Polytrop exponent

K = Adiabatic exponent, Cp/Cv N = Polytropic exponent, (N - 1)/N - (K Pi, P- = Suction, discharge pressures, psia Ti, = Suction, discharge temperatures, °R Ep = Polytropic efficiency, fraction... 

To start, convert the flow to values estimated to be the compressor inlet conditions. Initially, the polytropic head equation (Equation 2.73) will be used with n as the polytropic compression exponent. If prior knowledge of the gas indicates a substantial nonlinear tendency, the real gas compression exponent (Equation 2.76) should be substituted. As discussed m Chapter 2, an approximation may be made by using the linear average ut the inlet and outlet k values as the exponent or for the determination of the polytropic exponent. If only the inlet value of k is known, don t be too concerned. The calculations will be repeated several times as knowledge of the process for the compression cycle is developed. After selecting the k value, u,se Equation 2.71 and an estimated stage efficiency of 15 / to de clop the polytropic compression exponent n. 

At this point, after a first pass through the calculation, a new polytropic exponent should be calculated. All values calculated to this point should be rechecked to see if original estimates were reasonable. If the deviation appears significant, a second pass should be made to improve the accuracy. Equation 2.78 can be used to calculate the power for the uncooled section. For an estimate, use a value of 1% for the mechanical losses. 

Step 6. Recalculate the polytropic exponent using Equation 2.71 and the new efficiency. 

With the new polytropic exponent, calculate the discharge temperature by substituting into Equation 5.16. 

Step 5. Calculate the discharge temperature for the total pressure ratio to check against the stated temperature limit, using the assumed efficiency, rjp =. 75 and the polytropic exponent. Apply Equation 5.14. 

Step 6. Evaluate the discharge temperature, continuing the use of the previously calculated polytropic exponent. 

Step 14. Use the polytropic exponents calculated in the previous step and recalculate the discharge temperature of each section to correct for the average stage efficiency. 

Pitch line velocity, 330 Polytropic compression exponent, 160 Polytropic efficiency, 34 Polytropic exponent, 34 Polytropic head... 

Woodhouse presents the following relation for the polytropic exponent, n, based on actual inlet and discharge specific volumes of the gas being compressed ... 

Vj = specific volume of gas at suction conditions, fP/lb n = polytropic exponent Hp = polytropic head, ft-lb/lb = ft Pj = discharge pressure, psia Tj = inlet temperature, °R... 

His charts for X and Y as functions of reduced temperature and pressure are reproduced as Figures 3.9 and 3.10. The functions are used to determine the polytropic exponent n... 

D =deton velocity, and y = the polytropic exponent of the deton products... 

The polytropic exponent y is the exponent in the polytropic or "gamma-law equation of state, PV =a constant (See item (w) under Detonation, Equations of State) (Dunkle s letter of April 16, 1968)... 

The computed C-J detonation properties D (detonation velocities in cm//nsec), p (pressure in megabars), T (temperature, °K), and y (polytropic exponent) are given in Table III, pp 14-17 of Addnl Ref N. The C-J volume in cc/g of expl and some other properties were also determined, but they are not shown in Table III they are li ted on pp 26-324... 

Exponents of a Poly tropic Curve of Explosion Products of Condensed Explosives. Accdg to Apin et al(Ref 1), the adiabatic curve of expln products at the front of a detonation wave may be described by the polytropic law p=Av-n, where p=pressure, A=function of entropy, v=volume of expln products and n=polytropic exponent (See Ref 2, pp D290-R D474-R). The exponent n (also designated as y) depends mainly on the composition. The influence of temperature and pressure may be neglected. Experiments performed with expl compds and mixtures showed that over a wide range of temps and pressures of detonation, the exponent (n) of the polytropic curve of expln products may be obtd from the values of exponents of the individual products ... 

Such a process is called polytropic. The equation is analogous to the isentropic equation (7.20) but the polytropic exponent n is different from the heat capacity ratio k. 

Polytropic exponents are deduced from PV measurements on the machine in question. With reciprocating machines, the PV data are recorded directly with engine indicators. With rotary machines other kinds of instruments are used. Such test measurements usually are made with air. 

M molecular weight n number of moles or polytropic exponent... 

Figures 2 and 3 show Urbanski s data (Ref 1) for the expln properties of low density Pentolite charges as a function of the PETN/TNT compn Dobratz (Ref 13) lists a computed CJ pressure of 250kbar at d 1.66g/cc and a polytropic exponent (r) of 2.73. Theoretical computations by Shear (Ref 6) give CJ pressure (232kbar), detonation product compn, and isentropic expansion for Pentolite...

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