Through a pipe 15.0cm in diameter, water is pumped from the Colorado River up to Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564m, and the village is at an elevation of 2096m (a) What is the minimum pressure at which the water must be pumped if it is to arrive at the village? (b) If 4500m^3 are pumped per day, what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow?(adsbygoogle = window.adsbygoogle || []).push({});

(Assume that the freefall acceleration and the density of air are constant over this range of elevations).

I can get (a) and (b) easily. For (a) the minimum pressure would be 1atm + the pressure necessary to balance the weight of the water in the pipe. For (b), one can use the equation of continuity to find the speed. (c) is what gets me. I'm supposing its asking the question in respect to (b)...but isn't the rate of volume flow and speed explicitly independent of the pressure: (PV)/t = p[power] = Fv, P*(V/t) = Fv, P*(V/t)/v = F, P*A = F, P = F/A....so then the speed and volume flow can be a varying value under the same pressure. How would I interpret what (c) is asking?

The answer to (a) is ~1atm + 15.0MPa, (b) is ~2.95m/s, and (c) is 4.34kPa

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# Homework Help: Fluid Dynamics Water Pipe

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