Explain — 3 marks
A water treatment plant uses pipes of different diameters to transport water at different stages of the filtration process. Engineers notice that the water flows more slowly through wider pipes and faster through narrower pipes, even though the same volume of water enters and leaves each section per second.
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Explain why the water flows at different speeds in pipes of different diameters.
[1 mark]
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The continuity equation for fluid flow states that A₁v₁ = A₂v₂, where A is the cross-sectional area and v is the velocity. Using this relationship, explain what happens to the velocity when the cross-sectional area of the pipe doubles.
[1 mark]
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At one point in the treatment process, the pipe narrows from a diameter of 10 cm to a diameter of 5 cm. Explain the relationship between the change in pipe diameter and the change in water velocity, using the concept of conservation of mass.
[1 mark]
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Show — 2 marks
A garden hose is used to fill a water tank. When the tap is fully open, water flows quickly out of the hose. When the tap is partially closed, the water flows more slowly.
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Show that the volume of water flowing through the hose depends on both the cross-sectional area of the hose and the speed of the water.
[2 marks]
Show mark scheme
- {'mark': 1, 'description': 'States that volume flow rate equals cross-sectional area multiplied by fluid speed (Q = A × v or equivalent)'}
- {'mark': 1, 'description': 'Explains that increasing either the cross-sectional area OR the speed of water increases the volume of water flowing per unit time'}