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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 2 096 m. 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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In this problem, we use Bernoulli's equation. The summation of the kinetic energy per unit volume, the pressure and the potential energy of the fluid is constant when it flows through a streamline. Equations (9.17) shows Bernoulli's equation in the form

$\begin{equation} P_{1}+\frac{1}{2} \rho v_{1}^{2}+\rho g y_{1}=P_{2}+\frac{1}{2} \rho v_{2}^{2}+\rho g y_{2} \end{equation}$

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