Saturated steam enters a converging–diverging nozzle at 1.75 MPa, 10 percent moisture, and negligible velocity, and it exits at 1.2 MPa. For a nozzle exit area of 25 cm2, determine the throat area, exit velocity, mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 92 percent.
(a)
The exit velocity for isentropic converging-diverging nozzle.
The mass flow rate for isentropic converging-diverging nozzle.
The exit Mach number for isentropic converging-diverging nozzle.
The throat area for isentropic converging-diverging nozzle.
Answer to Problem 137RP
The exit velocity for isentropic converging-diverging nozzle is
The mass flow rate for isentropic converging-diverging nozzle is
The exit Mach number for isentropic converging-diverging nozzle is
The throat area for isentropic converging-diverging nozzle is
Explanation of Solution
Determine the initial specific enthalpy of the isentropic converging-diverging nozzle.
Here, the specific enthalpy of saturated liquid is
Determine the initial entropy of the isentropic converging-diverging nozzle.
Here, the specific entropy of saturated liquid is
Determine the final quality of the isentropic converging-diverging nozzle.
Here, the final entropy of the isentropic converging-diverging nozzle is
Determine the final specific enthalpy of the isentropic converging-diverging nozzle.
Determine the final specific volume of the isentropic converging-diverging nozzle.
Determine the exit velocity of the isentropic converging-diverging nozzle.
Note: the fluid flow was complete stop at the initial exit velocity then it becomes zero.
Determine the mass flow rate of the isentropic converging-diverging nozzle.
Determine the velocity of sound at the exit of the isentropic converging-diverging nozzle.
Determine the exit Mach number for isentropic converging-diverging nozzle.
Determine the critical pressure at the throat.
Here, the stagnation pressure at the initial state is
Determine the velocity of throat using steady-flow energy balance.
Note: the initial velocity is zero.
Determine the throat area for isentropic converging-diverging nozzle.
Conclusion:
At the inlet,
Perform unit conversion of pressure at state 1 from MPa to kPa.
From the Table A-5, “Saturated water-Pressure table”, obtain value of the specific enthalpy of saturated liquid, the specific enthalpy change upon vaporization, specific entropy of saturated liquid, and the specific entropy change upon vaporization at 1750 kPa of temperature as:
Substitute
Substitute
At the exit,
Perform unit conversion of pressure at state 2 from MPa to kPa.
From the Table A-5, “Saturated water-Pressure table”, obtain value of the specific volume of saturated liquid, the specific volume change upon vaporization, specific enthalpy of saturated liquid, the specific enthalpy change upon vaporization, specific entropy of saturated liquid, and the specific entropy change upon vaporization 1200 kPa of temperature as:
Substitute
Substitute
Substitute
Substitute
Thus, the exit velocity for isentropic converging-diverging nozzle is
Substitute
Thus, the mass flow rate for isentropic converging-diverging nozzle is
At state 2 entropy value for the specific volume of steam and at pressure just below and just above the specified pressure
Substitute 1.1 MPa for
Substitute
Thus, the exit Mach number for isentropic converging-diverging nozzle is
Substitute 1.75 MPa for
From the above throat pressure the value of enthalpy and specific volume as:
Substitute
Substitute
Thus, the throat area for isentropic converging-diverging nozzle is
(b)
The exit velocity for isentropic converging-diverging nozzle.
The mass flow rate for isentropic converging-diverging nozzle.
The exit Mach number for isentropic converging-diverging nozzle.
The throat area for isentropic converging-diverging nozzle.
Answer to Problem 137RP
The exit velocity for isentropic converging-diverging nozzle is
The mass flow rate for isentropic converging-diverging nozzle is
The exit Mach number for isentropic converging-diverging nozzle is
The throat area for isentropic converging-diverging nozzle is
Explanation of Solution
Determine the initial specific enthalpy of the isentropic converging-diverging nozzle.
Here, the specific enthalpy of saturated liquid is
Determine the initial entropy of the isentropic converging-diverging nozzle.
Here, the specific entropy of saturated liquid is
Determine the final quality of saturated steam for the isentropic converging-diverging nozzle.
Here, the final entropy of the isentropic converging-diverging nozzle is
Determine the final specific enthalpy of saturated steam for the isentropic converging-diverging nozzle.
Determine the enthalpy of steam at the actual exit state for the isentropic converging-diverging nozzle.
Determine the final specific enthalpy for the isentropic converging-diverging nozzle.
Determine the exit entropy of the isentropic converging-diverging nozzle.
Determine the final specific volume of the isentropic converging-diverging nozzle.
Determine the exit velocity of the isentropic converging-diverging nozzle.
Note: the fluid flow was complete stop at the initial exit velocity then it becomes zero.
Determine the mass flow rate of the isentropic converging-diverging nozzle.
Determine the velocity of sound at the exit of the isentropic converging-diverging nozzle.
Determine the exit Mach number for isentropic converging-diverging nozzle.
Determine the critical pressure at the throat.
Here, the stagnation pressure at the initial state is
Determine the actual enthalpy of steam at the throat.
Determine the velocity of throat using steady-flow energy balance.
Note: the initial velocity is zero.
Determine the throat area for isentropic converging-diverging nozzle.
Conclusion:
At the inlet,
Perform unit conversion of pressure at state 1 from MPa to kPa.
From the Table A-5, “Saturated water-Pressure table”, obtain value of the specific enthalpy of saturated liquid, the specific enthalpy change upon vaporization, specific entropy of saturated liquid, and the specific entropy change upon vaporization at 1750 kPa of temperature as:
Substitute
Substitute
At the exit,
Perform unit conversion of pressure at state 2 from MPa to kPa.
From the Table A-5, “Saturated water-Pressure table”, obtain value of the specific volume of saturated liquid, the specific volume change upon vaporization, specific enthalpy of saturated liquid, the specific enthalpy change upon vaporization, specific entropy of saturated liquid, and the specific entropy change upon vaporization 1200 kPa of temperature as:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the exit velocity for isentropic converging-diverging nozzle is
Substitute
Thus, the mass flow rate for isentropic converging-diverging nozzle is
At state 2 entropy value for the specific volume of steam and at pressure just below and just above the specified pressure
Substitute 1.1 MPa for
Substitute
Thus, the exit Mach number for isentropic converging-diverging nozzle is
Substitute 1.75 MPa for
From the above throat pressure and entropy at the state 2ts the value of enthalpy as:
Substitute
From the above throat pressure and enthalpy at the state 2 the value of specific volume as:
Substitute
Substitute
Thus, the throat area for isentropic converging-diverging nozzle is
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