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 must the water be pumped to arrive at the village? (b) If 4500 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.

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Asked Dec 23, 2019
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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 must the water be pumped to arrive at the village? (b) If 4500 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.

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Expert Answer

Step 1

(a)

Height difference,

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Ah =h - h, = (2096 – 564) m = 1532 m

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Step 2

Using Bernoulli’s equation

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PpV P+pv²+pgh + pgh river rim

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Step 3

The required minimum pressure for the water...

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min = (1000 kg/m²)(9.8 m/s² )(1532 m) = 1.5x10' Pa

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