In: Mechanical Engineering
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.
(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