Isentropic

The turbine isentropic efficiency tjt measures the ratio of the actual to ideal work obtained ... 

Turbine outlet conditions for isentropic expansion to 150°C from steam tables are... 

For a single-stage expansion with isentropic efficiency of 85 percent, from Eq. (6.2),... 

Exampie A.3.1 The pressures for three steam mains have been set to the conditions given in Table A.l. Medium- and low-pressure steam are generated by expanding high-pressure steam through a steam turbine with an isentropic efficiency of 80 percent. The cost of fuel is 4.00 GJ and the cost of electricity is 0.07 h. Boiler feedwater is available at 100°C with a heat capacity... 

Figure A2.1.4. Adiabatic reversible (isentropic) paths that do not intersect. (The curves have been calculated for the isentropic expansion of a monatomic ideal gas.)...

Now the system is thennally insulated and the magnetic field is decreased to zero in this adiabatic, essentially reversible (isentropic) process, the temperature necessarily decreases since... 

Compression. The work of compression is typically compared against the isentropic—adiabatic case. 

Fig. 28. Rankine cycle for superheat, where ( ) represents adiabatic (isentropic) compression ( ), isobaric heating ( ), vaporization (x x x x), superheating turbine expansion and (-----), heat rejection. To convert kPa to psi, multiply by 0.145. To convert kj to kcal, divide by 4.184.

Values rounded off from Chappell and Cockshutt, Nat. Res. Counc. Can. Rep. NRC LR 759 (NRC No. 14300), 1974. This source tabulates values of seven thermodynamic functions at 1-K increments from 200 to 2200 K in SI units and at other increments for two other unit systems. An earlier report (NRC LR 381, 1963) gives a more detailed description of an earlier fitting from 200 to 1400 K. In the above table h = specific enthalpy, kj/kg, and = logio for m isentrope. In terms of... 

These derivatives are also of interest for free expansions or isentropic changes. 

Calculation of Actual Work of Compression For simplicity, the work of compression is calciilated by the equation for an ideal gas in a three-stage reciprocating machine with complete intercoohng and with isentropic compression in each stage. The work so calculated is assumed to represent 80 percent of the actual work. The following equation may be found in any number of textbooks on thermodynamics ... 

V/c is the ratio of fluid velocity to the speed of sound or aeoustie veloeity, c. The speed of sound is the propagation velocity of infinitesimal pressure disturbances and is derived from a momentum balance. The compression caused by the pressure wave is adiabatic and frictionless, and therefore isentropic. 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

FricHonal pipe flow is not isentropic. Strictly speaking, the flashes must be carried out at constant h + V /2 + gz, where h is the enthalpy... 

Polytropic efficiency is the hmited value of the isentropic efficiency as the pressure ratio approaches 1.0, and the value of the polytropic efficiency is higher than the corresponding adiabatic efficiency as seen in Fig. 10-66. 

Although the T-s diagram is veiy useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice due to the fact that both evaporation and condensation are isobaric processes so that heat exchanged is equal to enthalpy difference A( = Ah. For the ideal, isentropic compression, the work could be also presented as enthalpy difference AW = Ah. The vapor compression cycle (Ranldne) is presented in Fig. H-73 in p-h coordinates. 

Refrigerating capacity is the product of mass flow rate of refrigerant m and refrigerating effect R which is (for isobaric evaporation) R = hevaporator outlet evaporator mJef Powei P required foi the coiTipressiou, necessary for the motor selection, is the product of mass flow rate m and work of compression W. The latter is, for the isentropic compression, W = hjisehatge suction- Both of thoso chai acteristics could be calculated for the ideal (without losses) and for the ac tual compressor. ideaUy, the mass flow rate is equal to the product of the compressor displacement per unit time and the gas density p m = p. 

Similar to volumetric efficiency, isentropic (adiabatic) efficiency T is the ratio of the work required for isentropic compression of the gas to work input to the compressor shaft. The adiabatic efficiency is less than one mainly due to pressure drop through the valve ports and other restricted passages and the heating of the gas during compression. 

For the actual systems, compressor work will be higher than for ideal for the isentropic efficiency and other losses. In the case of hermetic or accessible compressors where an elec trical motor is cooled by the refrigerant, condenser capacity should be ... 

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