Exam 14: Fluid Dynamics

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.

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 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 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 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 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.

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.

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?

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?

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?

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.

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.

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 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 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 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?

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?

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?

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