Question

# A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 ft and the deep end, 9 ft. If the pool is full of water, estimate the hydro static force on the deep end.

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(If you read and understood my solution for part (a), this is mostly the same, just with the deep end side instead so the only difference in the work is we integrate from $x=0$ to 9. So you can skip down to the bottom where we get to the integral step.)

\begin{align*} F &= PA = \rho g d A \end{align*}

$P =$ pressure

$A =$ area

$\rho =$ mass density

$g =$ acceleration due to gravity

$d =$ depth

this problem uses non-metric units so we have

\begin{align*} \delta &= \rho g = 62.5 \text{ lb/ft}^3 \qquad \text{ weight density of water} \\\\ F &= \delta d A \end{align*}

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