Deck 14: Fluid Dynamics

Question 1

How much power is theoretically available from a mass flow of 1000 kg/s of water when it falls a vertical distance of 100 metres?

A)980 kW
B)98 kW
C)4900 W
D)980 W
E)9600 W

Answer 1

980 kW

Question 2

The water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface?

A)2.4 m/s
B)3.0 m/s
C)5.4 m/s
D)7.7 m/s
E)49 m/s

Answer 2

7.7 m/s

Question 3

Water pressurised to 3.5 * 105 Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area. What are the pressure and velocity of the water after the contraction?

A)2.5 * 105 Pa, 15 m/s
B)3.0 *105 Pa, 10 m/s
C)3.0 * 105 Pa, 15 m/s
D)4.5* 105 Pa, 1.5 m/s
E)5.5 * 105 Pa, 1.5 m/s

Answer 3

2.5 * 105 Pa, 15 m/s

Question 4

A venturi tube may be used as the inlet to an automobile carburettor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? ( $\rho$ = 1.2 kg/m3.)

A)70 Pa
B)85 Pa
C)100 Pa
D)120 Pa
E)81 Pa

Question 5

The pressure inside a commercial airliner is maintained at 1 ATM (1.01*105 N/m²). What is the outward force exerted on a 1.0 m * 2.0 m cabin door if the outside pressure (at 10 km height) is 0.3 ATM?

A)1.4*102 N
B)1.4*103 N
C)1.4 * 104 N
D)1.4 * 105 N
E)7.0 * 103 N

Question 6

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 *104 N/m and the pressure on the bottom surface is 9.0 * 104 N/m². If the area of the top and bottom surfaces of each wing is 2.0 m², what is the total lift on the model airplane?

A)2.0 *103 N
B)8.0 * 103 N
C)1.6 * 104 N
D)3.6 * 104 N
E)1.0 * 103 N

Question 7

A hot air balloon of radius 10m is floating at a constant altitude over Parliament House in Canberra. It is initially at rest. Suddenly, an easterly breeze of speed 10 cm s-1 starts blowing. Assuming that Stokes' law applies, how much force does the wind apply to the balloon? The viscosity of air is 1.8x10-5 Pa s.

A) 3.4x10-5 N
B) 3.4x10-4 N
C) 3.4x10-3 N
D) 3.4x10-2 N
E) 3.4x10-1 N
ANS

Question 8

A cricket ball is resting on a picnic table. There is a gentle wind moving at 1m s-1. Assuming that Stokes' law applies, how much force does the wind apply to the ball? The radius of a cricket ball is 3.6 cm and the viscosity of air is 1.8x10-5 Pa s.

A) 1.2x10-5 N
B) 2.4x10-4 N
C) 1.2x10-3 N
D) 2.4x10-2 N
E) 1.2x10-1 N
ANS

Question 9

A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow?

A)1.4 m/s
B)2.0 m/s
C)2.8 m/s
D)3.9 m/s
E)4.2 m/s

Question 10

A sphere of radius 1 cm and mass 100 g is sinking at a steady speed of 1 mm per second down through a fluid with viscosity of 300 Pa s. Assuming that Stokes' law applies, what is the density of the viscous fluid?

A) 500 kg m-3.
B) 1000 kg m-3.
C) 1500 kg m-3.
D) 2000 kg m-3.
E) 5000 kg m-3.ANS

Question 11

A Boeing 737 airliner has a mass of 20 000 kg and the total area of both wings (top or bottom) is 100 m². What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

A)1 960 N/m²
B)3 920 N/m²
C)7 840 N/m²
D)4 560 N/m²
E)3 070 N/m²

Question 12

A fountain sends water to a height of 100 metres. What must be the pressurisation (above atmospheric) of the water system? 1 ATM = 1.01 *105 N/m².

A)1.0 ATM
B)4.2 ATM
C)7.2 ATM
D)9.7 ATM
E)8.2 ATM

Question 13

A sphere of radius 1 cm is moving through a vat of corn syrup, which has a viscosity of 1.4 Pa s. A force of 0.01 N is needed to keep it moving at a constant speed. What is the speed? You may assume that Stokes' law applies.

A) 3.8 cm s-1.
B) 26 cm s-1.
C) 23 cm s-1.
D) 12 cm s-1.
E) 6.8 cm s-1.ANS

Question 14

Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream?

A)1.0 m/s
B)2.0 m/s
C)8.0 m/s
D)16 m/s
E)4.0 m/s

Question 15

What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 ATM.) $\rho$ (sea water) = 1.02 *103 kg/m3.

A)1.26 * 104 N
B)1.26 * 106 N
C)1.26 * 108 N
D)1.26* 1010 N
E)1.26 * 102 N

Question 16

Water is sent from a firehose at 30.0 m/s at an angle of 30.0 $\degree$ above the horizontal. What is the maximum height reached by the water?

A)7.50 m
B)11.5 m
C)15.0 m
D)19.0 m
E)30.0 m

Question 17

Air within the funnel of a large tornado may have a pressure of only 0.2 ATM. What is the approximate outward force on a (5 m * 10 m) wall if a tornado suddenly envelops the house? (1 ATM = 1.01*105 N/m².)

A)4 * 103 N
B)4 * 104 N
C)4 * 105 N
D)4 * 106 N
E)7*105 N

Question 18

A sphere of radius 2 cm is moving at a speed of 1 mm per second through a fluid with viscosity of 1000 Pa s. Assuming that Stokes' law applies, what is the viscous force on the sphere?

A) 377 N
B) 37 700 N
C) 63 N
D) 120 N
E) 3.8 N
ANS

Question 19

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 metres. What is the maximum power output if 30.0% of the wind's energy can be extracted? $\rho$ air = 1.25 kg/m3.

A)7.20 kW
B)14.7 kW
C)21.3 kW
D)29.4 kW
E)39.6 kW

Question 20

The siphon shown is used to transfer liquid from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m.

A)1.1 m/s
B)2.2 m/s
C)4.4 m/s
D)9.8 m/s
E)6.5 m/s

Question 21

An evaporative cooling unit needs to pump 100 litres of air per second through a pipe of radius 10 cm and length 10 m. How much of a pressure difference must be applied to the air to produce this flow rate? The viscosity of air is 1.8x10-5 Pa s.

A) 4.6x10-9 Pa
B) 1.44 Pa
C) 0.46 Pa
D) 460 Pa
E) 0.057 Pa
ANS

Question 22

Water flows down a pipe of radius 5 cm at a speed of 5 cm s-1. What is the Reynolds number of this flow and will it be turbulent? The density of water is 1000 kg m-3 and the viscosity of water is 0.001 Pa s.

A) Re = 5000, so the flow is turbulent.
B) Re = 10 000, so the flow is extremely turbulent.
C) Re = 3000, so the flow is probably part laminar and part turbulent.
D) Re = 2000, so the flow is laminar.
E) Not enough information is provided to answer this question.ANS

Question 23

Imagine that you have been given the job of designing a fountain to be the centrepiece of a new shopping mall on the Gold Coast. The fountain will consist of a single upward jet of water, launched from a pipe of radius 2 mm and length 1.2 m. The pipe is fed by recycled water, pushed by a pump which produces a pressure difference of 50 000 Pa. How high will the water in the fountain go? The viscosity of water is 0.001 Pa s, and g = 9.8 m s-2.

A) 1.3 m.
B) 5 m.
C) 11 m.
D) 22 m.
E) 44 m.ANS

Question 24

A natural gas pipeline with a diameter 0.250 m delivers 1.55 cubic meters of gas per second. What is the flow speed of the gas in the pipeline?

Question 25

Imagine that you are working at an outback mine. In part of the on-sight mineral separation plant, a slurry consisting of a mixture of mineral dust and water flows from one part of the plant to another down a pipe of diameter 10 cm. The flow needs to remain turbulent, as otherwise the mineral dust will settle to the bottom of the pipe and block it. If the density of the flurry is 2000 km m-3 and its viscosity is 0.001 Pa s, what is the minimum velocity the slurry must flow at to ensure it remains turbulent?

A) 2.0 cm s-1.
B) 4.0 cm s-1.
C) 6.0 cm s-1.
D) 12.0 cm s-1.
E) 24.0 cm s-1.ANS

Question 26

A water pipe must deliver at least 10 litres per second to a water tank on a property on the outskirts of a country town. The pipe will have to be 2 km long, and is fed by the town water supply which delivers a pressure difference of 100 000 Pa. What is the minimum radius this pipe needs? The viscosity of water is 0.001 Pa s.

A) 1.0 cm
B) 1.6 cm
C) 3.5 cm
D) 2.7 cm
E) 15 cm
ANS

Question 27

Filtered air is pumped down a tube of diameter 50 cm into a hospital operating theatre. The idea is that a laminar flow over the patient will prevent contamination. What is the maximum safe speed at which the air can be pumped which will ensure that the flow is not turbulent? The density of air is 1.2 kg m-3 and its viscosity is 1.8x10-5 Pa s.

A) 1.2 cm s-1.
B) 3.4 cm s-1.
C) 6.9 cm s-1.
D) 12.0 cm s-1.
E) 23.4 cm s-1.ANS

Question 28

Water flows through a pipe of radius 1 cm and length 1 m. The pressure difference is 100 Pa. What is the rate of flow, in litres per second? The viscosity of water is 0.001 Pa s.

A) 0.39
B) 3.9x10-4
C) 3.1
D) 0.125
E) 390
ANS

Question 29

Imagine that you work at a forensics laboratory and have been asked to identify a strange, highly viscous transparent fluid found at a crime scene. The fluid has a density of 2 g cm-3. To measure the density, you drop a lead sphere of radius 2mm into the fluid, and observe that it drops at a steady speed of 8.1 mm s-1. What is the viscosity of the unknown fluid? You may assume that Stokes' law applies and that g = 9.8 m s-2.

A) 12.1 Pa s
B) 10.0 Pa s
C) 5.7 Pa s
D) 5.0 Pa s
E) 1.0 Pa s
ANS

Question 30

A fountain sends a stream of water 20.0 m up into the air. If the base of the stream is 10.0 cm in diameter, what power is required to send the water to this height?

Question 31

Imagine that you have been given the job of designing a fountain to be the centrepiece of a new shopping mall on the Gold Coast. The fountain will consist of a single upward jet of water, launched from a pipe of radius 5 mm and length 2 m. The pipe is fed by recycled water, pushed by a pump which produces a pressure difference of 100 000 Pa. What volume of water will come out of the pipe? The viscosity of water is 0.001 Pa s.

A) 0.012 m3 s-1.
B) 98 200 m3 s-1.
C) 1.2x1010 m3 s-1.
D) 1.2 m3 s-1.
E) 12 m3 s-1.ANS

Question 32

Honey is around 3000 times more viscous than water, but has a similar density. How much faster could honey flow though a pipe compared to water, while still maintaining a laminar flow?

A) 3000 times
B) 9 000 000 times
C) 55 times
D) It will become turbulent at the same speed, but a much greater pressure difference would be needed to make it flow at that speed
E) It will become turbulent at the same speed, but a much smaller pressure difference would be needed to make it flow at that speed
ANS

Question 33

The water supply to an old suburb in Perth is no longer adequate, and the water company is planning to put in a higher capacity supply. Which of the following options would give the biggest increase in the water flow into the suburb?

A) Re-route the water supply pipeline to a new route that is 13% shorter.
B) Dig up the water supply pipeline and replace it with one that has a 10% larger diameter.
C) Replace the pumps with ones that provide a 15% larger pressure difference.
D) Replace the buried water supply pipeline with one that is on the surface and hence exposed to the sun. The heat from the sun will warm the water and hence reduce its viscosity by around 7%.
E) All the other solutions will have the same results.ANS

Question 34

You have been asked to modify the nozzle of a rocket engine. The existing rocket produces a laminar flow of exhaust gasses, but is not powerful enough to lift a new generation of communication satellites. You have been asked to advise on the best way to increase the thrust without causing the flow to become turbulent. The rocket thrust is proportional to the density of the exhaust, to its velocity, and to the square of the nozzle diameter. What is the best approach?

A) Increase the diameter of the nozzle and decrease the velocity by the same factor.
B) Increase the density of the exhaust and decrease the velocity by the same factor.
C) Increase the velocity of the exhaust and decrease the diameter of the nozzle by the same factor.
D) All the other proposed solutions are feasible.
E) None of the other proposed solutions are feasible.ANS

Question 35

Imagine that you have been given the job of designing a fountain to be the centrepiece of a new shopping mall on the Gold Coast. The fountain will consist of a single upward jet of water, launched from a pipe of radius 4 mm and length 1.5 m. The pipe is fed by recycled water, pushed by a pump which produces a pressure difference of 100 000 Pa. With what speed will the water come out of the pipe? The viscosity of water is 0.001 Pa s.

A) 1.3 m s-1.
B) 4.2 m s-1.
C) 13.3 m s-1.
D) 419 m s-1.
E) 133 m s-1.ANS