Chapter 8, Problem 4PC

Calculate the pressure in $\text{N}/{\text{m}}^{\text{2}}$ at the bottom of the Hoover dam. The depth of water behind the dam is $220\text{m}$. (Neglect the pressure due to atmosphere.)

To determine

The pressure at the bottom of the Hoover dam.

Answer to Problem 4PC

The pressure at the bottom of the Hoover dam is $22\times {10}^5\text{}\text{Pa}$.

Explanation of Solution

Given info: The depth of the water behind the dam is $220\text{m}$.

Write the expression for the water pressure at the bottom.

$P=\rho gh$

Here,

$\rho$ is the density of water

$g$ is the acceleration of gravity

$h$ is the depth of water

Substitute $1000\text{kg}/{\text{m}}^{\text{3}}$ for $\rho$ , $10\text{}\text{m}/{\text{s}}^{\text{2}}$ for $g$ and $220\text{m}$ for $h$ in the above equation to get $P$.

$\begin{array}{l}P=1000\text{kg}/{\text{m}}^{\text{3}}\times 10\text{}\text{m}/{\text{s}}^{\text{2}}\times 220\text{m}\\ P=22\times {10}^5\text{}\text{Pa}\end{array}$

Conclusion:

Therefore, the pressure at the bottom of the Hoover dam is $22\times {10}^5\text{}\text{Pa}$.