Talamancoeb

2022-01-06

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.

Suhadolahbb

Beginner2022-01-07Added 32 answers

Step 1

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

$h}_{1}=310.24\frac{kj}{kg$

${P}_{r1}=1.5546$

The pressure ratio and the relative pressure at state 1 are used to calculate the relative pressure at state 2:

$P}_{r2}=\frac{{P}_{2}}{{P}_{1}}{P}_{r1$

$=8\cdot 1.5546$

$=12.44$

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

$h}_{2s}=562.58\frac{kj}{kg$

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

$h}_{3}=932.93\frac{kj}{kg$

${P}_{r3}=75.29$

Inferring from the relative pressure in state 3, one may calculate the relative pressure at state 4.

$P}_{r4}=\frac{{P}_{4}}{{P}_{3}}{P}_{r3$

$=\frac{1}{8}\cdot 75.29$

$=9.41$

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

$h}_{4s}=519.3\frac{kj}{kg$

Step 2

The power input of the compressor and the power output of the turbine can be used to calculate the mass flow rate:

$W=Wtask,outPSK-{W}_{c}$, in

$Q=m{n}_{T}({h}_{3}-{h}_{4s})-\frac{m}{{n}_{C}}({h}_{2}-{h}_{1})$

$m=\frac{W}{{n}_{T}({h}_{3}-{h}_{4s})-\frac{1}{{n}_{C}}({h}_{2s}-{h}_{1})}$

$=\frac{32000}{0.86(932.93-519.3)-\frac{1}{0.8}(562.58-310.24)}$

$=794\frac{kg}{s}$

sirpsta3u

Beginner2022-01-08Added 42 answers

A 32-MW has-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The mass flow rate of air through the cycle is to be determined.

Assumptions 1. Steady operating conditions exist. 2. The air-standard assumptions are applicable. 3. Kinetic and potential energy changes are negligible. 4. Air is an ideal gas with variable specific heats.

Analysis. Using variable specific heats,

and

karton

Expert2022-01-11Added 613 answers

Use the gas table for initial state,

22+64

When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?

How many minutes are there in $2\frac{3}{5}$ hours?

Find the answer for $64$ power $\frac{1}{6}$.

The following law describes the relationship between gas volume and pressure: ________. A)Boyle's law; B)Henry's law; C)Charles' law; D)Dalton's law

If an electric switch is open then no current flows through the circuit.

A)True;

B)FalseThe price elasticity of supply of a good is 0.8. Its price rises by 50 per cent. Calculate the percentage increase in its supply.

How many quarts are in 10 gallons?

When the net force acting on an object is zero, the total momentum of the system will:

A)remain constant;

B)increase with time;

C)decrease with time;

D)None of theseHow many centimeters are in four meters?

A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?

If the dot product of two non-zero vectors is zero, then the vectors A)are parallel to each other. B)are perpendicular to each other. C)can have any orientation. D)are anti-parallel to each other.

Which is longer 5 miles or 10 kilometers?

9 grams is how many milligrams?

How to write $673.5$ in scientific notation?