It is noteworthy that during a holiday trip, the water is discharged from a high tank...

It is noteworthy that during a holiday trip, the water is discharged from a high tank with a 30 cm diameter plastic pipe into a stream in the valley, and the idea of generating power from this water comes to your mind. The bird flight from the reservoir stream is 100 m and the height difference between the free water surface and the stream in the tank is 75 m.
(a) Show the relationship between the water flow in the pipe and the power to be obtained for the power plant to be installed to obtain power from this source by drawing the flow-power graph.
(b) Calculate the required water flow to obtain the highest power.

Solutions

Expert Solution

(a)

The head loss in the pipe is related by Darcy-Weisbach equation:

The friction factor is found out by Colebrook equation (through iterative methods)

For plastic pipe,

Given in the problem, 0.3 m

Calculate Reynold’s number

For water at 300K, the properties are

The power generated by the power plant is related by the equation

Then the equation for power is rewritten

Maximum power is obtained at maximum .

Tabulate the values of V vs P

(b)

The water flow required to obtain the maximum power is 13 m/s

samet mamat answered 1 week ago

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