Name: ________________________
Bernoulli’s Equation and Continuity Equation Worksheet
1. The radius of the aorta is about 1 cm and the blood flowing through it has a speed of about 30 cm/s.
Calculate the average speed of the blood in the capillaries given the total cross section of all the
capillaries is about 2000 cm2.
2. How large must a heating duct be if air moving 3 m/s along it can replenish the air in a room of 300 m3
volume every 15 minutes? Assume the air’s density remains constant.
3. Water circulates throughout a house in a hot water heating system. If the water is pumped at a speed
of 0.5 m/s through a 2 cm diameter pipe in the basement under a pressure of 3 atm, what will be the
flow speed and pressure in a 1.3 cm diameter pipe on the second floor 5 m above?
4. Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000 Pa. At the nozzle the
pressure decreases to atmospheric pressure (101300 Pa), there is no change in height. Use the
Bernoulli equation to calculate the velocity of the water exiting the nozzle. (Hint: The density of water
is 1000 kg/m3. Pay attention to units!)
5. Through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 Pa.
The refinery needs the ethanol to be at a pressure of 2 atm (202600 Pa) on a lower level. How far must
the pipe drop in height in order to achieve this pressure? Assume the velocity does not change. (Hint:
Use the Bernoulli equation. The density of ethanol is 789 kg/m3. Pay attention to units!)
6. A certain New York City water-supply tunnel is almost 170 km long, is all at the same level, and has a
diameter of 4.10 m. Suppose water flows through the tunnel at a speed of 3.0 m/s until it reaches a
narrow section where the tunnel’s diameter is 2.70 m. The pressure in the narrow section is 82 kPa.
Use the continuity equation to find the water’s speed in the narrow section of the tunnel. Then find the
pressure in the wide portion of the tunnel.
Name: ________________________
Answers
1. 0.0471 cm/s
2. Cross-sectional area of 0.111 m2
3. v = 1.18 m/s; 2.51 atm
4. 14 m/s
5. -13.1 m
6. 102 kPa