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Finding Horsepower using Energy Equation

Please give me some feedback on this problem - In the figure attached, there are 150 feet of 2" diameter pipe, 90 feet of 6" diameter pipe, and 180 feet of 3" diameter pipe, all wrought iron. There are two 90 degree elbows and fully open globe valve. If the exit elevation is zero, what power in horsepower is extracted by the turbine from the 20 degrees celcius water when the flow rate is 0.15 feet^3?

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Solution Preview

The frictionless flow energy equation states that the sum of energies at any point on the flow energy line should be constant.

Therefore, we have the following:
Pressure energy + kinetic energy + potential energy = constant
Pressure energy = static pressure / density
Kinetic energy = half of square of velocity
Potential energy = static head x gravitational acceleration

Pressure/density + V^2/2 + gZ = constant across any point on the flow energy line

Applying the energy equation between points 1 and 2 (arbitrary points) on the energy line yields:
P1/density1 + 1/2 (V1)^2 + gZ1 = P1/density1 + 1/2 (V1)^2 + gZ1 (1)

If the flow experiences some pipe friction losses and energy lost in driving the turbine, the above equation is written as:
P1/density + 1/2 (V1)^2 + gZ1 = P2/density1+ 1/2 (V2)^2 + gZ2 + pipe friction and secondary energy losses + turbine energy (2)

The above equation can be also written ...

Solution Summary

The answer provides the horsepower from the turbine, with specified parameters, including length of diameter pipes, 90 degree elbows, and a fully open globe valve. The diagram provides an adequate illustration of what is occurring here, and the horsepower is calculated using a frictionless flow energy equation.