A man owns a land that includes a low head water fall and wants to build a small hydroelectric plant. The effective head of the reservoir is 20 m. He used a tube of 3 m length and 1 m diameter as a penstock. He computed the speed of the water inside the penstock by dropping a small ball at the entrance of the tube and measuring the time it took to reach the other end of the tube. The ball traveled the penstock in 2 s.
a. Compute the power at the outtake of the tube.
b. If the coefficient of performance of the turbine is 0.95, and the efficiency of the generator turbine and generator is 90%, compute the expected generation of the site.
c. If the cost of building the small hydroelectric system is $10 M, compute the payback period if the cost of electricity from the neighboring utilities is $0.2/kWh. Assume that the water flow is always constant.
d. Is building this small hydroelectric system a good investment?