Steam enters a turbine steadily at 7 MPa and 600°C with a velocity of 60 m/s and leaves at 25 kPa with a quality of 95 percent. A heat loss of 20 kJ/kg occurs during the process. The inlet area of the turbine is 150 cm2, and the exit area is 1400 cm2. Determine (a) the mass flow rate of the steam, (b) the exit velocity, and (c) the power output.
(a)
The mass flow rate of the steam.
Answer to Problem 178RP
The mass flow rate of the steam is
Explanation of Solution
The turbine operates steadily. Hence, the inlet and exit mass flow rates are equal.
Write the formula for inlet mass flow rate.
Here, the cross-sectional area is
At inlet:
The steam is at the state of superheated condition.
Refer Table A-6, “Superheated water”.
Obtain the inlet enthalpy
Conclusion:
Substitute
Thus, the mass flow rate of the steam is
(b)
The exit velocity of the steam.
Explanation of Solution
The turbine operates steadily. Hence, the inlet and exit mass flow rates are equal.
Write the formula for exit mass flow rate.
Here, the cross-sectional area is
Rearrange the Equation (II) to obtain exit velocity
At exit:
The steam is with the quality of
Write the formula for exit enthalpy
Write the formula for exit specific volume
Here, the enthalpy is
Refer Table A-5, “Saturated water—Pressure table”.
Obtain the following corresponding to the pressure of
Substitute
Substitute
Equation (V).
Thus, the exit enthalpy and exit specific volume of the steam is
Conclusion:
Substitute
Equation (III).
Thus, the exit velocity of the steam is
(c)
The power output of the turbine.
Answer to Problem 178RP
The power output of the turbine is
Explanation of Solution
Consider the steam flows at steady state. Hence, the inlet and exit mass flow rates are equal.
Write the energy rate balance equation for one inlet and one outlet system.
Here, the rate of heat transfer is
The refrigerant flows at steady state through the compressor. Hence, the rate of change in net energy of the system becomes zero.
Heat loss occurs at the rate of
The Equations (VI) reduced as follows to obtain the work output
Here,
Rewrite the Equation (VII) as follows.
Conclusion:
Substitute
Thus, the power output of the turbine is
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Chapter 5 Solutions
THERMODYNAMICS
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