Problem Description

On a busy day, a farmer is waiting for a tank to be filled with water. Water flows steadily from the faucet with a volumetric flow rate of 10 gal/min. The cylindrical tank has a radius of 1.5 ft and a height of 3 ft.

Find the time rate of change of the depth of water in the tank. Estimate the time it will take to fill up the empty tank so that the farmer can step away and finish other tasks at hand while the tank is being filled.

• Assume the fluid is incompressible.
• Assume the cross sectional area of the water flowing out of the faucet is negligible.