Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2096 m. a. At what minimum pressure, Pmin, must the water be pumped to arrive at the village? (In other words what pressure is needed at the bottom to get the water to the top with exactly no pressure remaining?) b. If 4500 m3 are pumped per day, what is the speed, vvillage, of the water in the pipe in the village? If the people at the top are seeing water move through the pipe, there has to be SOME pressure, therefore there must be more pressure pushing from the bottom, Pactual, than what you calculated in part (a). c. What ADDITIONAL pressure, Pextra, is necessary to deliver this flow? (Pactual = Pmin + Pextra)

College Physics
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Chapter12: Fluid Dynamics And Its Biological And Medical Applications
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Problem 28PE: A sump pump (used to drain water from the basement of houses built below the water table) is...
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Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon.

The river is at 564 m elevation and the village is at 2096 m.


a. At what minimum pressure, Pmin, must the water be pumped to arrive at the village? (In other words what pressure is needed at the bottom to get the water to the top with exactly no pressure remaining?)

b. If 4500 m3 are pumped per day, what is the speed, vvillage, of the water in the pipe in the village?

If the people at the top are seeing water move through the pipe, there has to be SOME pressure, therefore there must be more pressure pushing from the bottom, Pactual, than what you calculated in part (a).

c. What ADDITIONAL pressure, Pextra, is necessary to deliver this flow?
(Pactual = Pmin + Pextra)


[Note: You may assume that the free-fall acceleration and the density of air are constant over the given range of elevations.]

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