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Worksheet: Bernoulli's Equation

Q1:

When physicians diagnose arterial blockages, they quote the reduction in flow rate. The flow rate in an artery has been reduced to 1 0 . 0 % of its normal value by a blood clot and the average pressure difference between the ends of the artery has increased by 2 0 . 0 % . 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/m3 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 2 5 . 0 % 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?

Q3:

Water flows through a 10.0-meter-long section of 10.16-centimeter-diameter pipe that abruptly contracts to a 1.00-meter-long section of 0.635-centimeter-diameter pipe. If the water is flowing at 0.1515 L/s, calculate the total pressure drop over the two sections.

Q4:

If the pressure reading of your pitot tube is 15.0 mmHg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?

Q5:

Water enters a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose. 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 7 . 7 9 × 1 0 5 N/m2
  • B 4 . 4 9 × 1 0 5 N/m2
  • C 1 . 1 3 × 1 0 6 N/m2
  • D 1 . 5 8 × 1 0 6 N/m2
  • E 1 . 3 1 × 1 0 5 N/m2

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

Q6:

A container of water has a cross-sectional area of 0.100 m2. 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 7 . 0 0 × 1 0 4 m2.

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.

Q7:

Plaque deposits reduce a blood vessel’s radius to 9 0 . 0 % of its original value. The action of the heart compensates for the decrease by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase?

Q8:

Dray air is moved through a conduit at a volumetric rate of 0.167 m3/s. The pressure of the air in the flow is 124 kPa and its temperature is 2 7 . 0 C . Find the mass flow rate of air in the conduit. Use a value of 2 8 7 . 0 5 / J k g C for the specific gas constant of dry air.

Q9:

Water supplied to a house by a water main has a pressure of 3 . 0 0 × 1 0 5 N/m2 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 1 . 0 2 × 1 0 5 N/m2
  • B 0 . 9 3 7 × 1 0 5 N/m2
  • C 1 . 1 1 × 1 0 5 N/m2
  • D 1 . 2 0 × 1 0 5 N/m2
  • E 1 . 2 7 × 1 0 5 N/m2

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 5 . 0 0 × 1 0 5 N/m2, 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?

Q10:

Water is supplied to a 1 119-Watt-power pump at a flow rate of 18.9 L/s. What is the maximum upward vertical displacement possible for this water jet?

Q11:

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 3 . 0 0 × 1 0 5 N/m2. 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 2 . 9 5 × 1 0 5 N/m2
  • B 2 . 5 5 × 1 0 5 N/m2
  • C 3 . 2 3 × 1 0 5 N/m2
  • D 2 . 7 6 × 1 0 5 N/m2
  • E 3 . 3 6 × 1 0 5 N/m2

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

  • A 1 . 8 1 × 1 0 5 N/m2
  • B 1 . 6 8 × 1 0 5 N/m2
  • C 2 . 0 5 × 1 0 5 N/m2
  • D 2 . 3 0 × 1 0 5 N/m2
  • E 1 . 3 3 × 1 0 5 N/m2

Q12:

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 m2. Use a value of 1.14 kg/m3 for the density of air and a value of 8 . 8 9 × 1 0 4 N/m2 for the air pressure over the roof.

  • A 1 . 7 3 × 1 0 7 N
  • B 1 . 9 5 × 1 0 7 N
  • C 1 . 3 6 × 1 0 7 N
  • D 1 . 6 7 × 1 0 7 N
  • E 1 . 4 7 × 1 0 7 N

Q13:

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 2 . 0 0 × 1 0 5 N/m2 for the consumer?

Q14:

A ping-pong ball with a diameter of 3.8 cm is suspended in an upward airflow in which the air density is 1.184 kg/m3 and the air’s vertically upward velocity is 33.5 km/h. The drag coefficient of the ping-pong ball is 0.123. What is the mass of the ping-pong ball?

Q15:

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.