Concept explainers
The rate of shaft work done for the device.
The direction of shaft work done for the device.
Answer to Problem 3.165P
The rate of shaft work done for the device is
The direction of shaft work done for the device is negative . The work is done on the shaft for the device.
Explanation of Solution
Given information:
The flow of water is steady and isothermal. The diameter at the section (1) is
Write the expression for the flow rate at section (3).
Here, the flow rate at section (1) is
Write the expression for the steady and isothermal work.
Here, the shaft work done per unit time by the device is
Since the Equation (II) is the general form of the work transfer, so the work done at individual section is written by the above expression.
Write the expression for the work transfer at section (1).
Here, the work transfer at section (1) is
Write the expression for the work transfer at section (2).
Here, the work transfer at section (2) is
Write the expression for the work transfer at section (3).
Here, the work transfer at section (3) is
Write the expression for net work transfer by the device.
Here, the net work done is
Substitute
Write the expression for the flow rate at section (1).
Write the expression for the area at section (1).
Here, the diameter is
Substitute
Write the expression for the flow rate at section (2).
Write the expression for the area at section (2).
Here, the diameter is
Substitute
Write the expression for the flow rate at section (3).
Write the expression for the area at section (2).
Here, the diameter is
Substitute
Substitute
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Further solve the above expression.
Since the sign of the work done by the device is negative, so the work done on the shaft for the given device.
Thus, the work is done on the system.
Conclusion:
The rate of shaft work done for the device is
The direction of shaft work done for the device is negative . The work is done on the shaft for the device.
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Chapter 3 Solutions
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