 10 U 12 13 1U 15 16 17 18 19 20 21 22 23 2L 25 26 L.728 U.520 U.328 U.151 3.988 27 28 U.73U U.739 U.52U U.528 U.332 U.335 U.15U U.157 3.990 3.992 29 U.7U3 U.531 U.337 U.159 3.99U 30 L.7L6 U.53U U.339 U.160 3.995 31 U.7U9 U.536 u.3a U.161 3.996 32 U.751 U.538 U.3U2 U.162 3.997 33. U.753 U.539 U.3U3 U.163 3.997 3L i*. 755 L.5L0 U.3UU U.16U 3.998 35 U.756 u.sui U.3U5 U.16U 3.998 36 37 38 39 ilO U.757 U.758 U.759 U.759 U.760 U.5U2 U.5U3 U.5U3 U.5UU U.5UU U.3U5 U.3U6 U.3U6 U.3U6 U.3U7 U.165 U.165 U.165 U.166 U.166 3.999 3.999 3.999 3.999 3.999 ui U2 U.760 U.5UU U.3U7 U.166 U.ooo U.760 U.5UU U.3U7 U.166 L.000 1*3 U.761 U.5U5 U.3U7 U.166 U.ooo 1*1* U.761 U.5U5 U.3U7 U.166 U.ooo US U.761 U.5U5 U.3U7 U.166 U.ooo U6 U7 U.761 L.5L5 U.3U8 U.166 U.ooo U.761 U.5U5 U.3U8 U.166 U.ooo U8 U.761 U.5U5 U.3U8 U.167 U.ooo 1*9 U.761 U.5U5 U.3U8 U.167 U.ooo 50 U.762 U.5U5 U.3U8 U.167 U.ooo 3.837 3.839 3.8L0 3.81*1 3.81*2 3.696 3.698 3.699 3.700 3.701 3.566 3.567 3.568 3.569 3.569 3.UU1* 3.1*1*5 3.1*1*6 3.1*1*6 3.1*1*7 3.330 3.331 3.331 3.332 3.332 3.81*3 3.81*1* 3.8UU 3.8U5 3.81,5 3.701 3.702 3.702 3.703 3.703 3.570 3.570 3.570 3.571 3.571 3.UU7 3.UU7 3.1*1*8 3.1*1*8 3.1*1*8 3.332 3.333 3.333 3.333 3.333 3.BUS 3.81*5 3.81*6 3.81*6 3.8U6 3.703 3.703 3.703 3.703 3.703 3.571 3.571 3.571 3.571 3.571 3.UU8 3. LBS 3.1*1*8 3.1*1*8 3.UU6 3.333 3.333 3.333 3.333 3.333 3.8U6 3.8U6 3.8U6 3.81*6 3.81*6 3.703 3.70U 3.70L 3.70U 3.70U 3.571 3.571 3.571 3.571 3.571 3.LL8 3.1*1*8 3.UU8 3.LL8 3.LL8 3.333 3.333 3.333 3.333 3.333 3.BU6 3.8U6 3.8U6 3.8U6 3.8U6 3.70U 3.70U 3.70U 3.70U 3.70U 3.571 3.571 3.571 3.571 3.571 3.1*1*8 3.LL8 3.1*1*8 3.1*1*8 3.LL6 3.333 3.333 3.333 3.333 3.333 26 27 28 29 30 31 32 33 3L 35 36 37 38 39 LO la 1*2 U3 LL 1*5 1*6 L7 L8 1*9 50 CTD000786 IP--25M--9/78--43403 CTD000787 IP--25M--9/78--43403 - CTD000787