A man owns a land that includes a low head water fall and wants to build a small

Question

A man owns a land that includes a low head water fall and wants to build a small hydroelectric plant. 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 mechanical power
B)If the coefficient of performance of the turbine is 0.5 and the efficiency of the generator is 90%, compute the expected generation of the site.
C)If the cost of building the small hydroelectric system is $20 K, compute the payback period if the cost of electricity from the neighboring utilities is $0.2/kW h. Assume that the water flow is always constant.
d)Is building this small hydroelectric system a good investment?

Explanation / Answer

a) Mechanical power of water Pw = 1/2 * A * rho * v^3 = 1/2 * (pi*0.5^2) * 1000 * (3m/2s)^3 = 1.32 kW b) Expected generation Pg = Pw * Cg * ng = 1.32kW * 0.5 * 0.9 = 598 W c) Payback period $20000 / ($0.2/kWh) = 100000kWh time = Energy / Power = 100000kWh / 598W = 167224 hr = 19 yrs d) good investment? depending how long the dam is operational if it can work for 20 yrs

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