Steam enters a nozzle at 400°C and 800 kPa with a velocity of 10 m/s, and leaves at 375°C and 400 kPa while losing heat at a rate of 25 kW. For an inlet area of 800 cm2, determine the velocity and the volume flow rate of the steam at the nozzle exit.
FIGURE P5–33
The velocity and volume flow rate of the steam at the nozzle exit.
Answer to Problem 33P
The exit volume flow rate of the steam is
The exit velocity of the steam is
Explanation of Solution
Write the energy rate balance equation for one inlet and one outlet system.
Here, the rate of heat transfer is
Consider the steam flows at steady state through the nozzle. Hence, the rate of change in net energy of the system becomes zero.
Here, the heat loss from the nozzle is estimated as
There is no heat transfer at inlet i.e.
The Equations (I) reduced as follows to obtain the exit velocity.
At steady flow, the inlet and exit mass flow rates are equal.
Write the formula for inlet mass flow rate.
Here, the cross-sectional area is
Write the formula for exit volumetric flow rate.
At both the inlet and exit of the nozzle, the steam is at the state of superheated condition.
Refer Table A-6, “Superheated water”.
At inlet:
Obtain the following properties corresponding to the temperature of
At outlet:
Obtain the following properties corresponding to the temperature of
Write the formula of interpolation method of two variables.
Show the temperature and enthalpy values from the Table A-6 as in below table.
S.No. | x | y |
Temperature | Enthalpy | |
1 | 300 | 3067.1 |
2 | 375 | ? |
3 | 400 | 3273.9 |
Substitute
Thus, the enthalpy
Similarly, the exit specific volume
Conclusion:
Substitute
Substitute
Thus, the exit volume flow rate of the steam is
Substitute
Thus, the exit velocity of the steam is
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Chapter 5 Solutions
Thermodynamics: An Engineering Approach