Water is pumped from a river at an elevation of 500mto a village on a mountain s

Question

Water is pumped from a river at an elevation of 500mto a village on a mountain side at an elevation of 2,000mthrough a pipe 0.2m in diameter. A) What minimum pressure must be provided by thepump to bring water to the village? B) If 5,000 cubic meters of water are pumped each day, what isthe speed of the water in the pipe? C) What additional Pressure must the pump deliver to deliverthis flow? Water is pumped from a river at an elevation of 500mto a village on a mountain side at an elevation of 2,000mthrough a pipe 0.2m in diameter. A) What minimum pressure must be provided by thepump to bring water to the village? B) If 5,000 cubic meters of water are pumped each day, what isthe speed of the water in the pipe? C) What additional Pressure must the pump deliver to deliverthis flow?

Explanation / Answer

P = g h = 1000 * 9.8 * 1500 = 1.47 * 10E7 N /m2 V = A x    V / t  = A x / t = A v   where v isthe speed of the water v = ( V / t ) / A V / t   = 5000 / (24 * 3600) =.0579 m3 / sec v = .0579 / ( * .12 ) = 1.84 m /sec      1/2 m v2 = E = Fx     m = V = Ax F x = 1/2 A x v2 P = F / A = 1/2 v2 = 500 / 2 *.05792 = .838 N / m2 P = F / A = 1/2 v2 = 500 / 2 *.05792 = .838 N / m2

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