Question

A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high, and the depth of the water is 4 ft. how much work is required to pump all of the water out over the side? (use the fact that water weighs .) 62.5 lb

Answer 1

To calculate the work required to pump all of the water out of the swimming pool, we need to find the volume of water in the pool and then multiply it by the weight of the water. The work required to pump all of the water out is approximately 565,440 ft-lb.

Step-by-step explanation:

To calculate the work required to pump all of the water out of the swimming pool, we need to find the volume of water in the pool and then multiply it by the weight of the water.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

In this case, the radius is half the diameter, so it's 12 ft. The height is 5 ft.

Therefore, the volume of water in the pool is V = π(12^2)(5) = 720π ft³.

Using the fact that water weighs 62.5 lb/ft³, we can calculate the weight of the water: Weight = Volume x Density = (720π)(62.5) lb.

To find the work required to pump all of the water out, we need to multiply the weight of the water by the height that it needs to be lifted. In this case, the water needs to be lifted 5 ft.

Therefore, the work required to pump all of the water out is Work = Weight x Height = (720π)(62.5)(5) ft-lb.

Using the value π ≈ 3.14, we can calculate the work required to pump all of the water out as approximately 565,440 ft-lb.

Answer 2

The pumping work has the equation written below:
W = mΔh,
where m is the mass
Δh is the difference in height

We determine the mass from the density of water which is 62.5 lb/ft³.
Density = Mass/Volume
Mass = m = Density*Volume
m = (62.5 lb/ft³)(π/4)(24 ft)² = 9,000π
The lb is in lbm or pound-mass. To convert it to pound-force, lbf, we use the g/gc conversion factor which is equal to 1 lbf/lbm. Thus,

W = (9,000π lbm)(5 ft - 4 ft)(1 lbf/lbm) = 28,274 lbf·ft