Question

Consider a 8-m-long, 8-m-wide, and 2-m-high aboveground swimming pool that is filled with water to the rim. (a) Determine the hydrostatic force on each wall and the distance of the line of action of this force from the ground. (b) If the height of the walls of the pool is doubled and the pool is filled, will the hydrostatic force on each wall double or quadruple? Why?

Answer 1

Answer:

The hydrostatic force of 313920 N is acted on each wall of the swimming pool and this force is acted at 1 m from the ground. The hydrostatic force is quadruple if the height of the walls is doubled.

Explanation:

To calculate force on the walls of swimming pool whose dimensions are given as 8-m-long, 8-m-wide, and 2-m-high. We know that formula for hydrostatic force is $\text {hydrostatic force}=\text {pressure} \times \text {area,}=\rho g h \times(l \times h)$  

$\equiv \rho g h^{2} l$, we know ρ=density of fluid=1000 $g / c m^{3}$,

g=acceleration due to gravity=9.81 $m / s^{2}$, h=height of the pool=2 m and l=length of the pool=8 m.  

hydrostatic force on each wall=$1000 \times 9.81 \times 2^{2} \times 8$ = 313920 N.

The distance at which hydrostatic force is acted is half of the height of the swimming pool.

At 1 m from the ground this hydrostatic force is acted on each wall.  

The force is quadruple if the height of the walls of the pool is doubled this is because, the height is doubled and taken as h=4 m and substitute in the equation =$\rho g h^{2} l$ = $1000 \times 9.81 \times 4^{2} \times 8$ = 1255680 N. This is 4 times 313920 N.