Steam enters a converging nozzle at 5.0 MPa and 400°C with a negligible velocity, and it exits at 3.0 MPa. For a nozzle exit area of 75 cm2, determine the exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 94 percent.
a)
The exit velocity, mass flow rate, and exit Mach number if the nozzle is isentropic.
Answer to Problem 110P
The exit velocity of the stream is
The mass flow rate is
The Mach number at the exit of nozzle is
Explanation of Solution
For isentropic,
The flow of steam through the nozzle is steady and isentropic.
Write the expression of energy balance equation for the converging-diverging nozzle.
Inlet velocity is equal to zero
Here, enthalpy at exit is
Write the expression to calculate the exit area of the nozzle.
Here, mass flow rate of steam is
Write the expression to calculate the velocity of sound through the steam at the exit of nozzle.
Here, pressure drop in the nozzle is
Write the expression to calculate the Mach number for the steam at the exit of nozzle.
Here, Mach number of the steam at the exit is
Conclusion:
Refer Table A-6, “Superheated water”, obtain the values of
Here, stagnation enthalpy at the inlet is
Refer Table A-6, “Superheated water”, obtain the values of
The stagnation enthalpy of steam at the inlet is equal to the actual enthalpy
at the inlet
Substitute
Thus, the exit velocity of the stream is
Refer Table A-6, “Superheated water”, obtain the value of
Substitute
Therefore, the mass flow rate is
Refer Table A-6, “Superheated water”, obtain the value of specific volume of steam at the entropy of
Substitute
Substitute
Hence, the Mach number at the exit of nozzle is
b)
The exit velocity, mass flow rate, and exit Mach number if the has an efficiency of 94 percent.
Answer to Problem 110P
The exit velocity of the stream is
The mass flow rate is
The Mach number at the exit of nozzle is
Explanation of Solution
Nozzle has an efficiency of 94 percent:
Write the expression for the efficiency of nozzle.
Here, efficiency of nozzle is
Write the expression of energy balance equation for the converging-diverging nozzle.
Inlet velocity is equal to zero
Here, velocity of steam at the inlet of nozzle is
Write the expression to calculate the exit area of the nozzle.
Here, mass flow rate of steam is
Write the expression to calculate the velocity of sound through the steam at the exit of nozzle.
Here, pressure drop in the nozzle is
Write the expression to calculate the Mach number for the steam at the exit of nozzle.
Here, Mach number of the steam at the exit is
Conclusion:
Refer Table A-6, “Superheated water”, obtain the values of
Here, at superheated condition the entropy of saturated steam is
Refer Table A-6, “Superheated water”, obtain the values of
Substitute
The stagnation enthalpy of steam at the inlet is equal to the actual enthalpy
at the inlet
Substitute
Thus, the exit velocity of the stream is
Refer Table A-6, “Superheated water”, obtain the value of
Substitute
Thus, the mass flow rate is
Refer Table A-6, “Superheated water”, obtain the value of specific volume of steam
Substitute
Substitute
Thus, the Mach number at the exit of nozzle is
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