Adiabatic Compression Formula

Hydrogen compression energy is estimated with the adiabatic compression energy formula  

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For mnltistage compressors of JX, number of stages with adiabatic-compression in each stage, equal division of work between stages, and intercoohng to the irit e temperature, the following formulas ai e helpful ... 

The adiabatic compression of saturated vapours was considered by Bruhat, who also calculated the angle between the liquid and vapour phase isochores in the entropy-temperature diagram. Amagat investigated the discontinuity in specific heats where an isothermal cuts the saturation curve. Hausen, from a complicated formula for the specific heat of steam involving two Einstein terms ( 2.IX N), calculated the heat content and entropy of steam. Leduc found the value of n for dry steam in Rankine s equation for adiabatic... 

With adiabatic compression, the final temperature T (degrees Fanrenheit absolute) is given by the formula T = Ti(p2/pi)° for single-stage compression by... 

Theoretical horsepower = 0.901Qpi(p2/pi)° — 1 or, for small pressure rise = 0.2618Qpe, where pe = P2 — pi. This formula may also be used for higher pressures if pi = 14.7 lb. per square inch and pe ( = 50.6A) is regarded as the mean effective pressure for adiabatic compression from pi to p2. Table 13 gives values of the mean effective pressure pe against values of p2 — Pi for the usual case of pi = 14.7. 

This formula is the preferred formula to calculate/estimate the temperature of a gas under adiabatic compression and we will become familiar with it after working out some problems. Suffice it to say that when you hear the word diesel you should think of P Vj = PiV -... 

FIG. 10-66 Factors for use in adiabatic formula. Values of X to be used in finding Xq may be obtained from Table 10-3. (By permission of Compressed Air Data.)... 

Moving on to compressible flow, it is first of all necessary to explain the physics of flow through an ideal, frictionless nozzle. Chapter S shows how the behaviour of such a nozzle may be derived from the differential form of the equation for energy conservation under a variety of constraint conditions constant specific volume, isothermal, isentropic and polytropic. The conditions for sonic flow are introduced, and the various flow formulae are compared. Chapter 6 uses the results of the previous chapter in deriving the equations for frictionally resisted, steady-state, compressible flow through a pipe under adiabatic conditions, physically the most likely case on... 

Examples.—(1) Assuming the Newton-Laplace formula that the square of the velocity of propagation, V, of a compression wave (e.g., of sound) in a gas varies directly as the adiabatic elasticity of the gas, E, and inversely as the density, p, or V2 cc E /p show that F2 oc yRT. Hints Since the compression wave travels so rapidly, the changes of pressure and volume may be supposed to take place without gain or loss of heat. Therefore, instead of using Boyle s law, pv = constant, we must employ pvy = constant. Hence deduce yp = v. dp/dv = Eq. Note that the volume varies inversely as the density of the gas. Hence, if... 

Using the formula for one-dimensional compressible flow presented in Section IV.B, we calculated the pressure, temperature, and velocity profiles describing the subsonic adiabatic expansion of pure carbon dioxide inside the orifice and the capillary up to the nozzle exit (i.e., point 2 in Figures 3 and 5). Both the Bender (38) and Camahan-Starling-van der Waals (39) equations of state were used to calculate the necessary PvT properties for CO2, and results using either of the two equations were essentially identical. Downstream of the nozzle exit, we calculated the pressures and temperatures on the upstream and downstream sides of the Mach disk by using the formulas of Ashkenas and Sherman (36) (see Section V). These formulas assume an ideal gas with y = 1.286, close to the value of CO2 at ambient conditions. We should remember, however. 

Figure2.10 summarizes our results (solid lines— Eqs.(2.82) and (2.85) dashed line—Eq.(2.84)) and compares them to data (crosses) taken from the literature (here http //www.usatoday.com/weather/wstdatmo.htm Source Aerodynamics for Naval Aviators ). Notice that the temperature data are not direct measurements but rather data points computed from simple formulas describing the average temperature profile at different heights. Our calculation applies to the troposphere, i.e. to a maximum altitude of roughly 10000 m. Beyond the troposphere other processes determine the temperature of the atmosphere. We see that our result somewhat underestimates the actual temperature. The middle graph shows the pressure profile. We notice that the two theoretical models Eq.(2.84) (isothermal case ) and Eq.(2.85) (adiabatic case) bracket the true pressure profile. The bottom graph shows the compressibility factor, Z = PV/ nRT), versus h. The data points scatter because of scatter in the density values. Nevertheless the graph shows that our assumption of ideal gas behavior is very reasonable.

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