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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

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 2 096 in. (a) At what minimum pressure must the water be pumped to arrive at the village? (b) If 4 500 m3 are pumped per day what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.

(a)

To determine
The minimum pressure must the water be pumped to arrive at the village.

Explanation
Bernoulli’s equation is used for to calculate the minimum pressure required to pump the water where the flow speed at the upper end of the pie would be zero and the pressure at the end must be equal to the atmospheric pressure. We arrive minimum pressure as [P+(1/2)ρv2+ρgy]river=[P+(1/2)ρv2+ρgy]rim and which reduced to the minimum pressure (Priver)min=Patm+ρg(yrimyriver) .

Given info: The atmospheric pressure is 1.013×105Pa , acceleration due to gravity is 9.80m/s2 , the elevation of river is 564m , the density of water is 1.00×103kg/m3 , and the elevation of the village is 2096m .

The formula for the minimum pressure must the water be pumped to arrive at the village is,

(Priver)min=Patm+ρg(yrimyriver)

  • Patm is atmospheric pressure

(b)

To determine
The speed of the water in the pipe.

(c)

To determine
The additional pressure that necessary to deliver the flow.

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