Tutorial: Bernoulli’s Equation

1. A bathtub is being filled with water, but the drain plug does not fit properly and water

leaks out. The volumetric flow rate of water down the drain is proportional to the

pressure drop across the plug according to V = 90(P – Patm) where flow rate is in gal/min

and pressure is PSIA. The flow rate from the faucet is 30 gal/min. Bathtub size is 5 ft long,

2.5 ft wide and 2 ft high.

a. What is the final height of water in the tub?

b. How long will it take the tub to 90% of the final height?

2. Air enters a nozzle at 90C, 180 kPa with an average of 60 m/s. The duct has an inlet

diameter of 10 cm. The exit has a diameter of 6.3 cm and is open to the atmosphere. If

the velocity at the exit is 249 m/s, what is the temperature at exit?

3. Water drains at a steady rate from a very large tank through a pipe of diameter 4 cm.

Assume frictionless, incompressible flow. Assume velocity of the receding top surface is

negligible. Find the rate at which mass drains from the tank.

Water

0.8 m

Air in Air out