Document 3QGewVkB07R7jB22JZdoXxBdD

36 CHAPTER 3 I960 Guide .*. =? ? ? a k K " enthalpy correction term to be added to enthalpy. See Table 6. A =* enthalpy of dry air, Btu per pound. h*4 " A, -- K " the difference between the enthalpy of moist air of saturation per pound of dry air, and the specific enthalpy of the dry air itself, Btu per pound of dry air. kf enthalpy of liquid water, Btu per pound. ~ enthalpy of saturated water vapor, Btu per pound. h, -- enthalpy of ice, Btu per pound. K, enthalpy of moist air at saturation per pound of dry air, Btu per pound of dry air. A,* * enthalpy of moist air at saturation at thermodynamic wet-bulb temperature (*, Btu per pound of dry air. K m enthalpy of water vapor, Btu per pound. A TM enthalpy of condensed water (liquid or solid) at stand ard pressure, Btu per pound water. A* enthalpy of water as added at the thermodynamic teef- buU> temperature t*, Btu per pound of dry air. = flow rate of liquid water, pounds per hour. *=- molecular weight, pounds per mol. -b mols dry air. mols of water vapor at saturation, mols of water vapor. * pressure, pounds pet square foot absolute. * atmospheric pressure, inches Hg. * standard atmospheric pressure by definition 1,013,250 dynes per square centimeter, or approximately 29.921 in. Hg. P, " vapor pressure of water in saturated moist air, pounds per square inch or inches Hg, absolute. P differs from the saturation pressure of pure water because of the presence of the air. Pm =* saturation pressure of pure water at prevailing tem perature, inches Hg. iQt " energy added to the system between states t and 2, Btu. ip - rate of energy addition to flow system between sec tions 1 end 2, Btu per minute, fit " universal gas constant, 1544 foot-pounds per (Fahren heit degree) (mol), fi, -- gas constant for dry air. fi* gas constant for water vapor. S * flow rate of solid water, pounds per hour, s = entropy, Btu per (pound) (Fahrenheit degree, abso lute). a -- entropy of moist air per pound of dry cur, Btu per (pound) (Fahrenheit degree). ! correction to be added to entropy of moist air obtained from Table 2. i ** additional correction to be added to entropy because of "mixing entropy" (obtained from Table 5). Correc tion to be added to value of * obtained from Table 2. s, entropy of dry air, Btu per (pound) (Fahrenheit de gree, absolute). *M " the difference between the entropy of moist air at satu ration per pound of dry air,'and the specific entropy of the dry air itself, Btu per (pound of dry air) (Fahren heit degree, absolute). i, = entropy of moist air at saturation per pound of dry air, Btu per (pound of dry air) (Fahrenheit degree, abso lute). " entropy of water vapor, Btu per (pound) (Fahrenheit degree, absolute). ** specific entropy of condensed water (liquid or solid) at standard atmospheric pressure, Btu per (pound of water) (Fahrenheit degree, absolute). T * temperature, absolute, Fahrenheit. T. * standard atmospheric temperature, by definition 518.4 F, absolute. t * temperature, Fahrenheit. t* * thermodynamic wet-bulb temperature, Fahrenheit. U = internal energy of system, Btu. V b internal energy. V * volume, cubic feet. e* -- volume of moist air per pound of dry air, cubic feet per pound. 0 3 correction to be added to volume of moist air per pound of dry air. See Table 6. e, " specific volume of dry air, cubic feet per pound. p, -- p, -- o,, the difference between volume of moist air at saturation, per pound of dry air, and the volume of the dry air itself, cubic feet per pound of dry air. v, =* volume of moist air at saturation per pound of dry air, cubic feet per pound of dry air. W " rate of work output of the system between sections 1 and 2, Btu per minute. W = humidity ratio of moist air, pounds of water per pound of dry air. W, *= humidity ratio, at saturation, weight of water vapor per pound of dry air, pound per pound. IF.* " humidity ratio corresponding to thermodynamic wet- bulb temperature t*, pounds of water per pound of dry sir.w b. mass of gas, pounds. Z * elevation above any datum, feet. Subscripts with symbols have following meanings: l, 2, 3 indicate section of flow; a * air, v water vapor, vs = pure saturated water vapor, w = water, wl * liquid water, toe solid water, s * saturation, m TM mixture; * indicates that the value is at thermodynamic wet-bulb temperature. REFERENCES 1J. A. Goff and S. Gratch: The humidity ratio of moist air at saturation (University oj Pennsylvania Thermodynamic Re search Laboratory Special Report,,bl&rtb 1948). * J. A. Goff: Standardisation of thermodynamic properties of moist air (ASHVE Transactions, Vol. 55, 1949, p. 459). * J. H. Arnold: The theory of the psychrometer (Physics, Vol. 4, 1933). 4 O. A. Hougen and K. M. Watson: Chemical Process Prin ciples (John Wiley and Sons, New York). * Tables of Thermal Properties of Gases (National Bureau of Standards Circular 564, November 1955). * J. H. Keenan and F. G. Keyes: Thermodynamic Properties of Steam (John Wiley and Sons, New York, 1936). TJ. A. Goff and S. Gratch: Thermodynamic properties of moist air (ASHVE Transactions, Vol. 51,1945, p. 125). * Smithsonian Meteorological Tables (Smithsonian Institu tion, 1951). * J. A. Goff and B. Gratch: Low pressure properties of water in the range--160 to 212 F (ASHVE Transactions, Vol. 52, 1946, p. 95). WR. Mollier: Em neues diagramm fdr dampfluftgenusche . (ZVDI, Vol. 67, September 8,1923, p. 869). u R. Mollier: Dae i-x diagramm filr dampfluftgenusche (ZVDI, Vol. 73, July 20, 1929, p. 1009). Walter S. Diehl, Standard Atmosphere--Tables and Data, national Advisory Committee for Aeronautics Technical Report No. 218, 1925. f*W. G. Bombacber: Altitude-Pressure Tables Based on United Slates Standard Atmosphere, National Advisory Commit tee for Aeronautics Technical Report No. 536,1935. I CHAPTER 4 FLUID FLOW Theory of Fluid Flow, Pressure Loss in Circular Pipes, Pressure loss in Non-Circtrfor Pipes; F/ow of Compressible Fluids, Ideal Flow Through Nozzle or Orifice; Flow Measurement, Head Meters, location of Head Meters and Pressure Taps, Pifof Tube, Variable Area Flow Meters THE flow of fluids which is part of the branch of engineer ing science known as fluid mechanics will be discussed Replacing e by its equal g/gj> (where p is density in pounds weight per cubic foot) and rearranging, Equation 3 becomes here insofar as it applies to the work of engineers in the fields of bearing, ventilating, and air conditioning. Probably air is the most frequently bandied fluid, but other gases and liquids dV* +'- dp + dt + --[J du + pdv -- J dq + dW) 0 (4) 29 0 0 are often involved. Compressible fluids (gases) and incom In the case of flow through a pipe, no outside work is per pressible fluids (liquids) vary somewhat in behavior, though formed bo that dW = 0.. Furthermore, in cases where pressure and density changes are small, the gases may be treated as incompressible fluids. J du + p dv - JT ds = J dq + JT ds' (5) THEORY OF RUID ROW The following energy equation for one dimensional steady flow processes will serve as a basis for the theory of the flow of fluids. This equation is presented in several ways in various texts, but a suitable form is where ds -- total change in entropy. ds` change in entropy due to internal irreversibility from turbulence and friction. Accordingly, Equation 4 may be written Ft* 0 + Jui + pii + Jq + -- *i *0e 0* n* -- + Jut + P*P* + W + -- 2* (1) 2* 0 - tcAere V => velocity, feet per second. 0 gravitational acceleration, feet per (second) (sec ond). 0c w. gravitational conversion factor *=> 32.174 (pounds mass per pound force) X ft per-(second) (second). J = mechanical equivalent of heat = 778 foot pounds per Btu. u -- internal energy, Btu per pound of fluid. p pressure per square foot, pounds. v -- specific volume, cubic feet per pound. W * mechanical work done by the fluid, foot pounds per pound of fluid. 9 = heat transferred to the fluid, Btu per pound of fluid flowing. elevation >bove some arbitrary datum, feet. Subscript l refers to the entrance, subscript 2 to the exit. + -- + di + i-JTit' - 0* 2p p 0 In where there is no internal irreversibility, dd and Equation 6 may be integrated to give (6) 0. V* pi TV pi -- H------- U-t-H----- tt 20 Pm 20 pm CD where Pm =* proper mean density. This is commonly called the Bernoulli equation, named after Introducing the enthalpy h, which by definition is u -fexpressed in Btu per pound of fluid, Equation 1 becomes P* + n, + J, + a - I? + Jh, + W + r H (2) 2p* 0* 20* 0, The equivalent differential form for energy Equation 1 is in Bernoulli Equation -- dV* -f- J du + d(pv) + Zds - J dq + dW - 0 (3) 20. 0. * Id the efieljei* af lubeeqmat portion of thi* chapter the dbtlnctioo i tad u will be omitted. Aside from the dimenniiwei coosateney the factor, t/tt, is oot ia feaenl sifaifiesat ia fluid Sow eaalytis.