Document ga0ZxBQdNd8MM1G7wpN7xe57q

36 Chapter 1 1945 Guide Steady-flow Energy"Equation------------------------------------------------------- A complete energy accounting takes the form of Equation 31 which , is usually referred to as the steady-flow energy equation. iS* -- (lh -j- KEj + PEi) -- (hi + KEi T PEi) + it* (31) where itfr = heat added from outside between sections 1 and 2, Btu per pound dry.air. = enthalpy of the mixture at section 2, Btu per pound dry air. KEi = average kinetic energy at section 2, Btu per pound.dry air. PEt = average potential energy at section 2, Btu per pound dry air. hi = enthalpy at section 1, Btu per pound dry air. KEi = average kinetic energy at section 1, Btu per pound dry air. PEi = average potential energy at section 1, Btu per pound dry air. = shaft work withdrawn between sections 1 and 2, Btu per pound dry air. In Equation 31 all quantities are per pound of dry air. If Equation 28 is used in computing average kinetic energy, the result will be in Btu per pound of dry air if v is taken as volume per pound of dry air. If. Equation 29 is used, multiplication by (1 + W) as in Equation 30 is required though this is a refinement seldom justified. - Properties of saturated steam are given in Table 8 and for additional definitions refer to Chapter 47. U. S. STANDARD ATMOSPHERE The so-called U. S. Standard Atmosphere is an essential standard of reference in aeronautics and as such has become important to the air conditioning engineer who frequently has to simulate atmospheric con ditions at high altitudes in connection with aeronautical research. : In defining this standard it is first assumed that temperature IT varies linearly with altitude Z above sea level, at any rate up to the lower limit of the isothermal layer at 35,332 ft. Thus,' T = T0 - 0.0019812 Z (32) or A.'F = --0.0019812 (degree Centigrade per foot) (33) The second assumption is the validity of the perfect gas laws, namely, Pv = BT (34) An horizontal disc of air having unit cross-sectional area (1 sq ft) and vertical thickness dZ (ft) weighs dZfv (lb). This accounts for the dif ference of pressure dP (lb per sq ft) between the upper and lower faces of the disc; hence, using Equation 34 BT dP dZ = (35) Equations 33 and 35 can be combined to eliminate Z and then in tegrated to obtain the relation between pressure and temperature, namely, * = ()"" The values T0 = 288 K and Pa -- 29.921 in. Hg are parts of the definition of the standard atmosphere. Thermodynamics of Air and Water Mixtures Table 10. Pressure and Temperature for Altitudes in ----------------- --U. S. Standard Atmosphere zAltitude Feet - 1,000 - 500 0 + 500 + 1,000 + 5,000 10,000 15.000 20.000 25,000 30.000 35.000 40.000 45.000 50.000 Pressure In. of Hg P 31.02 30.47 29.921 29.38 28.86 24.89 20.58 16.88 13;75 11.10 8.88` 7.04 5.54 4.36 3.436 Temp F I +62.6 +60.8 +59.0 +57.2 +55.4 +41.2 +23.4 + 5.5 -12.3 -30.1 -47.9 -65.8 -67.0 -67.0 -67.0 37 Values of pressure and temperature are listed in Table 10 for altitudes in the standard atmosphere from --1,000 to 50,000 ft above sea level. Values for altitudes below the lower limit of the isothermal layer conform to Equations 32 and 36. For further explanation, reference (11) should be consulted. REFERENCES [1] Rational Psychrometric Formulae, by W. H. Carrier (A.S.M.E. Transactions, Vol. 33, 1911, p. 1005). [2] Heat and Thermodynamics, by J. K. Roberts (Chapter IV), (Blackie and Son, London, 1928). [3] Das i, x-Diagramm fur Dampfluftgemische, by R. Mollier (ZVDI, 1929). [4] The Theory of the Psychrometer, by J. H. Arnold (Physics, Vol. 4, 1933). . [5] Thermodynamic Properties of Moist Air, by John A. Goff (A.S.H.V.E. Trans actions, Vol. 40,1934, p. 199). 16] Thermodynamic Properties of Steam, by J. H. Keenan and F. G. Keyes (John Wiley and Sons, Inc., New York, 1936). [7] Notes on Thermodynamics, by John A. Goff (John S. Swift Company, St. Louis, 1939). [8] Thermal Properties of Saturated Water and Steam, by N. S. Osborne, H. F. Stimson and D. C. Ginnings (National Bureau of Standards, Research Paper No. RP 1229,1939). [9] Psychrometric Chart, Its Application and Theory, by William Goodman (Heating, Piping and Air Conditioning, June, 1939 to August, 1940). [10] A.S.H.V.E. Research Report No. 1186--The Interaction Constant lor Moist Air, by John A. Goff and A. C. Bates (A.S.H.V.E. Transactions, Vol. 47,1941, p. 373). Ill] National Advisory Committee for Aeronautics, Technical Report No. 538,1935.