## Related questions with answers

A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.

Solution

VerifiedThe enthalpy and the relative pressure at the initial state are taken from A-17 for the given temperature:

$\begin{align*} &h_{1}=310.24\:\dfrac{\text{kJ}}{\text{kg}}\\ &P_{r1}=1.5546 \end{align*}$

The relative pressure at state 2 is determined from the pressure ratio and the relative pressure at state 1:

$\begin{align*} P_{r2}&=\dfrac{P_{2}}{P_{1}}P_{r1}\\ &=8\cdot1.5546\\ &=12.44 \end{align*}$

From this the enthalpy at state 2 for an isentropic process can be obtained using interpolation with data from A-17:

$\begin{align*} h_{2s}=562.58\:\dfrac{\text{kJ}}{\text{kg}} \end{align*}$

The relative pressure and the enthalpy at state 3 are determined from A-17 for the given temperature:

$\begin{align*} &h_{3}=932.93\:\dfrac{\text{kJ}}{\text{kg}}\\ &P_{r3}=75.29 \end{align*}$

The relative pressure at state 4 is determined from the relative pressure at state 3:

$\begin{align*} P_{r4}&=\dfrac{P_{4}}{P_{3}}P_{r3}\\ &=\dfrac{1}{8}\cdot75.29\\ &=9.41 \end{align*}$

From this value the isentropic enthalpy at state 4 can be obtained using interpolation with data from A-17:

$\begin{align*} h_{4s}=519.3\:\dfrac{\text{kJ}}{\text{kg}} \end{align*}$

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