The Cost of Draining an Olympic-sized Swimming Pool

Which method is more cost-effective: draining the pool from the surface of the water or draining it from the bottom?

To compare the costs of draining the pool from the surface of the water versus draining the pool from the bottom, we need to calculate the work done in lifting the water in each case.

When draining the pool from the surface, the pump needs to lift the water by a height equal to the depth of the water, which is 1.5 m. So the work done in lifting the water is given by the formula: work = force × distance. The force is equal to the weight of the water, which is the density of water × volume of water. The distance is 1.5 m.

When draining the pool from the bottom, the pump needs to lift the water by a height equal to the sum of the depth of the water and the height of the pump above the surface. So the work done in lifting the water is given by the same formula: work = force × distance. The force is equal to the weight of the water, which is the density of water × volume of water. The distance is 1.5 m + 0.5 m.

By comparing the two works, we can determine which method is more cost-effective.