# Worksheet: Bernoulli’s Equation

In this worksheet, we will practice using Bernoulli’s equation to calculate the pressure exerted by a fluid and the potential and kinetic energy of a fluid.

**Q1: **

When physicians diagnose arterial blockages, they quote the reduction in flow rate. The flow rate in an artery has been reduced to of its normal value by a blood clot and the average pressure difference between the ends of the artery has increased by . By what factor has the clot reduced the radius of the artery?

**Q2: **

The wings of an aircraft are required to produce 1.00 kN
of lift per square meter of wing, counting the
average area of the top and bottom wing surfaces as wing area. Lift is provided by the differential flow
of air around the wing surface and depends on the density and speed of air over the wing surfaces.
Use a value of 1.29 kg/m^{3}
for the density of air at
sea level and assume that the speed of airflow over the lower wing surface is equal to the speed of the aircraft.

At takeoff, an aircraft has a speed of 60.0 m/s. At what speed must air move over the upper wing surface for the required lift for the aircraft to be produced?

At an altitude where the density of air is of the sea level air density the aircraft has a speed of 245 m/s. At what speed must air move over the upper wing surface for the required lift for the aircraft to be produced?

**Q4: **

Water supplied to a house by a water main has a
pressure of N/m^{2}
early on a summer day when neighborhood use is low. This pressure produces a
flow of 20.0 L/min through a garden hose. Later in the day,
pressure at the exit of the water main and entrance to the
house drops, and a flow of only 8.00 L/min is obtained
through the same hose.

What pressure is now being supplied to the house, assuming resistance is constant?

- A N/m
^{2} - B N/m
^{2} - C N/m
^{2} - D N/m
^{2} - E N/m
^{2}

By what factor did the flow rate in the water main increase
in order to cause this decrease in delivered pressure? The
pressure at the entrance of the water main is N/m^{2}, and the original flow rate was
200 L/min.

How many more users are there, assuming each would consume 20.0 L/min in the morning?

**Q6: **

Water towers store water above the level of consumers for times of heavy use, eliminating
the need for high-speed pumps. What vertically upward displacement from a water consumer
must the water level be to create a gauge pressure of N/m^{2} for the consumer? Given 1,000 kg/m^{3} for
the desity of water.

**Q7: **

A container of water has a cross-sectional area of 0.100 m^{2}.
A piston sits on top of the water, as shown.
There is a spout located 0.150 m
from the bottom of the tank, open to the atmosphere,
and a stream of water exits the spout. The cross-sectional area of the spout is m^{2}.

What is the speed of the water as it leaves the spout?

How far from the spout does the water hit the floor? Ignore all friction and dissipative forces.

**Q8: **

Water enters a nozzle of diameter 3.00 cm from a fire hose of diameter 9.00 cm. 40.0 L/s of water passes through the nozzle.

What is the pressure drop due to the Bernoulli effect as the water enters the nozzle?

- A N/m
^{2} - B N/m
^{2} - C N/m
^{2} - D N/m
^{2} - E N/m
^{2}

To what maximum height above the nozzle can this water rise?

**Q9: **

A sump pump is used to drain water from the basement of houses built below the water table.
The pump drains a flooded basement at the rate of 0.750 L/s,
with an output pressure of N/m^{2}. Assume that water flows with negligible friction. The water enters a hose with a
3.000 cm inside diameter and rises to its highest point, 2.50 m vertically above the pump. The hose then runs over a foundation wall, to a point 0.500 m vertically below the highest point. The hose widens to a
4.000 cm diameter.

What is the pressure of the water at its highest point?

- A N/m
^{2} - B N/m
^{2} - C N/m
^{2} - D N/m
^{2} - E N/m
^{2}

What is the pressure of the water at the point where the hose widens?

- A N/m
^{2} - B N/m
^{2} - C N/m
^{2} - D N/m
^{2} - E N/m
^{2}

**Q12: **

Calculate the stagnation pressure at the nose of an aircraft that is in steady level flight at sea level at a speed of 134 m/s. Use a value of 323 K for the air temperature, use a value of 101 kPa for the air pressure, use a value of 1.4 for the the specific heat ratio of air, and use a value of 287 for the gas constant of air.

**Q15: **

Every few years, winds in Boulder, Colorado, attain steady speeds of
45.0 m/s when
the jet stream descends during early spring. Use Bernoulli’s equation to find
the magnitude of the force from these winds on a roof that has an area of
185 m^{2}. Use a value of
1.14 kg/m^{3} for the density of air and a value of N/m^{2} for the air
pressure over the roof.

- A N
- B N
- C N
- D N
- E N

**Q16: **

Water flowing at 0.152 L/s passes through a contraction from a 1.27 cm diameter pipe to a 0.635 cm diameter pipe. Calculate the pressure difference from immediately before the contraction to in the contraction. This pressure difference is defined as the pressure before the contraction minus the pressure in the contraction.

**Q17: **

Water flowing at 0.758 L/s passes through a contraction from a 1.27 cm diameter pipe to a 0.635 cm diameter pipe. Calculate the pressure difference from immediately before the contraction to in the contraction. This pressure difference is defined as the pressure before the contraction minus the pressure in the contraction.