An inflatable backyard swimming pool is being filled from a garden hose with a flowrate of 0.12 gal/s.
a. If the pool is 8 ft in diameter, determine the time rate of change of the depth of water in the pool.
b. Suppose that the pool has a drain port with a diameter 0.5 in. Immediately after the drain is opened, the rate of change of the depth of the water in the pool is observed to decrease to 80% of the value calculated in part (a). Determine the average fluid velocity at the drain port.