Question

water from a dam is channeled through a pipe unto a turbine for electricity generation.the pipe is 1.0 diameter and is always full of water.the water flows at a speed of 1.7m/s.the turbine was located 22m lower than the top of the dam wherr the water drops.the turbi e which operates at an efficiency of 80% drives a generator whuch has 5% losses due to friction.the actual power produced leaves the sub station after another 6% loss from transformers.calculate the actual power produced.

Answer 1

$P=\eta (1-\eta')Fv=\eta (1-\eta')mgv=\eta (1-\eta')\rho Vgv=$

$\eta (1-\eta')\rho Shgv=\eta (1-\eta')\frac{\pi d^2}{4}\rho hgv,$

$P=0.8\cdot 0.89\cdot \frac{3.14\cdot 1^2}{4}\cdot 1000\cdot 22\cdot 9.8\cdot 1.7=205~kW.$