Concept explainers
The efficiency of the turbine A.
The efficiency of the turbine B.
The actual efficiency of the turbine B by using Moody expected efficiency of the turbine.
Answer to Problem 122P
The efficiency of the turbine A is
The efficiency of the turbine B is
The actual efficiency of the turbine B is
Explanation of Solution
Given information:
The diameter of the turbine A is
Write the expression for the dimensionless turbine A parameter.
Here, the dimension less parameter for turbine A is
Write the equation for the dimensionless turbine B parameter.
Here, the dimensionless parameter for the turbine B is
Write the expression for the affinity law dimensionless parameter for turbine A.
Here, the affinity dimensional parameter for turbine A is
Write the expression for the affinity law dimensionless parameter for pump B.
Here, the affinity dimensional parameter for turbine B is
Equate Equation (I) and Equation (II).
Equate Equation (III) and Equation (IV).
Substitute
Write the equation for the angular velocity of the turbine A.
Here, the number of rotation for turbine A is
Write the equation for the angular velocity of the turbine B.
Here, the number of rotation for turbine B is
Write the expression for the volume flow rate for the turbine B.
Write the expression for the efficiency of turbine A.
Here, the efficiency of the turbine is
Write the expression for the efficiency of turbine B.
Here, the efficiency of the turbine B is
Write the expression for the Moody efficiency correction equation.
Write the expression for the actual efficiency of turbine B.
Here, the efficiency increase for turbine B is
Calculation:
Substitute
Substitute
Substitute
Substitute
The density of the fluid for both turbine is zero.
Substitute
Substitute
Substitute
Substitute
Substitute
The efficiency of the turbine B is increased too. The relative roughness on the surface of the prototypes runner blades may be significantly smaller than the model turbine. The larger turbine has smaller tips clearance relative to the blade diameter. The smaller turbines have larger tips clearance relative to the blade diameter. So the leakage is less in the larger turbine as compared to the leakage in the smaller turbine.
Conclusion:
The efficiency of the turbine A is
The efficiency of the turbine B is
The actual efficiency of the turbine B is
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Chapter 14 Solutions
Fluid Mechanics: Fundamentals and Applications
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