Concept explainers
Water enters a hydraulic turbine through a 30-cm-diameter pipe at a rate of 0.6 m3/s and exits
through a 25-cm-diameter pipe. The pressure drop in the turbine is measured by a mercury manometer to be 1.2 in. For a combined turbine-generator efficiency of 83 percent determine the net electric power output. Disregard the effect of the kinetic energy correction factors.
The net electric power output.
Answer to Problem 84P
The net electric power output is
Explanation of Solution
Given information:
The initial diameter of the pipe is
Write the expression for the initial velocity of the water.
Here, the initial diameter of the pipe is
Write the expression for the final velocity of the water.
Here, the final diameter of the pipe is
Write the expression for the pressure drop.
Here, the density of the mercury and water is
Write the expression for the turbine head using the Bernoulli's equation.
Here, the head loss is
Write the expression for the net electric power output.
Here, the turbine and generator efficiency is
Calculation:
Draw the diagram for a tank fitted with orifice.
Figure-(2)
Substitute
Substitute
Substitute
Here, the gravitational constant is
Here, the density of the water is
Substitute
Substitute
Conclusion:
Thus, the net electric power output is
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Chapter 5 Solutions
Fluid Mechanics: Fundamentals and Applications
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