Document baZoQO49rN6RoxJ7O8aJ9JRRk
American Water Works Association
ANSI/AWWA 0401-83 (Revision of AWWA C401-77)
AWWA STANDARD PRACTICE
for
THE SELECTION OF ASBESTOS-CEMENT DISTRIBUTION PIPE
4 IN. THROUGH 16 IN. (100 mm THROUGH 400 mm), FOR WATER AND OTHER LIQUIDS
[AMERICAN NATIONAL) VMSTANDARDHP
First edition approved by A WWA Board of Directors Jan 27, 1964. This edition approved Jan. 30, 1983.
Approved by American National Standards Institute, Inc., June 21, 1983.
AMERICAN WATER WORKS ASSOCIATION
6666 West Quincy Avenue, Denver, Colorado 80235
Committee Personnel
The Standards Committee on Asbestos-Cement Pressure Pipe, which reviewed and approved this standard, had the following personnel at the time of approval:
R.S. Bryant, Chairman J.L. WARDEN, Vice-Chairman
T.R. Gillen, Secretary
Consumer Members
S.C. Baker, Naval Facilities Engineering Command, Alexandria, Va. (NAVFAC)
Glenwood Bretz,* USNCBC CESO, Port Hueneme, Calif.
(NAVFAC)
R.S. Bryant, Department of Water and Power, Los Angeles, Calif. (AWWA)
Roger Graff, City of San Diego, San Diego, Calif.
(AWWA)
J.L. Warden, US Bureau of Reclamation, Denver, Colo.
(BUREC)
General Interest Members
G.C. Anderson, Insurance Services Offices, New York, N.Y.
(ISO)
R. A. Barrows, C.E. Maguire, Inc., Waltham, Mass.
(NEWWA)
V.R. BlCKEL, Department of Environmental Health, Albuquerque,
N.M.
(APWA)
S. L. Bishop,* Metcalf & Eddy, Boston, Mass.
(NEWWA)
T. J. Brown Jr., Factory Mutual Research Corporation, Norwood,
Mass.
(FMR)
F.V. Camarda, Crown Point, Ind.
(AWWA)
C.W. Cline, Thompson & Litton, Inc., Norton, Va.
(AWWA)
L.J. Dosedlo, Underwriters' Laboratories, Northbrook, 111.
(UL)
C.L. FRICK,* Insurance Services Office, Atlanta, Ga.
(ISO)
*A!ternate
Copyright 1983 by American Water Works Association Printed in USA
i
ASBESTOS-CEMENT DISTRIBUTION PIPE
R.S. Holmgren Jr., James M. Montgomery Consulting Engineers,
Pasadena, Calif. L. L. Lyles, W.M. Lyles Company, Visalia, Calif F.A. Obert, Metcalf & Eddy, Inc., Boston, Mass. M. R. Suchomel,* Underwriters' Laboratories, Northbrook, 111. D.F. Thomas, Waterous Company, South St. Paul, Minn. J.R. Williams, Fairfax, Va.
(AWWA) (AWWA) (WPCF)
(UL) (MSS) (AWWA)
Producer Members
J.F. Baker, Certain-Teed Products Corporation, Valley Forge, Pa. T.R. Gillen,* Asbestos-Cement Pipe Producers Association,
Lakewood, Colo. Gustavo Herrera, Asbestos Monterrey, S.A. Monterrey, N.L.,
Mexico J.C. Jackson, Asbestos-Cement Pipe Producers Association,
Arlington, Va. S.G. Leyshock, Cement Asbestos Products, Birmingham, Ala. H.L. OLSON, Johns-Manville Sales Corporation, Denver, Colo.
(AWWA)
(ACPPA)
(AWWA)
(ACPPA) (AWWA) (AWWA)
*Altcrnate
Table of Contents
SEC.
Foreword
PAGE
I. History of Standard ........................... II. Major Revisions .................................
v v
Standard
1 General................................................ 1.1 Scope.................................................. 1.2 References.......................................... 1.3 Symbols and Abbreviations.............
2 General Design................................. 2.1 Strength and Design Factors............ 2.2 Combined Loading Theory............. 2.3 Three-Edge Vee-Shaped Bearing
Load................................................
1 1 I 2
4 4 6
7
SEC 3
4
5 6 C. 1
PAGE
Values of Load Coefficients C, for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit...............
Superimposed (Wheel) Load-- Single Wheel = 16 0001b (7250 kg) ........................................
Design Internal Pressure and Design External Load...................
Design External Earth Load ........... Present Worth of an Income of
$1.00 per Year for the Next N Years..................................
18
19 37 38
50
Figures
3 External Loads................................. 3.1 Introduction......................................... 3.2 Earth Loads........................................ 3.3 Superimposed Loads.........................
4 Hydrostatic Pressure......................... 4.1 Introduction......................................... 4.2 Operating Pressure........................... 4.3 Surge Pressure....................................
5 Design Criteria and Use of Pipe Selection Charts ...........................
5.1 Combined Loading Curves................ 5.2 Safety Factors.................................... 5.3 Use of Selection Charts for
Economical Design....................... 5.4 Discussion.......................................... 5.5 Illustrative Problem on Pipe
Selection..........................................
Tables
F. 1 Conversion Factors............................ 1 Recommended Safe Design Values of c for Tunnel Conditions.......... 2 Impact Factors (F)...........................
7 7 7 17 20 20 20 20
20 20 21
21 21
22
v
17 17
1 Classes of Bedding for Conduits in Trench............................................
2 Load Pressure Curve......................... 3 Assembly for Three-Edge Vee-
Shaped Crushing Strength Test.................................................. 4 Classification of Construction Techniques...................................... 5 Values of Cj for Trench Conditions...................................... 6 Embankment Conditions................. 7 Values of C, for Positive Projecting Pipe................................................ 8 Values of Bdj B, at Which the Trench and Positive Projecting Pipe Equations Give Equal Loads.............................................. 9 Values of C,, for Negative Projecting Pipe and Imperfect Ditch Conditions........................... 10a Positive Projecting Pipe Projection
5 6
7 8 9 10 11
13
14
Ratio = -- Bc
15
111
ASBESTOS-CEMENT DISTRIBUTION PIPE
IV
10b Negative Projecting Pipe Projection X
Ratio = --
.......................
11 Projection Ratio p' for the Imperfect Trench Embankment Condition......................................
12 Values of Cyfor Tunnel Conditions...................................
13 Superimposed Loads....................... 14a Selection Curves for 4-in.
Asbestos-Cement Pipe............... 14b Selection Curves for 6-in.
Asbestos-Cement Pipe............... 14c Selection Curves for 8-in.
Asbestos-Cement Pipe............... 14d Selection Curves for 10-in.
Asbestos-Cement Pipe............... 14e Selection Curves for 12-in.
Asbestos-Cement Pipe............... I4f Selection Curves for 14-in.
Asbestos-Cement Pipe............... 14o Selection Curves for 16-in.
Asbestos-Cement Pipe............... I4A(m) Selection Curves for 100-mm
Asbestos-Cement Pipe .... 14b (m) Selection Curves for 150-mm
Asbestos-Cement Pipe .... 14c (m) Selection Curves for 200-mm
Asbestos-Cement Pipe........ 32 14D(m) Selection Curves for 250-mm 15 Asbestos-Cement Pipe........ 33 14E(m) Selection Curves for 300-mm
Asbestos-Cement Pipe........ 34 15 14f (m) Selection Curves for 350-mm
Asbestos-Cement Pipe........ 35 16 14g (m) Selection Curves for 400-mm 19 Asbestos-Cement Pipe........ 36
B. 1 Time (TE) = Effective for Full Cut 23 Off Uniformly at Maximum
Rate................................................ 42 24 C. 1 Yearly Power Cost to Compensate
for Friction Loss of Head............. 48
25
Appendices 26
A Friction Loss of Head Chart27 Coefficient of Flow, C = 140 .... 39
B Surge Pressure Analysis.................. 40 28 B. 1 Water Hammer or Surge................ 40
B.2 Water Hammer Analysis ................ 40 29 B.3 Valve Closure ................................... 41
B.4 Pumped Systems............................... 43 30 B.5 Methods of Control ........................ 44
B.6 Surge Calculation Example............ 45 31 B.7 Air in Pipelines................................ 46
C Frictional Power Requirements .... 47
Foreword
This foreword is for information only and is not a part of A WWA C401.
I. History of Standard
The information contained in this stan dard was first published as A WWA Hand book H2, with A WWA Board of Direc tors' approval on Jan. 17, 1964. The designation was later changed to, AWWA C40I-64. Originally, it covered sizes 4-36 in. (100-900 mm) although the design was primarily based on service conditions generally related to smaller (4-16 in. [100-400 mm]) distribution sizes. In 1977 the standard was revised. The title was changed to indicate the pipe is intended for use in distribution systems, and the size range was changed to limit the maxi mum size covered by this standard to 16 in. (400-mm) diameter pipe.
II. Major Revisions
Major revisions in this edition consist of the following:
1. The format has been completely revised so that the various sections in this standard correspond to the numbered sec tions in AWWA C403, Standard Practice for the Selection of Asbestos-Cement Transmission and Feeder Main Pipe,
Sizes 18 in. Through 42 in.
2. Bedding condition descriptions and load factors used in calculating earth loads have been revised to correspond to those contained in ASCE Manual of Engineering Practice No. 37, Design and Construction of Sanitary and Storm Sewers (1976).
3. The three-edge vee-shaped bearing method of ASTM C500 has been speci fied for crush testing.
4. The appendix has been enlarged to present data on flow calculations using the Hazen and Williams formula and data on surge pressure analysis.
5. The impact factor table was revised to conform with impact factors recom mended by the American Association of State Highway and Transportation Offi ces (AASHTO).
6. Metric conversion of all dimen sions and physical requirements are in cluded in this standard (Table F. 1). Metric dimensions are direct conversions of cus tomary US inch-pound units and are not those specified in International Standards Organization (ISO) standards.
Table F. 1 Conversion Factors
Inch-Pound System
Multiply By
To Obtain
Inches Feet Pounds Per Square Inch Pounds Pounds Per Foot Pounds Per Square Foot Pounds Per Cubic Foot
25.4 0.3048 6.894757 4.44822 0.014594 0.0478803 16.0185
Millimetres Metres Kilopascals Newtons Kilonewtons Per Metre Kilonewtons Per Square Metre Kilograms Per Cubic Metre
American Water Works Association
ANSI/AWWA C401-83 (Revision of AWWA C401-77)
AWWA Standard Practice for
The Selection of Asbestos-Cement Distribution Pipe, 4 in. Through 16 in. (100 mm Through 400 mm),
for Water and Other Liquids
Section 1--General
Sec. 1.1 Scope
This standard has been prepared so that design engineers may quickly deter mine the correct pressure classification of asbestos-cement distribution pipe to use under various combinations of internal pressure (static, operating, and surge) and external load (earth and superimposed live loads). Combined loading curves de picting the relationship between hydro static loading and external loading capa bilities are included to expedite the selec tion of the correct pipe strength classifi cation.
Note: Information to assist the engi neer in selecting the most economical size of pipe is in the appendices. 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 fric tion loss of head. The appendices are for information only and are not part of AWWAC401.
1.1.1 Pressure classes. Pipe pressure class designations of 100, 150, and 200
refer to the similarly numbered classes specified in AWWA C400, Standard for Asbestos-Cement Distribution Pipe, 4 in. Through 16 in. (100 mm Through 400 mm) NPS, for Water and Other Liquids."
1.1.2 Installation. Detailed coverage of the installation of asbestos-cement pipe can be found in AWWA C603, Standard for Installation of AsbestosCement Pressure Pipe.
Sec. 1.2 References
This standard references the following documents. They form a part of this standard to the extent specified herein. In any case of conflict, the requirements of this standard shall prevail.
SCHL1CK, W. J. Supporting Strengths for Cast-Iron Pipe for Water and Gas Service. Bull. 146. Iowa State Col. Engrg. Exp. Sta. (June 1940).
Design and Construction of Sanitary and Storm Sewers. Manual of Engrg. Prac. No. 37. Amer. Soc. Civ. Engrs. New York (1976).
Kerr, S. L. Practical Aspects of Water Hammer, Jour. A WWA, 40:6:699 (June 1948).
l
2 AWWA C401-83
Marston, Anson. The Theory of External Loads on Closed Conduits in the Light of Latest Experiments. Bull. 96. Iowa State Col. Engrg. Exp. Sta. (1930).
ASTM* C500, Methods of Testing Asbestos-Cement Pipe.
Sec. 1.3 Symbols and Abbreviations
Bc = Outside diameter of a pipe, in feet (metres).
Bd = Width of trench measured at the top of pipe, in feet (metres).
B. F. = Bedding factor, which is a load factor correlating three-edge vee-shaped bearing test loads to field loads associated with specific bedding conditions.
Bt -- Maximum width of a tunnel excavation, in feet (metres).
c = Coefficient of soil cohesion, in pounds per square foot (kilonewtons per square metre).
Cc = Load coefficient for the posi tive projecting embankment condition. It is a function of the ratio H/ Bc, the projection ratio p, and the settlement ratio rsd.
Cd = Load coefficient for the trench condition. It is a function of the ratio H/ Bd and the backfill material.
C,, = Load coefficient for the nega tive projecting embankment condition, as well as the im perfect ditch condition. It is a function of the ratio H/ Bd, the projection ratiop', and the set tlement ratio rSd.
Cs = Load coefficient for concen trated or distributed superim posed loads. It is a function of the ratio Bd2H and the ratio LI 2H for concentrated loads, or the ratio Dj2H and the
American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103.
ratio MI2H for distributed loads. Ct = Load coefficient for tunnel con ditions. It is a function of the ratio HI Bt and the type of soil surrounding the tunnel. D = Width of the area over which the distributed superimposed load acts, in feet (metres). F = Impact factor. H = Depth of cover, in feet (me tres), for all conditions except the tunnel condition. For the tunnel condition, H is the dis tance from the ground surface to the top of the tunnel excava tion, in feet (metres). k = Rankine's ratio of lateral earth pressure to vertical pressure. L = Effective length of the pipe, in feet (metres). For pipe less than 3 ft (1 m), the actual length of the section should be used. For all other lengths, an effective length of 3 ft (1 m) should be used. M = Length of the area over which the distributed superimposed load acts, in feet (metres). P = Internal pressure, in pounds per square inch (kilopascals), that the pipe will withstand when no external load exists. Pc = Concentrated loads, in pounds (kilonewtonsf). . Pd = Distributed load, in pounds per square foot (kilonewtons per square metret). P,, = Static, working, or operating pressure, in pounds per square inch (kilopascals). Ps = Surge pressure or water ham mer, in pounds per square inch (kilopascals).
(Note: P, and P,i are loads measured as a mass. However, to use them in equations using SI units the mass unit must be converted to force by multiplying times 9.807 (g, the acceleration of gravity).
ASBESTOS-CEMENT DISTRIBUTION PIPE
3
PT = Total internal pressure, in pounds per square inch (kilopascals), above which, in com bination with some external load Wt applied in three-edge vee-shaped bearing, the pipe will withstand.
p = Projection ratio for the posi tive projecting embankment condition. It is defined as the ratio of the distance that the top of the pipe projects above the original ground surface in feet (metres) to the outside diameter of the pipe in feet (metres). (See Figure 10a.)
p' = Projection ratio for the nega tive projecting and imperfect ditch condition. It is defined as the ratio of the vertical dis tance from the original ground surface down to the top of the pipe, in feet (metres), divided by the width of the trench, in feet (metres), for negative pro jection, and as the ratio of the vertical distance from the top of the excavated trench down to the top of the pipe, in feet (metres), divided by the diam eter of the pipe, in feet (me tres), for the imperfect ditch condition. (SeeFigure lOBand Figure 11.)
rSd = Settlement ratio for positive projection, negative projection, and imperfect ditch condi tions.
S.F. = Safety factor. p = The coefficient of internal fric tion of backfill material. p' = The coefficient of friction be tween backfill material and the trench wall. W = External load, in pounds per linear foot (kilonewtons per metre), of pipe in the threeedge vee-shaped bearing test
that the pipe will withstand when no hydrostatic pressure exists.
We = Total earth load, in pounds per linear foot (kilonewtons per metre), to which the pipe is subjected.
Ws -- Total superimposed load, in pounds per linear foot (kilo newtons per metre), of pipe transmitted through the bur ial environment to the pipe by factors other than the earth loads.
Wsc = The concentrated superim posed load, in pounds per linear foot (kilonewtons per metre), of pipe transmitted through the burial environ ment to the pipe by factors other than the earth loads.
Wsd = Distributed superimposed load, in pounds per linear foot (kilonewtons per metre), of pipe transmitted through the burial environment to the pipe by factors other than the earth loads.
Wt = Total external load, in pounds per linear foot (kilonewtons per metre), of pipe applied in three-edge vee-shaped bearing above which, in combination with some internal pressure Pt, the pipe will withstand.
we = Weight of earth, in pounds per cubic foot (kilonewtons per cubic metre*).
Density, as used in the equations in this stand ard, refers to force exerted per unit volume under the acceleration of gravity, rather than mass per unit volume. Where true density is known in pounds per cubic foot, that value should be used in equations using US customary units; where true density is known in kilograms per cubic metre, it must be converted to newtons per cubic metre by multiplying times 9.807 (g. the acceleration of gravity) before the value is used in equations using SI units.
4 AWWA C401-83
Section 2--General Design
Sec. 2.1 Strength and Design Factors
The strength of asbestos-cement distri bution pipe must be sufficient to with stand the combined forces of all types of internal pressures (static, operating, and surge) and external loadings (earth, live, and impact). Sound engineering practice also requires that adequate safety factors be 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 confidence that the designer has in engineering esti mates of actual operating conditions. Safe ty factors are included under Sec. 5.
2.1.1 Bedding conditions. The bed ding conditions described below and shown in Figure 1 have been selected as representative of typical installation con ditions encountered in the field.
2.1.1.1 Class A--concrete cradle or concrete arch bedding. This class of bed ding may take either of two forms:
2.1.1.1.1 Concrete cradle. The pipe shall be bedded in a monolithic cradle of plain or reinforced concrete having a min imum thickness of one-fourth the outside pipe diameter (minimum of 4 in. [100 mm]) under the barrel and extending up the sides for a height equal to one-fourth the outside diameter. The cradle shall have a width at least equal to the outside diameter of the pipe barrel plus 8 in. (200 mm). Backfill shall be compacted above the cradle and extending to 12 in. (300 mm) above the crown of the pipe. The load factor for Class A concrete cradle bedding is 2.2 for plain concrete with lightly compacted (85 percent to 95 per cent proctor or 40 percent to 70 percent relative density) backfill; 2.8 for plain concrete with carefully compacted (95 percent proctor or 70 percent relative den
sity) backfill; and 3.4 for reinforced con crete withp = 0.4 percent, in whichp is the ratio of the area of steel to the area at the invert.
2.1.1.1.2 Concrete arch. The pipe shall be bedded in carefully compacted granu lar material having a minimum thickness of one-fourth the outside pipe diameter (minimum of 4 in. [100 mm]) between barrel and bottom of trench excavation and extending halfway up the sides of the pipe. The top half of the pipe shall be covered with a monolithic plain or rein forced concrete arch having a minimum thickness of one-fourth the outside diame ter (minimum of 4 in. [100 mm]) at the crown and having a minimum width equal to the outside pipe diameter plus 8 in. (200 mm). The load factor for Class A concrete arch type bedding is 2.8 for plain concrete; up to 3.4 for reinforced concrete with p = 0.4 percent; and up to 4.8 for reinforced concrete with p = 1.0 percent, in whichp is the ratio of the area of steel to the area of concrete at the crown.
2.1.1.2 Class B--first class bedding. Class B bedding may be achieved by either of two construction methods:
2.1.1.2.1 Shaped bottom with care fully compacted backfill. The bottom of the trench excavation shall be shaped to conform to a cylindrical surface with a radius at least 2 in. (50 mm) greater than the radius to the outside of the pipe and with a width sufficient to allow six-tenths of the width of the pipe barrel to be bedded in fine granular fill placed in the shaped excavation. Carefully compacted backfill shall be placed at the sides of the pipe to a thickness of at least 12 in. (300 mm) above the top of the pipe. Shaped trench bottoms are difficult to achieve under current construction techniques.
2.1.1.2.2 Compacted granular bed ding with carefully compacted backfill.
ASBESTOS-CEMENT DISTRIBUTION PIPE
5
Bc+8" min
Plain or reinforced concrete
I;
, f<
j-D, 4" min
Bc+8ff min 'A--
.A 4 min
CLASS A
Concrete arch
Fine granular fill
0.6 Bc
Shaped bottom with tamped backfill,
load factor 1.9
CLASS B*
Compacted granular bedding, load factor 1.9
Flat bottom, load factor 1.1, impermissible bedding, not recommended
'Carefully compacted backfill: 95% proctor or 70% relative density. fLightly compacted backfill: 85-95% proctor or 40-70% relative density.
Figure 1. Classes of Bedding for Conduits in Trench NOTE: In rock trench, excavate at least 6 in. (150 mm) below the coupling ofthe pipe except
where concrete cradle is used.
Revised and reprinted with permission from ASCE, Manual 37, Design and Construction of Sanitary and Storm Sewers. 1976.
6 AWWA C401-83
The pipe shall be bedded in compacted granular material placed on a flat trench bottom. The granular bedding shall have a minimum thickness of one-fourth the outside pipe diameter (minimum of 4 in. [100 mm]) and shall extend halfway up the pipe barrel at the side. The remainder of the backfill to a minimum depth of 12 in. (300 mm) overthe top of the pipe shall be filled with highly compacted material.
2.1.1.2.3 The load factor for either construction method is 1.9.
2.1.1.3 Class C--ordinary bedding. Class C ordinary bedding may be achieved by either of two construction methods:
2.1.1.3.1 Shaped bottom. The pipe shall be bedded with "ordinary"care in an earth foundation formed in the trench bottom by a shaped excavation that will fit the pipe barrel with reasonable close ness for a width of at least 50 percent of the outside pipe diameter. The side fills and area over the pipe to a minimum depth of 6 in. (150 mm) above the top of the pipe shall be filled with lightly com pacted fill. The shaped bottom bedding is not recommended for pipeline construc tion because it is impractical and costly.
2.1.1.3.2 Compacted granular bed ding with a lightly compacted backfill. The pipe shall be bedded in compacted granular material placed on a flat trench bottom. The granular bedding shall have a minimum thickness of 4 in. (100 mm) under the barrel and shall extend onetenth to one-sixth of the outside diameter up the pipe barrel at the sides. The remainder of the backfill to a minimum depth of 6 in. (150 mm) over the top of the pipe shall be filled with lightly compacted backfill.
2.1.1.3.3 The load factor for either construction method is 1.5.
2.1.1.4 Class D--flat bottom trench, impermissible bedding. In this class of bedding, the bottom of the trench is left flat, and no care is taken to secure com paction of backfill at the sides and imme
diately over the pipe. The load factor for Class D bedding is 1.1.
2.1.1.4.1 Class D bedding is not rec ommended for pipeline construction. Under present construction conditions. Class B or C bedding with a compacted granular bedding is generally a more prac tical and economical method of installa tion.
Sec. 2.2 Combined Loading Theory
Tests of asbestos-cement pipe under various combinations of internal pressure and external crush load applied in threeedge vee-shaped bearing (see Sec. 2.3) shows that there is a relationship between the combined loads at the point of pipe fracture. This relationship can be repre sented by a parabolic curve as shown in Figure 2. The equation for the load pres sure parabolic curve, which is known as the Schlick formula, may be expressed as:
Wt =
P~pPr Eq 1
P represents the internal pressure; W the external load.
Figure 2. Load Pressure Curve
ASBESTOS-CEMENT DISTRIBUTION PIPE
7
Sec. 2.3 Three-Edge Vee-Shaped Bearing Load
The combined loading curve shown in Figure 2 is calculated on the basis of crush strengths determined by laboratory tests employing the three-edge vee-shaped bearing test method (see ASTM C500, Methods of Testing Asbestos-Cement Pipe and Figure 3). Because the field-sup porting strength of a pipe is influenced by the bedding conditions and by the lateral
pressure acting against the sides of the pipe, it is necessary to apply a bedding load factor to the laboratory three-edge vee-shaped bearing loads to correlate them to the actual field loads. Since the external load equals the bedding factor times the vee-shaped bearing load, the bedding fac tor equals the external load divided by the three-edge vee-shaped bearing load. Fig ure I shows the load factors to be applied for each bedding class.
12"(305mm) minimum
12"(305mm) minimum
Figure 3. Assembly for Three-Edge Vee-Shaped Crushing Strength Test
Section 3--External Loads
Sec. 3.1 Introduction
For the design of asbestos-cement dis tribution pipe, external loads Wt are defined by the following equation:
WE + Ws X (S.F.) (B.F.)
Eq 2
Sec. 3.2 Earth Loads
Earth loads WE to which pipe is sub jected are a function of the soil density, pipe diameter, depth of cover, and con struction techniques employed in laying the pipeline. They depend on the interplay
between the weight of the prism of earth directly over 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 varies with the construction technique employed. There are two major construction tech niques normally encountered: trench and embankment. Another technique, the tun nel condition, is not normally found, but nevertheless, has unique design methods, which make its inclusion in this discussion necessary. Figure 4 shows these three con struction techniques.
AWWA C401-83
3.2.1 Marston's equation. For asbes tos-cement distribution pipe design, earth loads are calculated by the general form of Marston's equation:
WE = CW'BI
Eq 3
NOTE: Density as used in this equation and the following equations actually re fers to force exerted per unit volume (pounds per cubic foot or kilonewtons per metre) under the acceleration of gravity, rather than mass per unit volume. Where true density is known in pounds per cubic foot, that value should be used in equa tions using US customary units; where true density is known in kilograms per cubic metre, it must be converted to new tons per cubic metre by multiplying times
9.807 (g, the acceleration ofgravity) before the value is used in equations using SI units.
Soil densities we range in value from 100 to 135 lb/cu ft (16 to 21 kN/m3). In the absence of actual site information, a value of 120 lb/cu ft (19 kN/m3) is recommended for asbestos-cement dis tribution pipe design.
3.2.1.1 C is a coefficient that is de pendent on:
1. Ratio of the height of fill to the width of trench or pipe diameter.
2. Shearing forces between the inte rior and adjacent earth prisms.
3. Direction and amount of relative settlement between interior and adjacent earth prisms for embankment conditions.
The calculations used to find the value
Figure 4. Classification of Construction Techniques
Reprinted with permission from ASCE, Manual 37, Design and Construction of Sanitary and Storm Sewers. 1976.
ASBESTOS-CEMENT DISTRIBUTION PIPE
9
Figure 5. Values of Cj for Trench Conditions
Reprinted with permission from ASCE, Manual 37, Design and Construction of Sanitary and Storm Sewers. 1976.
of the coefficient will depend on the instal lation conditions employed in laying the
Pipe3.2.1.2 Values for B,i and C must be
determined to calculate earth loads by Eq 3 for the trench, embankment, and tunnel construction techniques. The following
subsections describe the different condi tions and explain the methods for finding the values needed to use Marston's equa tion for soil loading.
3.2.2 Trench condition. A trench con dition is defined as that in which the pipe is installed in a narrow trench, generally
10 AWWA C401-83
less than two to three diameters in width, cut in undisturbed ground, and backfilled to the original ground surface, as illus trated in Figure 4. For this condition, Eq 3 is rewritten as:
We = CdWeBj
Eq 4
3.2.2.1 The values of Cd are obtained from Figure 5, in which curves A, B, C, D, and E take into account the friction coef ficient between the backfill and the sides of the trench for the various soil composi tions 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.
3.2.3 Embankment condition. An embankment condition is defined as either that condition where the pipe is installed in a trench that is wider than two to three pipe diameters and that is cut in undis turbed ground, or that condition where the pipe is covered with fill above the original ground surface. Embankment conditions are further subdivided into positive and negative projecting pipe cat egories, depending on the location of the top of the pipe relative to the original undisturbed ground. A special case where compressible material is used as part of the backfill, called an imperfect trench,
also is classified as an embankment condi tion. The various embankment conditions are illustrated in Figures 4 and 6.
3.2.4 Positive projecting pipe condi tion. A positive projecting pipe condi tion is defined as either that condition where the pipe is installed in a trench cut in undisturbed ground that is wider than two to three pipe diameters, or that condi tion where the top of the pipe is above the adjacent original ground surface and cov ered with fill above the original ground surface. For this condition, Eq 3 is rewrit ten as:
We = CcweBc2
Eq 5
3.2.4.1 The values of Cc are obtained from Figure 7. Cc also may be obtained from Eq 6 when the following conditions exist simultaneously:
1. The ratio H/ Bc is greater than 1.3 2. The product p (rSd) = 0.7
Cc - 1.892///B, -- 0.96
Eq 6
3.2.4.2 The recommended value for the settlement ratio rSd is +0.7 for asbes tos-cement distribution 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
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.
Figure 6. Embankment Conditions
ASBESTOS-CEMENT DISTRIBUTION PIPE
11
0) <0
>
Figure 7. Values of Cc for Positive Projecting Pipe
Reprinted with permission from ASCE, Manual 37, Design and Construction of Sanitary and Storm Sewers. 1976.
available: (1) the trench condition and (2) the positive projecting pipe embankment condition. The method chosen is depend ent on the ratio of the trench width to the pipe diameter. As previously stated, when the trench width is less than two to three times the pipe diameter, earth loads are computed by the trench condition equa tion (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 exter nal earth load that can be transmitted to the pipe for any given depth of cover. For all trench widths greater than the transi tion width, earth loads are computed by the positive projecting pipe embankment 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 equa tion (Eq 4). (See Figure 6.)
12 AWWA C401-83
3.2.5.1 The transition width is deter mined from Figure 8 by multiplying the applicable ratio Bdj Bc by the applicable pipe outside diameter Bc. The applicable ratio of trench width to pipe outside diameter, Bd/ Bc, can be obtained from Figure 8 for any given ratio of backfill height to pipe outside diameter, Hj Bc.
3.2.6 Negativeprojectingpipe embank ment condition. A negative projecting 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 back filled and compacted, and embankment is constructed thereon to finished grade (Figure 4). For this condition, Eq 3 is rewritten as:
WE = CnWeBa
Eq 7
3.2.6.1 The various values of C,, are obtained from Figure 9. For asbestoscement pipe design the recommended value for the settlement ratio rSd is zero.
3.2.6.2 When calculating earth loads under negative projecting pipe embank ment conditions, consideration must be given to the transition width as defined in Sec. 3.2.5. For values of the ratio Bd/ Bc less than those given in Figure 8, the load on a pipe is determined from Eq 7 for negative projecting pipes. However, as the trench width increases and the ratio Bd/ Bc becomes greater than that given in Figure 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 condition. The imperfect trench condition occurs rather infrequently and is included for general information. The imperfect trench embank ment condition refers to that construction technique wherein the pipe is first in
stalled 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 back filled with loose compressible material. The remainder of the embankment is then built up to final elevation (Figure 11). For this condition, Eq 3 is rewritten as:
WE = CnWeBc1
Eq 8
3.2.7.1 The various values of C,, are obtained from Figure 9. For asbestoscement pipe design the recommended value for the settlement ratio rSd is equal to -0.3.
3.2.8 Tunnel conditions. There are two types of tunnel construction encoun tered in normal pipe laying operation.
3.2 8.1 The first type is the most fre quently encountered and occurs when a sleeve of a larger diameter than the speci fied pipe is first jacked through an em bankment. The pipe is then placed into the sleeve without 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 pres sure needs to be considered for design.
3.2.8.2 The second type of tunnel condition is rarely encountered in distri bution pipe 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 sup ports. The pipe then is placed in the tun nel, and the void between the pipe and tunnel braces is backfilled with compacted earth, grout, or concrete. Once this opera tion is completed, the earth load automat-
kfji = 0.1924
kp -- kp' -- 0.130
kn' = 0.130
r _________ A------------- V
ASBESTOS-CEMENT D ISTR IBU TIO N PIPE
Ratio
Bc
(a)
(b)
Figure 8. Values of Bj/ Bc at Which the Trench and Positive Projecting Pipe Equations Give Equal Loads
Reprinted with permission from ASCE, Manual 37, Design and Construction ot Sanitary and Storm Sewers. 1976.
U>
14 AWWA C401-83
Coefficient C,,
Figure 9. Values of C,, for Negative Projecting Pipe and Imperfect Ditch Conditions
Reprinted with permission from ASCE, Manual 37, Design and Construction of Sanitary and Storm Sewers. 1976.
ASBESTOS-CEMENT DISTRIBUTION PIPE
15
-Top of embankment
Natural ground surface
B&p.
Figure 10a. Positive Projecting Pipe Projection Ratio = ,vv
Figure 10b. Negative Projecting Pipe
Projection Ratio = Bj
Top of embankment
/
Compressible backfill
Top of stage construction compacted fill
Projection ratio = --Br
Figure 11. Projection Ratio p' for the Imperfect Trench Embankment Condition
AWWA C401-83
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 23
Values of coefficient Cj Figure 12. Values of Cj for Tunnel Conditions
with permission from ASCE, Manual 37, Design and Construction ol Sanitary and Storm Sewers. 1976.
ASBESTOS-CEMENT DISTRIBUTION PIPE
17
ically transfers from the tunnel supports to the pipe itself. For this condition, Eq 3 is rewritten as:
We = CtBt(wcBt 2c) Eq 9
3.2.8.3 Values of CY for different types of soil are obtained from Figure 12. If the value for the coefficient of cohesion is not available from laboratory tests, then the recommended safe design values in Table 1 are to be used.
Table 1
Recommended Safe Design Values of c for Tunnel Conditions
Materials
Clay, very soft Clay, medium Clay, hard Sand, loose dry Sand, silty Sand, dense Top soil, saturated
Values of c
lb (ft2 (kNIm2)
40(1.63) 250 (10.19) 1000 (40.77)
0(0) 100 (4.007) 300(12.23) 100(4.007)
3.2.8.4 When, in tunnel construction, the excavation becomes excessive, 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 using Eq 4 for trench conditions. Since it can be exceed ingly difficult to either predict or assess whether the tunnel excavation is exces sive, it is recommended that Eq 4 be used for most installations for safe asbestoscement pipe design.
3.2.8.5 It should be noted that the preceding discussion is based on the pre mise that the tunnel would be constructed in homogeneous soils that do not create unusual pressures and stresses. Tunnel construction should not be utilized through
materials that tend to squeeze or swell, such as some types of clay or shale, or through blocky and seamy rock. Under these conditions, the construction method described in Sec. 3.2.8.1 is recommended.
Sec. 3.3 Superimposed Loads
Superimposed loads Ws are external loads other than the normal earth loads transmitted to the pipe. There are two types of superimposed loads as illustrated in Figure 13: (1) concentrated lFsi,and(2) distributed IVS2. Superimposed loads are frequently referred to as live loads.
3.3.1 Concentratedloads. A concen trated load is a load caused by a single force, which may be either static or dy namic in nature. In normal pipe design, vehicular wheel loads are the most fre quently encountered concentrated loads. The magnitude of the load produced by concentrated superimposed forces is deter mined by:
CPF
WK =
Eq 10
(see Tables 2 and 3)
3.3.2 Distributed load. A distributed 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 pro duced by distributed forces is determined by:
Wsd = CsPjFB, (see Table 4)
Eq 11
Table 2 Impact Factors F
Depth of Cover /,(,,,)
Impact Factor F
1.0-2.0 (0.3-0.6) 2.0-3.0 (0.6-1.0) 3.0 or greater (1.0 or greater)
1.2 1.1 1.0
00
A W W A C401-8.7
Pipe Size in. (mm)
4(100) 6(150) 8 (200) 10(250) 12 (300) 14(350) 16(400)
Table 3
Values of Load Coefficients C, for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit
Depth of cover ft (m)
2(0.61)
0.105 0.147 0.191 0.237 0.279 0.317 0.354
2.5 (0.76)
0.076 0.106 0.137 0.174 0.202 0.232 0.259
3 (0.91)
0.055 0.078 0.102 0.129 0.153 0.175 0.197
4(1.22)
0.033 0.046 0.061 0.078 0.092 0.106 0.121
5(1.52)
0.022 0.031 0.041 0.052 0.062 0.071 0.081
6(1.83)
0.016 0.023 0.029 0.037 0.044 0.050 0.057
8 (2.44)
0.009 0.013 0.017 0.022 0.025 0.030 0.034
10(3.05)
0.006 0.008 0.010 0.013 0.016 0.018 0.021
12(3.66)
0.004 0.006 0.008 0.009 0.011 0.013 0.015
16(4.87)
0.002 0.003 0.004 0.006 0.007 0.008 0.009
20 (6.09)
0.0015 0.002 0.003 0.0035 0.004 0.005 0.0055
ASBESTOS-CEMENT DISTRIBUTION PIPE
Table 4 Superimposed (Wheel) Load--Single Wheel = 16 000 Ih (7250 kg)
19
Pipe Diameter--in. (mm)
Cover Over Top of Pipe ft (m)
2(0.61) 2.5 (0.76) 3 (0.91) 4(1.22) 5(1.52) 6(1.83) 8 (2.44) 10(3.05) 12 (3.66) 16 (4.87) 20 (6.09)
6(150)*
797 (11.6) 693 (10.1) 425 (6.20) 256 (3.73) 176 (2.56) 149 (2.17)
69(1.00) 43 (0.63) 37 (0.54) 21 (0.39)
5 (0.07)
8(200)
932 (13.6) 907 (13.2) 544 (7.93) 331 (4.83) 218(3.18) 197 (2.87)
91 (1.33) 59 (0.86) 48 (0.70) 27 (0.39) 11 (0.16)
10(250)
12 (300)
14 (350)
16(400)
Wheel Load---Ihlft (kN/m)
1272 (18.5) 1076 (15.7) 693 (10.1) 421 (6.14) 277 (4.04) 245 (3.57)
112(1.63) 74 (1.08) 53 (0.77) 32 (0.47) 16(0.23)
1488 (21.7) 1167(17.0) 816(11.9) 490(7.15) 330 (4.81) 235 (3.43)
139(2.03) 85 (1.24) 59 (0.86) 37 (0.53) 21 (0.30)
1691 (24.7) 1237(18.0) 933 (13.6)
565 (8.24) 378 (5.51) 267 (3.89) 160 (2.33)
96(1.40) 69(1.01) 43 (0.62) 26 (0.38)
1888 (27.5) 1382 (20.2) 1048 (15.3) 645 (9.41) 432 (6.30)
304 (4.44) 181 (2.64) 112(1.63)
80(1.17) 48 (0.70) 29 (0.42)
For 4-in. (100-mm) pipe use same value as for 6-in. (150-mm) pipe.
Concentrated superimposed load, Wsi vertically centered over pipe.
Distributed superimposed load, Ws2, vertically centered over pipe.
Figure 13. Superimposed Loads
20 AWWA C401-83
Section 4--Hydrostatic Pressure
Sec. 4.1 Introduction
For the design of asbestos-cement dis tribution pipe, the internal hydrostatic pressure Pt is defined by:
PT = (Po + Ps) S.F. Eq 12
S.F. is the design safety factor. Safety factors are based on judgment, past expe riences, and sound engineering principles. For asbestos-cement distribution pipe, a safety factor of 4 is recommended when surge or water hammer is not calculated and added to operating pressure.
Sec. 4.2 Operating Pressure
The operating pressure P0 is the pres sure that 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 ele vated water tank), or a combination of both pumps and gravity. Under a 100 per cent 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 pres sure at a given point, measured in feet (metres) 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 reduced 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 Appendix 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 Ps are of a transient nature and are caused by unsteady or changing conditions in the pipeline. The terms water hammer, surge, or transient pressure are often used interchangeably to refer to these pressures, which are of brief duration but often of considerable magni tude. 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 stop ping. Surge pressures in a distribution sys tem can be of considerable magnitude, particularly when fire hydrants are rapidly opened or closed. The magnitude of this surge is difficult to determine and it is generally beyond the control of the design engineer as it depends on the speed at which the firemen open or close the hydrants. For this reason, design criteria for asbestos-cement distribution pipe in corporate a large minimum fixed safety factor of 4 to the operating or pressure class of the pipe to allow for an unknown amount of surge pressure that will occur in the system. Appendix B presents a dis cussion of surge pressures and how they may be controlled for the engineer who determines that surge should be incorpo rated in hydrostatic design calculations.
Section 5--Design Criteria and Use Of Pipe Selection Charts
Sec. 5.1 Combined Loading Curves Extensive testing and application of
statistical analysis have shown that the strength characteristics of asbestos-cement pipe conform to the principles of the
combined loading theory developed by the late W.J. Schlick. This theory, cornmonly discussed in terms of the Schlick formula represented graphically as a parabola, is used as the basis for the design
ASBESTOS-CEMENT DISTRIBUTION PIPE
21
and class selection of asbestos-cement distribution pipe. [See Figures 14a through 14Gand Figures 14A(m)through 14c(m).]
5.1.1 Curve development. The fam ilies of selection curves presented in this standard Were developed using the Schlick formula that establishes a functional rela tionship between external load and inter nal pressure. The external and internal load intercepts are tabulated in Table 5.
Sec. 5.3 Use of Selection Charts for Economical Design
The charts may be used conveniently by entering them through the depth of cover and bedding condition scale. The scales are correlated to the three-edge vee-shaped bearing equivalent of 2.5 times the earth load calculated using a soil density of 120 lb/cu ft (19 kN/m3) and a trench width equal to the inside diameter of the pipe plus 2 ft (0.6 m) (or the positive projecting conduit condition if lesser).
Sec. 5.2 Safety Factors
In the smaller diameters, the effect of water hammer generated by the opening and closing of fire hydrants can be of significant magnitude because of the high velocities generated by open hydrant flow conditions on small-diameter lines in dis tribution systems. It is difficult to evaluate accurately the magnitude of surges, and if calculated, it would be impractical to attempt to control the surge by the use of surge tanks or other devices. Rather than employ a rule-of-thumb surge allowance based on an assumed velocity change, a large minimum safety factor of 4 is app lied to the class pressure rating of the pipe to take into account the undetermined surges.
5.2.1 Design criteria. The design criteria for asbestos-cement distribution pipe is based on a design point on the combined loading parabolic curve where the following minimum conditions are met: (1) a factor of safety of 4 times the pressure class of the pipe (2) a factor of safety of 2.5 times the three-edge veeshaped bearing equivalent of an earth load calculated as 5 ft (1.52 m) depth of cover, a trench width equal to pipe inside diameter plus 2 ft (0.6 m) (or a positive projecting conduit condition if lesser), a soil density of 120 lb/cu ft (19 kN/m3), and Class C bedding condition.
5.3.1 Design earth loads. Table 6 gives the design earth load values, which are obtained by calculating the external earth load based on a trench width equal to the I.D. of the pipe plus 2 ft (0.6 m) (or the positive projecting conduit condition if lesser). The earth load is then divided by the appropriate bedding factor for the class of bedding and multiplied by a safety factor of 2.5. The design earth load values from Table 6 can then be used to enter the selection curve charts using the design external load values given at the top of the selection curve charts. The field support ing strength listed for pipe so selected has been proved conservative during many years of performance under various field conditions. When there is an external condition that would warrant considering all external loading factors and/or a change in the safety factor, the equivalent external load should be determined and the selection chart entered at the proper value of the design external load scale found at the top of the chart.
Sec. 5.4 Discussion
AWWA C403, Standard Practice for the Selection of Asbestos-Cement Trans mission and Feeder Main Pipe, Sizes 18 in. Through 42 in., is a standard contain ing information similar to that contained herein but dealing with larger diameter pipes. In AWWA C403 the design is based
22 AWWA C401-83
on evaluation of all design conditions including surge pressures. Adequate fac tors of safety are applied to the combina tion of loads to which the pipeline will be subjected. The primary differences be tween AWWA C401 and AWWA C403 are those of differing methods of design ing pipelines to account for interal and external load conditions. In the smaller sizes covered by AWWA C401, surge pressures can be of great magnitude and are difficult or impractical for the engi neer to control in design. A large min imum safety factor of 4 is suggested to compensate for the unknown. In the larger sizes covered in AWWA C403, the design is based on an evaluation of surge pressure, which can be controlled in de sign. Calculated surge pressure is added to operating pressure before a safety factor of 2 is applied. For external loads, AWW A C401 considers only earth loads and a recommended safety factor of 2.5 is app lied. In AWWA C403, both earth loads and live loads are added before a factor of safety of 1.5 is applied to the combination of these external loads. In summary.
AWWA C403 design is based on a more detailed evaluation of the magnitude of surge pressure and live loadings, and fac tors of safety based on this more precise knowledge of actual operating conditions are applied.
Sec. 5.5 Illustrative Problem on Pipe Selection
The application of the curves to design is shown in the following problem:
Required: A 6-in. pipe to operate at a pressure of 120 psi at 8 ft depth of cover, bedding condition Class C, soil weight 120 lb/cu ft.
Solution: Enter the selection curve for 6-in. pipe at bedding condition Class C, 8-ft cover. The intersection of the 8-ft cover line with the 120-psi operating pres sure line falls between pipe classes 100 and 150. Use 6 in., Class 150. The intersection of the 8-ft cover line with the Class 150 curve is at 140-psi operating pressure, or 560-psi design pressure. Therefore, the pressure safety factor equals 560/120 = 4.66, with a safety factor of 2.5 for exter nal earth load.
ASBESTOS-CEMENT DISTRIBUTION PIPE
23
2S0 1,000
--1--
Design External Load-lb./lin.ft.
2,000
3,000
4,000
5,000
- - - - - - - 1- - - - - - - - - - - - - - 1- - - - - - - - - - - - - - 1- - - - - - -
O perating Pressure-psi Design P ressure-psi
200 --.
Class 200*
Class 150s --
100
Class 100*
800 --
600 --
400 --
200
_____L
1
1 ' s_ _ _ _ 1_ _ _ _ _
oo
2.5 5
8
III
12
1
16 20
II
0o3
2.5 5
8
12 16
20
_ _ _ 1_ _ _ _ 1_ _ _ _ _ 1_ _ _ _ _ _ 1_ _ _ _ _ _ 1 1___________ _________________________________
Depth of Cover-ft.
Figure 14a. Selection Curves for 4-in. Asbestos-Cement Pipe
O perating Pressure-psi Design Pressure -p s i
24 AWWA C401-83
Depth of Cover-ft.
Figure 14B. Selection Curves for 6-in. Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE
25
O perating Pressure-psi Design Pressure-psi
Depth of Cover-ft
Figure 14c. Selection Curves for 8-in. Asbestos-Cement Pipe
26 AWWA C40I-83
2,000
250 --1--
Design External Load-lb/lin ft
4,000
6,000
8,000
10,000
1 1 1 1 1,000 ------------- ------------- ------------- ------------- ------------- ------------
Operating Pressure-psi Design P ressure-psi
200
Class 200 %^ 150
Class 15o\ Class 10o\ 100 -- 50
800 --
600 --
400 \--
200
0 _____1_________1_____
5
2.5 5 8 12 16 20
II 1 III
____1____
2.5 5 8 12 16 20
___1____1_____1______1___u_________________________ Depth of Cover-ft
Figure 14d. Selection Curves for 10-in. Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE Design External Load-lb/lin.ft.
27
Design Pressure-psi
Figure 14e. Selection Curves for 12-in. Asbestos-Cement Pipe
Operating Presure-psi Design Pressure-psi
28 AWWA C401-83
Design External Load-lb/lin ft
Figure 14f. Selection Curves for 14-in. Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE Design External Load-lb/lin ft
29
Operating Pressure-psi Desicfn P ressure-psi
Figure 14c. Selection Curves for 16-in. Asbestos-Cement Pipe
30 0
AWWA C401-83
Design External Load-kN/m 20 30 40 50 60 70
Design Pressure-kPa
Figure 14A(m). Selection Curves for 100-mm Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE Design External Load-kN/m
Design Pressure-kPa
31
32 0
AWWA C401-83
Design External Load-kN/m 25 50 75 100
125 150
O perating Pressure-kPa Design Pressure-kPa
Depth of Cover-meters
Figure 14c(m). Selection Curves for 200-mm Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE Design External Load-kN/m
33
Operating Pressure-kPa Design Pressure-kPa
Figure 14D(m). Selection Curves for 250-mm Asbestos-Cement Pipe
34 AWWA C401-83
25
1,750 --1--
Design External Load-kN/m
50 75 100
-----1------------1------
125 150
------1----- 7,000
1,500 --
1,250
Class 200N
1,000 --
Class 150s
750 Class 100
500 --
250
6,000
--
5,000
--
4,000
--
3,000
\--
2,000
--
1,000
Operating Pressure-kPa Design Pressure-kPa
| 0 1. . . 5co 1
OB 1
1
2
1
i :___________ _________
3 4 56
1 1 11
1
1 2 3 4 56
1 _____1___ 1 1 J______________ Depth of Cover-meters
Figure 14E(m). Selection Curves for 300-mm Asbestos-Cement Pipe
ASBESTOS-CEMENT DISTRIBUTION PIPE Design External Load-kN/m
35
Operating Pressure-kPa Design Pressure-kPa
Figure 14F(m). Selection Curves for 350-mm Asbestos-Cement Pipe
Operating Pressure-kPa Design Pressure-kPa
36 AWWA C401-83 Design External Load-kN/m
Figure 14G(m). Selection Curves for 400-mm Asbestos-Cement Pipe
ASBESTOS-CEM ENT D ISTR IBU TIO N PIPE
Table 5 Design Internal Pressure and Design External Load*
Class 100
Class 150
Class 200
Nominal Pipe Size
in. (mm)
4(100) 6(150) 8 (200) 10(250) 12 (300) 14(350) 16(400)
Internal Pressure
psi (kPa)
417(2900) 441 (3000) 472 (3300) 490 (3400) 490 (3400) 500 (3400) 500 (3400)
External Load
Ibjlin.ft (kN/m)
4100(60) 4000(58) 4000 (58) 4400 (64) 5200 (76) 5200(76) 5800(85)
Internal Pressure
psi (kPa)
616(4200) 632 (4400) 653(4500) 650(4500) 658 (4500) 650(4500) 654(4500)
External Load
Ibjlin.ft (kNjm)
5400(79) 5400(79) 5500 (80) 7000(102) 7600 (111) 8600(126) 9200 (134)
Internal Pressure
psi (kPa)
809 (5600) 815(5600) 824 (5700) 826(5700) 830 (5700) 826(5700) 825 (5700)
It is necessary to apply a load factor to the three-edge bearing loads obtained in the crushing tests in order to correlate them to the field loads.
External Load
Ib/lin.ft (kNjm)
8 700(127) 9 000(136) 9 300(136) 11 000(161) 11 800(172) 13 500(197) 15 400(225)
Pipe Size in. (mm)
4(100) 6(150) 8(200) 10(250) 12(300) 14(350) 16 (400)
Pipe Size in. (mm)
4 (100) 6(150) 8(200) 10(250) 12 (300) 14 (350) 16(400)
H 2.5 ft (0.76 m)
290 (4.23) 390 (5.69) 490(7.15) 590(8.61) 670 (9.78) 740(10.80) 800(11.68)
H 2.5 ft (0.76 m)
370 (5.40) 500 (7.30) 620 (9.05) 750(10.95) 850(12.40) 940(13.72) 1010(14.74)
Table 6 Design External Earth Load
H 5.0 ft (1.52 m)
Class B Bedding
H 8.0 ft (2.44 m)
H 12 ft (3.66 m)
610(8.90) 840(12.26) 1070(15.62) 1330(19.41) 1550(22.62) 1760 (25.69) 1960 (28.60)
H 5.0 ft (1.52 m)
W--thjft (kN/m)
980 (14.30) 1380 (20.14) 1770 (25.83) 2220 (32.40) 2610 (38.09) 2860 (41.74) 2980 (43.49)
1490 (21.74) 2090 (30.50) 2710 (39.55) 3230(47.14) 3550 (51.81) 3810(55.60) 4030(58.81)
Class C Bedding
H 8.0 ft (2.44 m)
H 12 ft (3.66 m)
770 (11.24) 1060(15.47) 1360 (19.85) 1690(24.66) 1970 (28.75) 2240 (32.69) 2490 (36.34)
W--lb/fi (kN/m)
1250 (18.24) 1740 (25.39) 2250 (32.84) 2820 (41.15) 3310 (48.31) 3620(52.83) 3770 (55.02)
1890 (27.58) 2650 (38.67) 3430 (50.06) 4090 (59.69) 4500 (65.67) 4820 (70.34) 5100(74.43)
H 16 ft (4.88 m)
1990(29.04) 2800 (40.86) 3380 (49.33) 3730 (54.44) 4120(60.13) 4520 (65.96) 4990 (72.82)
H 16 ft (4.88 m)
2530 (36.92) 3550(51.81) 4280 (62.46) 4730 (69.03) 5220 (76.18) 5730 (83.62) 6320 (92.23)
H 20 ft (6.10 m)
2500 (36.48) 3360 (49.04) 3770 (55.02) 4170 (60.86) 4620 (67.42) 5000 (72.97) 5250 (76.62)
H 20 ft (6.10 m)
3170 (46.26) 4250 (62.02) 4780 (69.76) 5290 (77.20) 5850 (85.37) 6330 (92.38) 6650 (97.05)
A W W A C401-83
W
00
ASBESTOS-CEMENT DISTRIBUTION PIPE
39
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 WWA C401.
Loss of Head in Feet Per Thousand Feet of Length
8di|ou| `jeieuieiQ edjd
40 AWWA C401-83
Appendix B
Surge Pressure Analysis
This appendix is for information only and is not a part of A WWA C40I.
B.1 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 defined in these terms: the closing of a valve or the stop ping of a pump causes a moving column of water in the 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 operating 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 developed by, and increase in direct proportion to, the internal pressure that builds up as the column of water decelerates. The slower the deceleration, the less the pressure builds up and the less the pipe wall stresses increase. It is, therefore, of importance to the pipe designer to know how to control the rate of velocity fluctuation, since by controlling this rate he controls the mag nitude of the pressure variations during the transitional periods. By such control he can keep the pipe wall stresses during surge to a predetermined value that will allow an economical installation.
B. 1.3 Wave motion. Water, being liquid, will act in a fairly complex manner when undergoing acceleration or deceler
ation. Pressure waves are set up, which move along the pipeline at a rate of 2500-4500 ft/sec (760-1370 m/sec), the rate depending on the pipe wall material. The waves will continue until they en counter a boundary condition, 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.1.4 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 conse quently in the quantity, of water flowing in the pipeline.
B.1.5 Effects. Ignoring the effects of surge in the pipeline can lead to difficul ties after the line is in operation. Surge can result in damaged equipment and serious ly reduced capacity.
B.2 Water Hammer Analysis
The elastic wave theory for surge analy sis has been empirically established to be correct by many experiments, 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
ASBESTOS-CEMENT DISTRIBUTION PIPE
41
mer pressures are a function of the maxi mum rate of change of flow. When a valve is closed or a pump stops, a pressure wave is propagated along a pipeline. The veloc ity of the wave is the same as the velocity of sound in water, modified by physical characteristics of the pipeline; it is des cribed by the following equation:
= Vs
a + kd/Ee
Eq 81
per second (metres per second) g = acceleration due to gravity, 32.2
ft/sec2 (9.81 m/s2) B.2.3 Critical time. The longest elapsed time before final flow stoppage that will still permit this maximum pres sure 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:
Where a = pressure wave velocity, in feet per second (metres per second) k = modulus of compression of water, 300 000 psi (2070 MPa) d = internal diameter of pipe, in inches (millimetres) E = modulus of elasticity of asbes tos-cement pipe, 3 400 000 psi (23 400 MPa) e = wall thickness, in inches (milli metres) Vs = velocity of sound in water, 4660 ft/sec (1420 m/s) 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 by
Where h = surge pressure, in feet of water (metres of water) V = velocity of water in the pipeline during normal conditions, in feet
( per second (metres per second) a = pressure wave velocity, in feet
U=-- a
Eq B3
Where U = 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 (metres) a = pressure wave velocity, in feet per second (metres 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 progressively cut off is not gener ally proportional to the reduction in flow. In Figure Bl, Graph 1 presents a plot 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 pre viously, water hammer pressure is a func tion of the maximum rate of change of flow. Therefore, if tangents to the curves in Figure Bl are drawn at the fastest rate of change (or steepest slope), the effective time of closure Te is obtained. (See the curves in Figure 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
42 AWWA C401-83
closing time. This indicates that if the crit ical 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 that will cause maximum pressure to occur will be approximately 2x seconds.
B.3.2 Relation to surge control. In the design of a water system, one of the major considerations in the selection of a pipe is the design internal pressure that the pipe will be required to carry in service. The design internal pressure is the operat
ing pressure plus the water hammer pres sure. In order to keep the water hammer or surge pressures at a controlled 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 B1 presents a convenient threestep 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 criti cal time).
Time --(TE) = Effective For Full Cut Off Uniformly at Maximum Rate Full Area Gate,
4--------Te = 39.2%Tt--------->1
Reduced Area Globe, 14--------------- Te = 51.7% Tt------------- H |4-Full Area Cone, TE = 48.6% Tt-H
Open
Percent Time of Valve Stem Travel - Tt
Closed
Percent Full Fi'~"
"N" = (Te) Effective Closing Time -- in Units of 2 L/a Seconds Figure B.l Time (T/r) = Effective for Full Cut Off Uniformly at Maximum Rate
Reprinted by permission of the Johns-Manvllle Sales Corporation.
ASBESTOS-CEMENT DISTRIBUTION PIPE
43
1. Determine the pipeline constant K given by
\
Where K = pipeline constant a -- pressure wave velocity, in feet per second (metres per second) V = velocity of water in the flow line under normal conditions, in feet per second (metres per second) g = acceleration due to gravity, 32.2 ft/sec2 (9.81 m/s2) h0 -- operating pressure in the line under normal conditions, in feet of water (metres of water)
2. Determine the maximum head that might be developed from the surge by using the formula hmax aV/g.
3. Determine the percentage of hmax and find the corresponding effective clos ing time shown on the horizontal axis. This is given in units of 2L/a, which represents the critical time for the pipe line. 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 that closes off the flow. The second half is the effective closing time. Therefore, 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.4.1 Complexity. The surge anal ysis of a pumped system is more complex
than in a 100-percent gravity system because
1. In a pumped system, the problem begins in the slowing down of the rising water column when the pump is shut off (because of power failure or otherwise). Consideration 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 normally 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 variable slopes. These conditions may give rise to water column separation, causing severe surges and operational troubles. Surges from water column separation do not follow a standard pattern and they have been mea sured at many times the calculated values.
B.4.2 Alternative layouts. The de sign of a pumped system may involve the consideration of alternative layouts to keep surges and the consequent opera tional difficulties to a minimum. This work should be directed toward reducing the magnitude of surges and toward reduc ing 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.
44 AWWA C401-83
B.4.4 Entrapped air. Water column separation can cause difficulties not only because of the before-mentioned 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 seriously reduce the capacity of the system.
B.5 Methods of Control
The two types of surge to be controlled 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 dan gerous, except when they cause water column separation. If this occurs, extreme ly high positive surges result when the cavity closes, and this frequently causes serious problems. 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 ac complished by several types of surge con trol devices. These devices include:
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 gradu ally 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 stop page and consequent reduced 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 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 stand pipe, with water reentering the line during negative surge and leaving during positive surge. The major difference is that the air in the vessel is under pressure and much higher heads can be employed 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 sim ilar to the one-way surge tank, but pro vides 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 back flow into the reservoir. It effectively redu ces 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--posi tive 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 measure of relief to positive pressure. However, 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.
ASBESTOS-CEMENT DISTRIBUTION PIPE
45
then positive surges will be developed by the sudden stopping of the backflowing column of water. The pump should be designed to run reversed without 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 usu ally worthwhile to properly evaluate the surge potential in a system under design. The cost of control devices may be bal anced against the added strength ol pipe, valves, and other equipment that will be needed if surges are not controlled, and the most advantageous conclusion reached. Manufacturers of surge control equip ment or consultants in this field should be sought for advice in complex situations.
4660 3 X 10s X 24 3.4 X 10 X 1.5
= 3000 ft/sec.
2. Determine maximum surge pres sure if the valve closes within the critical time
, aV 3000 X 5 ~ g ~ 32.2 = 465 ft of water (200 psi)
3. Determine the critical time
1L_ 2 X 5000 3.33 sec
a 3000
B.6 Surge Calculation Example
f The following example problem illus trates the calculation that may be fol lowed to determine valve closing time for the control of surge within prescribed limits.
Problem: A 24-in. gravity transmis sion line is to operate at a pressure of 100 psi. Velocity in the line is to be 5 ft/sec. A valve is to be included in the line at a distance of 5000 ft from the reservoir. If positive surge pressure is to be controlled within 50 psi, determine the minimum time for valve closure. Assume that the effective closing time is one half of the actual valve stem travel time. (E for asbes tos-cement pipe = 3.4 X 106, wall thick ness is 1.5 in., k for water = 3 X 105.)
Solution'. 1. Determine surge wave velocity
Vs
4. Determine constant K for use in Graph 2 (Figure Bl)
- = 3000 X 5 =
K ~ 2gho ~ 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 200 F
6. Enter Graph 2 (Figure Bl) with percent of/jmax(25 percent). Go horizon tally to the curves where K = 1.0. Read the effective closing time along the hori zontal axis. This value is 2.6 and is given in units of IL/a sec. The effective closing time in seconds would be IL/a X 2.6 = 3.33 X 2.6 = 8.7 sec. The 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.
46 AWWA C401-83
B.7 Air in Pipelines
Air in pipelines can cause serious oper ational difficulties, including reduction in capacity because of reduced cross-sec tional area and fluctuation in flow caused by expanding and contracting air in the line. These fluctuations in flow cause sud den 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 of 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. Nega tive 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 opera tional difficulties. Suggested solutions for control are as follows:
1. Intake. Correct design proce dures, 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 exhausting can be made by means of air valves. There are various types of air valves with differ ent 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 drain ing, of course. Large orifice air valves should be provided for exhausting the air during refilling. Draining and then refil ling does not often occur; therefore, long filling times may be satisfactory.
4. Drainage during shut down. This can be a serious problem. Open stand pipes can be provided for air entry and exhaust. Sweeping air out using high velocities is another method.
5. Negative surges. The best way to prevent air from entering under these conditions is to design 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 Sec. B.5.2 will normally be adequate.
B.7.2 Recommendations to combat air entrapment. Colorado State 1) niversity has conducted studies to determine the effect of air entrapment in pipelines. The result of the studies proved that sud denly released entrapped air, under ap parently static conditions, creates a situa tion similar to that of classic water ham mer. Pressures are generated that may be on the order of 15 times the pipeline test pressure. Any pipeline material is serious ly affected by this rapid magnitude of load increase. Hydrostatic failure due to defec tive pipe may in all probability be traced to suddenly released entrapped air. Thi initial filling and testing of a pipeline is often the most critical period of its service life. Recommendations to combat air entrapment were made as follows:
1. Pipeline should be laid to grade wherever possible.
2. Automatic continual acting air re lease valves should be used at all high points.
3. Air should be bled from pipeline slowly.
4. Limit filling velocity in the pipeline to 1 ft/sec (3 m/s) or less.
5. Use d/D = 1/10 to 1/100. Where
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 perform ing pipeline tests. Such recommenda tions also have been found to be useful to engineers from the standpoint of design ing pipelines to minimize air problems.
ASBESTOS-CEMENT DISTRIBUTION PIPE
47
Appendix C
Frictional Power Requirements
This appendix isfor information only and is not a part of A WWA C401.
The chart shown in Figure Cl permits rapid calculations of the yearly power costs to overcome friction loss of head. This chart is based on continuous pump ing operation (24 hours per day and 365 days per year), a power cost of $0.01 per kW h, and a motor-pump efficiency of 100 percent. For actual operating condi tions and local power costs, appropriate factors must be applied to the values shown in the chart. By calculating power costs to overcome friction in two pipe sizes, or for two different types of pipe having different flow coefficients, an an nual power cost savings can be deter mined. Economic justification for going o 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 economicjustification exists for the added capital expenditure.
Nomograph values for Figure Cl are based on the following:
Cost per 1000 ft of pipe per year, in dollars
Power cost = $0.01 kW-h Motor-pump efficiency (combined) = 100 percent Friction coefficient C = 140 Continuous operation.
*This table is reprinted by permission of the Johns-Manville Sales Corporation from their publiation, "Discounted Cash Flow Method of Invest ment Appraisal."
Note: Yearly power cost values de rived in Figure Cl are for coefficient of flow C-- 140. They may be converted to yearly power cost values for other coeffi cients 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 Figure Cl are for coefficient of flow C-- 140. These may be converted to other diameters for other coefficients of flow by means of the fol lowing 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
Apply the following formula to Table Cl.
\ r/ r(\ + rf
Where r = rate of yield in percent N = number of years from present
Derived from the Hazen and Williams formula: V= 1.318 C7? 63S 54
Note Power cost values derived from this chart are for coefficient
of flow C = 140. They may be converted to other coefficients of
flow by means of the following multiplying factors:
1.15 for C = 130
2.26 for C = 90
1.34 for C = 120
2.83 for C = 80
1.57 for C = 110
4.82 for C = 60
1.86 for C = 100
Asbestos-cement pressure pipe has a coefficient of C = 140.
Example G/ven:size of pipe = 6 in. (150 mm), length of line = 3000 ft (914 m),
rate of flow = 500 gpm (1893 L/ min), power cost = $0.02/kW-h, combined efficiency of pump and motor = 50% Required: Power cost to compensate for friction loss of head for C = 140 and C = 100. Solution: On right edge of chart select 6-in. pipe and extend a horizontal line to left until it intersects diagonal line indicating 500 gpm. Using this point and applying it to scale on diagonal lines indicating dollars, the yearly power cost is found to be $145.00. Total power cost for 3000 ft of 6-in. pipe is 3 X 145 = 435 for C = 140 and 435 X 1.86 = 809 for C= 100. Converting to 50% combined efficiency of pump and motor and power cost of $0.02/kW-h, we find: power cost for C = 140 is $1740.00 and power cost for C = 100 is $3236.00.
A W W A C401-83
Figure C.l Yearly Power Cost to Cc pnsate for Friction Loss of Head
ASBESTOS-CEMENT DISTRIBUTION PIPE
49
Example:
When using a 10 percent rate of yield, an income of $1.00 occurring each year for the next five years has a present worth of $3,791; for the next seven 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 for known life in Table Cl.
i
50 AWWA C401-83
TABLE Cl
Present Worth of an Income of $1.00 per Year for the Next N Years
r*ors .5% I.0X 1.5% 2.0% 25%
3.0% 3.5% 4.0% 4.5% 5.0% Years
1 .995 .990 .985 .980 .976 2 1.965 1.970 1.956 1.91*2 1.927
3 2.970 2.91a 2.912 2.881* 2.656
1* 3.950 3.902 3.851* 3.808 3.762
L L5 .926 1*. 853 1*.783 .713 1*.61*6
6 5.896 5.795 5.697 5.601 5.508 7 6.862 6.728 6.598 6.1*72 6.31*9 8 7.823 7.652 7.1*86 7.325 7070 9 8.779 8.566 8.361 8062 7.971 10 9.730 9.1*71 9.222 8.983 8.752
n U10.68 10.37 10.07 9.787 9.5 *
12 11.62 11.26 10.91 10.58 10.26
li13 12.56 12.13 11.73 11.35 10.98 13.1*9 13.00 12.51* 12.11 11.69
15 111.1*2 13.87 13.31* 12. 12.38
H16 15.31* *.72 11*.13 13.58 13.06
17 16.26 15.56 U*.91 ll*.29 13.71
18 19
17.17 18.08
16.1*0 17.23
15.67 16.1*3
lit. 99
15.68
ll*.3S ll*.98
20 18.99 18.05 17.17 16.35 15.59
21 22
19.89 20.78
18.86
19.66
17.90 18.62
17.01 17.66
16.19 16.77
23 21.68 20.1*6 19.33 18.29 17.33
lt2 22.56 21.21* 20.03 18.91 17.89
25 23.1*5 22.02 20.72 19.52 18.1*2
.971 1.913 2.829
3L..751870
.966 1.900 2.802
3.673
lt.515
.962 1.886
2.775 3.630 1*.1*52
.957 1.873 2.71*9 3.588
U.390
.952 1.859
32..752L36 U.329
5.ia7
6.230
7.020
7.786
8.530
5.329 6.115 6.871* 7.608
8.317
5.21*2 6.002
6.733 7.1*35 8.111
5.158
5.893 6.596
7.269 7.913
5.076
5.7 6.1*63 7.108 7.722
9.253 9.951* 10.61* 11.30
11.91*
9.002
9.663 10.30 10.92 11.52
8.760
9.3 9.966 10.56 11.12
8.529 9.119 9.683 10.22
10.71*
8.306
8.3 9.391* 9.899 10.38
12.56
13.17 13.75 11*.32
lit. 88
12.09 12.65
13.19 13.71
lli.21
11.65 12.17 12.66
13.13 13.59
11.23
11.71 12.16
12.59 13.01
10.81*
11.27 11.69 12.09
12.1*6
15.1*2 15.91* 16.1*1*
16.91*
17.1a
lit. 70
15.17 15.62 16.06
16.1*8
ll*.03 lliitt..1*5
15.25 15.62
13.1a
13.78
Hil**..l55o
11*.
12.82 13.16
13.1*9 13.
ll*.09
1 2 3 1* 5
6 7 8 9 10
11 12 13 11* 3-5
16 17 18 19 20
21 22 23 21* 25
l26 2 *.32 22.80 21.1*0 20.12 18.95
27 25.20 23.56 22.07 20.71 19.1*6 28 26.07 21*.31 22.73 21.28 19.97
29 26.93 25.07 23.38 21.81* 20.1*5 30 27.79 25.81 21*.02 22.1*0 20.93
31 28.65 26.51* 21**65 22.91* 21.1*0 32 29.50 27.27 25.27 23.1*7 21.85
33 30.35 27.99 25.88 23.99 22.29
U l3 31.20 28.70 26.1*8 2 *.50 22.72 a35 32.01* 29.1 27.08 25.00 2305
36 32.87 30.11 27.66 25.1*9 23.56 37 33.70 30.80 28.21* 25.97 23.96 38 31*. 53 31.1*9 28.81 26.1*1, 21*.35
39 35.35 32.16 29.37 26.90 21*.73 1,0 36.17 32.81* 29.92 27.36 25.10
111 36.99 33.50 30.1*6 27.30 25.1*7
lIi2 37.80 3 *.16 30.99 28.21* 25.82 ii3 38.61 31*. 81 31.52 28.66 26.17
tiii 39.1*1 35.1*6 32.01* 29.08 26.50
1*5 1*0.21 36.09 32.55 29.1*9 26.83
1*6 1*7
ia.00 Ul.79
36.73 37.35
33.06 33.55
29.89 30.29
27.15 27.1*7
1*8 1*2.58 37.97 31*.01* 30.67 27.77
1*9 1*3.36 38.59 31*. 53 31.05 28.07
50 1*1*.11* 39.20 35.00 31.1*2 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 15.1*5 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 21.1*9
18.71, 19.07
19.39 19.70
20.00
17.59 17.87 18.15
18. ia
18.67
16.51* 16.79 17.02
17.25 17.1*6
15.59 15.80 16.00
16.19
16.37
31 32 33 31* 35
21.83 22.17 22.1*9 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 18.1*0
16.55 16.71 16. 17.02
17.16
2233..710a
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 18.67 19.02
19.16
17.29 17.1*2
17.55 17.66
17.77
21*.78 25.03 25.27 25.50
25.73
22.70 22.90 23.09 23.28 23.1*6
20. 21.01* 21.20
21.31* 21.1*8
19.29 19.1*2
19.51* 19. 19.76
17. 17.98 18.06
18.17 18.26
36 37 38 39 1*0
ia 1*2
1*3
1*1* 1*5
1*6 1*7 1*8 1*9 50
Yhti 5.3%
ASBESTOS-CEMENT DISTRIBUTION PIPE
51
TABLE Cl (continued)
6.0% 6.5% 7.0% 7.S% 8.0% 8.9% 9J>% 9.9% 10.0% Ymt
1
.91*8 .91*3 .939 .935 .930
.926 .922 .917 .913 .909
1
2 1.81*6 1.833 1.821 1.808 1.796 1.783 1.771 1.759 1.71*7 1.736 2
3 2.698 2.673 2.61*8 2.621* 2.601 2.577 2.551* 2.531 2.509 2.1*87 3
i* 3.505 3.1*65 3.1*26 3.387 3.31*9 3.312 3.276 3.21*0 3.201* 3.170 k L L l l 3 91a5 .270 1*.212 .156 1*.100 *.0 *6 3.993 . 3.890 3.81*0 3.791 5
6 L.996 1*.917 i*.aia L.767 l*.69l* U.623 1*.551* l*.l*86 It.1*20 L.355 6 7 5.683 5.582 5.1*85 5.389 5.297 5.206 5.U9 5.033 lt.950 It. 868 7
8 6.335 6.210 6.089 5.971 5.857 5.71*7 5.639 5.535 5.1*33 5.335 8
9 6.952 6.802 6.656 6.515 6.379 6.21*7 6.119 5.995 5.875 5.759 9
.las10 7.538 7.360 7.189 7.021* 6.861* 6.710 6.561 6
6.279 6.11*5 10
n11 8.093 7.887 7.689 7.1*99 7.315 7.139 6.969 6.805 6.61*7 6.1*95
12 8.619 8.381* 8.159 7.91*3 7.735 7.536 7.31*5 7.161 6.981* 6.811* 12
13 9.117 8.853 8.600 8.358 8.126 7.901* 7.691 7.1*87 7.291 7.103 13
11* 9.590 9.295 9.011* 8.71*5 8.1*89 8.21*1* 8.010 7.786 7.572 7.367 11*
8 301 7.60615 10.01* 9.712 9.1*03 9.108 8.827 8.559 . * 8.061 7.828
15
16 10.1*6 10.11 9.768 9.1*1*7 9.11*2 8.851 8.575 8.313 8.062 7.821* 16
17 10.87 10.1*8 10.11 9.763 9.1*31* 9.122 8.825 8.51*1* 8.276 8.022 17 18 11.25 10.83 10.1*3 10.06 9.706 9.372 9.055 8.756 8.1*71 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
li20 11.95 11.1*7 11.02 10.59 10.19 9.818 9.1*63 9.129 8.812 8.5 * 20
21 12.28 11.76 11.29 10.81* io.ia 10.02 9.61*1* 9.292 8.961 8.61*9 21 22 n12.58 12.01* .51* 11.06 10.62 10.20 9.ao 9.1*1*2 9.097 8.772 22
23 12.88 12.30 11.77 11.27 10.81 10.37 9.963 9.580 9.221 8.883 23
2l* 13.15 12.55 11.99 11.1*7 10.98 10.53 10.10 9.707 9.331* 8.985 21*
.la25 13
12.78 12.20 11.65 11.15 10.68 10.23 9.823 9.1*38 9.077 25
a26 13.66 13.00 12.39 11.83 11.30 10. 10.35 9.929 9.532 9.161 26
27 13.90 13.21 12.58 11.99 11.1*1* 10.91* 10.1*7 10.03 9.618 9.237 27
28 11*. 12 13 .ia 12.75 12.11* 11.57 11.05 10.57 10.12 9.697 9.307 28
L .a29 11*.33 13.59 12.91 12.28 11.70 11.16 10.66 10.20 9.769 9.370 29
30 1 .53 13.77. 13.06 12.ia 11
11.26 10.75 10.27 9.835 9.1*27 30
31 11*.72 13.93 13.20 12.53 11.92 11.35 10.83 10.31* 9.895 9.1*79 31
32 11*.90 11*.08 13.33 12.65 12.02 11.1*1* 10.90 io.ia 9.950 9.526 32 ll33 15.08 11*.23 13.1*6 12.75 12.11 11.51 10.97 10.1*6 10.00 9.569 33
3k 15.21* *.37 13.58 12.85 12.19 11.59 11.03 10.52 10.05 9.609 31* 35 15.39 11*.50 13.69 12.95 12.27 11.66 11.09 10.57 10.09 9.61*1* 35
36 15.51* 11*.62 13.79 13.01* 12.35 11.72 11.11* 10.61 10.13 9.677 36 37 15.67 11*.71* 13.89 13.12 12.1*2 11.78 11.19 10.65 10.16 9.706 37 38 15.81 11*.85 13.98 13.19 12.1*8 11.83 11.21* 10.69 10.19 9.733 38
n39 15.93 11*.95 11*.07 13.27 12.51* 11.88 .28 10.73 10.22 9.757 39 l*o 16.05 15.05 11*.15 13.33 12.59 11.93 11.32 10.76 10.25 9.779 1*0
ia ia16.16 15.11* 11*.22 13.39 12.65 11.97 11.35 10.79 10.27 9.799 10 a ak2 16.26 15.23 11*. 29 13.1*5 12.69 12.01 11.38 . 10.29 9. 7 1*2
k3 kk
ll l16.36 15.31 11*.36 13.51 12.71*
16.1*6 15.38 *. *2 13.56 12.78
12.01* 11 .ia 10.81* 10.31 9.831*
12.08 11.1*1* 10.86 10.33 9.81*9
1*3
1*1*
1*5 16.55 15.1*6 11*.1*8 13.61 12.82 12.11 11.1*7 10.88 10.35 9-863 1*5
H1*6 16.63 15.52 *. 51* 13.65 12.86 12.11* 11.1*9 10.90 10.36 9.875 1*6
H n i1*7 16.71 15.59 *.59 13.69 12.89 12.16 .5 10.92 10.38 9.887 1*7
1*8 16.79 15.65 11*.61* 13.73 12.92 12.19 11.53 10.93 10.39 9.897 1*8
1*9 16.86 15.71 11*.68 13.77 12.95 12.21 11.55 10.95 10.1*0 9.906 1*9
io.ia50 16.93 15.76 11*. 73 13.80 12.98 12.23 11-57 10.96
9.915 50
52 AWWA C401-83
TABLE Cl (continued)
Ymts 10.5% 11.0% 11.5% 120% 12.5%
13.0% 13.5% 14.0% 14.5% 15.0% Yaon
1 .905 .901 .897 993 .889 2 1.721* 1.713 1.701 1.690 1.679 3 2.1*65 2.1*1*1* 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 1*.170 l*.lll l*.o51* 7 1*. 7 89 1*.712 1*. 637 1*.561* L .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
.885 1.668 2.361
2.971* 3.517
.881
1.657 2.31*1 2.91*1* 3.1*75
.e77 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*.l*23
L.799 5.132 5.1*26
3.91*3 I*.355 1*.718
5.038 5.320
3.889 L.288
1*.639 l.9l*6 5.216
3.836 1*. 221* L.562
1*.858 5.116
3.781* It. 160
1.1*87 1*.772 5.019
1 2 3 1* 5
6 7 8 9 10
11 6.31*8 6.207 6.070 5.938 5.810 12 6.650 6.1*92 6.31*1 6.191, 6.053 13 6.923 6.750 6.583 6.1*21* 6.270 m 7.170 6.982 6.801 6.628 6.1*62 IS 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 7.21*1
21 8.351* 8.075 7.811 7.562 7.326 22 8.1*65 8.176 7.903 7.61*5 7.1,01 23 8.566 8.266 7.981* 7-718 7.1*67 2l* 8.657 8.31*8 8.058 7.781* 7.526 25 8.739 8.1*22 8.121* 7.81*3 7.579
5.687 5.918 6.122 6.302
6.1*62
5.568
5.787 5.979 6.11*9 6.299
5.1*53 5.66o 5.81* 6.002
6.11*2
5.31*1 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 6.399
6.1*31* 6.1*61*
11 12 13 11* IS
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 6.91*2 8.602 8.283 7.981* 7.701* 29 8.997 8.650 8.326 8.022 7.737 30 9.01*7 8.691* 8.361* 8.055 7-766
31 9.093 8.733 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 7.836 31* 9.201* 8.829 8.1*81 8.157 7.851* 35 9.235 8.855 8.503 8.176 7.670
36 9.262 8.879 8.523 8.192 7.885 37 9.287 8.900 8.51*1 6.208 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
1*1 9.365 8.965 8.595 8.253 7.936 1*2 9.380 8.977 8.606 8.262 7.91*3 1*3 9.391* 8.989 8.615 8.270 7.91*9 1*1* 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 9.1*52 9.036 8.651* 8.301 7.975 50 9.1*59 9.01*2 8.658 8.301* 7.978
7.372
7.1,09
7.1*1*1 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.S51 6.566
7.518
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
7.61*1
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
7.386
7.388 7.390
7.392 7.391*
7.126 7.128 7.130
7.131 7.133
6.883
6.885 6.886
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
ASBESTOS-CEMENT DISTRIBUTION PIPE
53
TABLE Cl (continued)
Yaors 15.5% 16.0% 16.3% 17.0% 17.3%
B.0% 18.3% 19.0% 19.9% 20.0% Ywi
1 .866 .862 .858 .855 .851 2 1.615 1.605 1.595 1.585 1.575 3 2.261* 2.21*6 2.228 2.210 2.192 it 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 1*.31*1* 1*. 271* 1.207 1*.11*2 9 a. 688 L.607 U.527 l*.l*5l 1*.376 10 1*. 925 1*.833 l*.7l*5 a. 659 1*.575
11 5.130 5.029 1*.931 1*. 836 1*.71*5 12 5.307 5.197 5.091 1*.988 lt.889 13 5.1*61 5.31*2 5.228 5.118 5.012 lit 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 5.668 5.531* 5.1*05 5.281 17 5.895 5.71*9 5.609 5.1*75 5.31*6 18 5.969 5.818 5.673 5.531* 5.1*01 19 6.031* 5.877 5.728 5.581* 5.1*1*7 20 6.090 5.929 5.775 5.628 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* 2k 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
.8ao i.5a7 2.iao 2.639 3.058
.837
1.537 2.123 2.613
3.02a
.833 1.528 2.106
2.589
2.991
1 2
3 1* 5
3.1*98 3.812 1*.078
a. 303 1*.1*91*
3.1*53 3.758 a.015 a.232 a.ai5
3.iao 3.706
3.95a a.163 a.339
3.367 3.655 3.895 a.096
a.265
3.326
3.605 3.837 a.031 a.192
6
7 8
9 10
1*.656
1*.793 1*.910 5.008 5.092
a.570 a.700
a. 810 a.903 a.982
a.i*86 a.611
a.715 a. 802 a.876
a.ao6
a.523 a.622 a.705 a. 77a
a.327
a.l*39 a.533 a.6u a.675
11
12 13 lit 15
5.162 5.222
5.273 5.316
5.353
5.01*8 5.10U 5.151 5.191 5.22a
a.938 a.990
5.033 5.070 5.101
a. 832 a. 880
a.921 a.95a a.983
a. 730
a.775 a.812 a.ea3 a.870
16
17 18 19 20
5.381* 5.U10
5.1*32 5.1*5l 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
5.01a 5.057 5.069
a. 891
a.909
a.925 a.937 a.9ae
21 22
23 21*
25
26 6.299 6.118 5.91*6 5.783 5.628 27 6.320 6.136 5.962 5.798 5.6la 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.iao 6.215 6.032 5.858 5.691*
36 6.ia6 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* 10 6.1*31 6.233 6.01*7 5.871 5.705
la 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 la 6.1*38 6.239 6.052 5.875 5.709 Uii 6.1*1*0 6.2la 6.053 5.876 5.710 1*5 6.162 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*1*1* 6.21*1* 6.056 5.879 5.7U 1*8 6.10*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*8o
5.1*92 5.502 5.510
5.517
5.3ao 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 5.1oa
a.956
a. 96a a. 970 a.975 a.979
5.523 5.528 5.532 5.536
5.539
5.377 5.382 5.385 5.389 5.391
5.239 5.21*3 5.2a6
5.21*9 5.251
5.108 5.111 5.1ia 5.116
5.118
a.982 a.985 a.988 a.990
a.992
5.5U1 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 5.12a
a.993 a.99a a.995 a. 996
a.997
5.51*9 5.550
5.551 5.552 5.552
s.aoo 5.aoi 5.a02 5.ao2 5.ao3
5.259 5.260 5.260
5.261 5.261
5.125 5.125 5.126 5.126
5.127
a.997 U.998 a.998 a.998
a.999
5.553 5.553 5.551* 5.551*
5.551*
5.ao3 5.aoa 5.aoa 5.aoa
5.aoa
5.261 5.262 5.262 5.262
5.262
5.127 5.127
5.127
50.27 5.128
a.999 a.999 a.999 a.999
a.999
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
54 AWWA C401-83
TABLE Cl (continued)
Years 21% 22% 23% 24% 2S%
76% 27% 28% 29% % Yoon
1 .826 .820 .813 .806 .800 2 1.509 l.a92 i.a7a l.a57 l.aao 3 2.07a 2.oa2 2.011 1.981 1.952 u 2.5LO 2.a9a 2.aas 2.aoa 2.362 5 2.926 2.86a 2.803 2.71*5 2.689
6 3.2L5 3.167 3.092 3.020 2.951 7 3.508 3.ai6 3.327 3.2a2 3.161 6 3.726 3.619 3.518 3.1*21 3.329 9 3.905 3.786 3.673 3.566 3.a63 10 1*.051 3.923 3.799 3.682 3.571
n 1*.177 a. 035 3.902 3.776 3.656
12 L.278 a.127 3.985 3.851 3.725 13 U. 362 a. 203 a. 053 3.912 3.780 11* a.i*32 a.265 a. 108 3.962 3.82a 15 a.1*69 a.315 a.153 a.001 3.859
16 1*.536 a.357 a.189 a.033 3.887 17 a.576 a.391 a. 219 a. 059 3.910 18 a.608 a.ai9 a.21*3 a.080 3.928 19 a. 635 a.ai*2 a. 263 a.097 3.91*2 20 a.657 a.i*6o a.279 a.no 3.95a
21 a.675 a.a76 a. 292 a.121 3.963 22 a.690 a.ae8 a.302 a.130 3.970 23 a. 703 a.a99 a.311 a.137 3.976 21* a.713 a.507 a.318 a.u*3 3.981 25 a.721 a.511* a.323 a.ia7 3.985
79a i.i*2a 1.923 2.320
2.635
.787 i.ao7 1.896
2.280
2.583
.781 1.392 1.868
2.21*1 2.532
.775 1.376
1.81*2 2.203 2.a83
.769 1.361 1.816 2.166
2.1*36
2.885 3.083 3.2ai 3.366
3.a65
2.821 3.009 3.156
3.273 3.36L
2.759 2.937 3.076
3.18L 3.269
2.700
2.868
2.999 3.100
3.178
2.61*3 2.802
2.925 3.019
3.092
3.5L3 3.606 3.656
3.695 3.726
3.1*37
3.1(93 3.538
3.573 3.601
3.335 3.387 3.1*27
3.1*59 3.a83
3.239 3.286
3.322
3.351 3.373
3.11*7 3.190
3.223 3-.2l*9 3.268
3.751 3.771 3.786
3.799 3.808
3.623 3.6L0
3.65L 3.66L
3.673
3.503 3.518
3.529
3.539 3.51*6
3.390
3.1*03 3.1*13 3.a21
3.1*27
3.283
3.295
33..330na
3.316
3.816 3.822 3.827 3.831
3.83a
3.679
3.68a 3.689 3.692
3.69a
3.551 3.556 3.559 3.562
3.56a
3.1*32 3.1*36 3.L38
3.aai 3.ai*2
3.320
3.323 3.325 3.327 3.329
l 2 3 a 5
6 7 8 9 10
n
12 13 11* 15
16 17 18 19 20
21 22 23
2L
25
26 a. 728 a.520 a.328 a. 151 3.988 27 a. 73a a.52a a.332 a.15a 3.990 28 a. 739 a.528 a.335 a.157 3.992 29 a. 71*3 a.531 a.337 a. 159 3.99a 30 a.7a6 a. 53a a.339 a.160 3.995 31 a. 71*9 a.536 a.31*1 a. 161 3.996 32 a. 751 a.538 a.3i*2 a.162 3.997 33 a. 753 a.539 a.3i*3 a. 163 3.997 31* a. 755 a.sao a.3i*a a. 16a 3.998 35 a. 756 a.5ai a.3a5 a.16a 3.998 36 a. 757 a.5i*2 a.315 a.165 3.999 37 a.758 a.5a3 a.3a6 a.165 3.999 38 a. 759 a.5i*3 a.3a6 a.165 3.999 39 a. 759 a.5aa a.3a6 a.166 3.999 1*0 a. 760 a.5i*a a.3a7 a.166 3.999 a a.760 a.saa a.3a7 a. 166 a.000 1*2 a.760 a.saa a.3a7 a.166 a.000 1*3 a. 761 a.5i*5 a.3a7 a. 166 a.000 1*1* a.761 a.5i*5 a.3a7 a.166 a.000 1*5 a. 761 a.5i*5 a.3a7 a.166 a.000 1*6 a. 761 a.5i*5' a.3ae a.166 a.000 1*7 a. 761 a.5a5 a.3ae a. 166 a.000 1*8 a. 761 1*.51*5 a.3as a.167 a.000 1*9 a. 761 a.51*5 a.3ae a.167 a.000 50 a. 762 a. 51*5 a.3a8 a.167 a.000
3.837 3.839 3.8ao
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.aaa 3.i*as 3.1*1*6 3.aa6
3.aa7
3.330
3.331 3.331 3.332 3.332
3.81*3 3.81*a
3.8aa 3.8a5
3.81*5
3.701 3.702 3.702
3.703 3.703
3.570 3.570 3.570
3.571 3.571
3.aa7 3.aa7 3.aaa 3.aa8
3.aae
3.332 3.333 3.333 3.333 3.333
3.8a5 3.81*5 3.aa6
3.8a6
3.8a6
3.703 3.703
3.703
3.703 3.703
3.571 3.571 3.571 3.571
3.571
3.aae 3.aa8 3.aae
3.UU8
3.aa8
3.333 3.333 3.333 3.333 3.333
3.ea6 3.8a6 3.8L6
3.81*6
3.8a6
3.703 3.571 3.70a 3.571 3.70a. 3.571 3.70a 3.571
3.70a 3.571
3.aas 3.aa8 3.aae 3.aa8 3.aa8
3.333 3.333 3.333 3.333 3.333
3.8a6 3.8a6 3.81*6 3.81*6 3.8L6
3.70a 3.70a 3.70a 3.70a 3.70a
3.571 3.571 3.571
3.571 3.571
3.aae 3.aae 3.aa8 3.1*J*8 3.UJU8
3.333 3.333 3.333 3.333 3.333
26 27 28 29 30
31 32 33 3a 35
36 37 38 39
ao
ai a2
1*3
aa
1*5
1*6
Ul as 1*9
50
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