Question

A rectangular swimming pool has dimensions of 25 m x 9 m and a depth of 1.8 m and is full to the brim with water. Determine a) the absolute pressure at the bottom of the pool, b) the total force on the bottom of the pool, and c) the absolute pressure at point P, a point on the side of the pool just near the bottom. (Worth 2 pts)

Answer 1

a)

Here we have given the dimensions of the swimming pool as,

Here the depth of the swimming pool ,

For the top and bottom face of the swimming pool,Length of the swimming pool,

Breadth of the swimming pool.

We have according to the Pascal's law,the gauge pressure at a point of 'h' depth from the surface is given by,

Also we have the atmospheric pressure here is,

So,the absoute pressure at the point,

We have the density of the water,

So,At the bottom of the pool,The depth from the surface to bottom,

So,The gauge pressure at the bottom of the pool,

So,The absolute pressure at the bottom of the swimming pool,

b)

We have the diomensions of the bottom face of the pool,

Length of the swimming pool,

Breadth of the swimming pool.

So,The base area of the bottom of the pool,

Also the force exerted on the face of area A where the pressure P is,

So,Here the total force on the bottom of the pool,

So,Total force on the bottom of the pool,

c)

We have according to the Pascals law,The pressure at all points at the same level in the pond which all points having the same depth from the surface of the pool having same pressure.

And the pressure at all the points with the depth h from the surface of the pool is given by,

Here for the point p,on the side of the pool just near the bottom,at the same level of the depth as bottom from the surface of the pool.

So,Here the depth of the point P on the side of pool is same as the depth of the pool at bottom from the surface of the pool.

So,The pressure at this point P on side and the pressure at the bottom will be same.

So,We have the depth of point from the surface of the pool,

Also we have the atmospheric pressure here is,

So,the absoute pressure at the point,

We have the density of the water,

So,The gauge pressure at the at point P,

So,The absolute pressure at the point P on side near the bottom of the swimming pool,