Q. 64 - Calculus

Question

Find the hydrostatic force described in each of Exercises
61–69.

The hydrostatic force exerted on one of the long sides of a rectangular swimming pool that is 8 feet long, 6 feet wide, and 4.5 feet deep.

Step-by-Step Solution

Answer

The hydrostatic force exerted on one of the long sides of a rectangular swimming pool that is 8 feet long, 6 feet wide, and 4.5 feet deep is $1498$ pounds.

Step 1. Given Information.

A rectangular swimming pool that is 8 feet long, 6 feet wide, and 4.5 feet deep

Step 2. Find A k , d k

Area of the rectangular tub$=6∆x$

Depth, $d=4.5-x_k^{*}$

The density of the water is $62.4$ pounds.

Step 3. Find the hydrostatic force.

The hydrostatic force is given by, 

$$\begin{gathered} F=\omega A_k{d}_k \\ \simeq 62.4(6∆x)4.5-x_k^{*} \\ =\sum _{k=1}^{n}62.4\left(6\right)(4.5-x_k^{*})∆x \\ F={\int }_0^{8}62.4\left(6\right)(4.5-x)dx \\ =374.4{[4.5x-\frac{x^2}{2}]}_0^8 =374.4\left(4\right) \\ =1498 \end{gathered}$$