1. What is meant by;
(i) Streamline flow (1mk)
✓ The flow in which the velocity of the fluid particles at any point is constant as time passes.
... [Show More] A
streamline flow is achieved only when the speed is low
(ii) Turbulent flow (1mk)
✓ The flow in which particles of the fluid flow through a point with different velocities and in
different directions.
2. State Bernoulli’s principle. (1 mk)
✓ Provided that a fluid is non viscous, incompressible and its flow streamline, an increase in velocity
produces a corresponding decrease in pressure
3. State one assumption made in Bernoulli’s fluid flow.
✓ The fluid is incompressible and non-viscous.
4. Give three examples of Bernoulli’s effect in air. (3 mk)
a) Blowing air over a flat paper
When air is blown over a paper, the paper is
observed to rise.
b) Blowing air between two sheets of papers or pith balls
When air is blown between two suspended pith
balls, they are seen to be pushed together.
c) Floating pith ball in a funnel
When a funnel is inverted over a pith ball and air blown in, the pith
ball floats.
5. State any three properties of an ideal fluid that obeys Bernoulli’s principle
(3mk)
✓ Incompressible, non-viscous and with streamline flow.
6. State the equation of continuity. Define any symbols used.(1 mk)
Av =constant.
A is cross sectional area.
V is the velocity of the fluid in the section.
Av is the rate of flow of the fluid in the section.
A1v1=A2v2
A1v1
is The rate of flow the fluid in the first section.
A2v2 Is therate of flowthe fluid in the second section.
7. In deriving the equation of continuity, what three assumptions are made?
a) The fluid has a streamline
flow.
b) The fluid is incompressible.
c) The fluid is nonviscous.
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8. An oil drop of volume V m3
introduced on the surface of water spreads to form a patch whose area is
a m2
. Derive an expression for obtaining the diameter, d of a molecule of oil.
(2mk)
Volume of the oil drop = V m3
Area of the oil patch = a m2
Diameter of the oil molecule, d = Volume of the oil drop
Area of the oil patch
d = V m3
a m2
d = V/am
9. The figure below shows an incompressible fluid flowing through a pipe, A1 and A2 are the crosssectional areas of the pipes in the larger section and smaller section of the pipe respectively, while V1
and V2 are speeds of the fluid at the two sections of the pipe.
Derive an expression for the ratio of the speeds
𝐕𝟐
𝐕𝟏
in terms of A1 and A2
By equation of continuity, A1V1 =A2 V2
V1= A2 V2
A1
Then, replacing V1 in V2 it becomes
V1
V2__
A2 V2
A1 then V2 = A1
V1 A2
10. State how the pressure in a moving fluid varies with speed of the fluid. (2mk)
An increase in its speed produces a corresponding decrease in the pressure it exerts while a
decrease in its speed produces a corresponding increase in pressure.
11. Explain one danger of Bernoulli’s effect (2mks)
✓ Blowing off of roof-tops
The air flowing over a roof-top has a high velocity compared to the one flowing underneath.
Consequently, the pressure acting on the roof from underneath will be higher than that acting from
above. Hence, the roof is blown off.
✓ Road accidents
A small car travelling at a very high velocity is likely to be dragged into a long track travelling in the
opposite direction, also at high speed.
This is because the air between them moves with very high speed, reducing the pressure between
them. The atmospheric pressure acting from the sides of the two vehicles will push them closer
together, increasing chances of an accident.
12. Explain why a fast moving car appear lighter. (1mk)
The air moving above the is moving at higher velocity than the air moving below it thus making
the pressure above less than the pressure below hence the pressure below it tends to push it
upwards making it appear lighter.
A1 V1 A2 V2
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13. A horse rider bends forward when the horse is on speed. Explain.(2mk)
The rider bends forwards so as to try and be streamlined so that he can cut through the air and
reduce air resistance (the eddy currents).
14. Give two examples of devices in which Bernoulli’s effect is applied. (2mk)
i. The Aerofoil
ii. Bunsen burner
iii. Spray gun
iv. The carburetor
15. It is observed that a vehicle which has a door at the rear side gathers more dust inside when moving
at high speed on a dusty road with the door open than the one which has an open door on the side.
Explain this observation (2mk)
✓ The vehicle with the door at the rear side is not streamlined at the back thus experiences
turbulent flow which cause eddies that push dust into the vehicle from the rear area.
16. Water flows in a horizontal smooth pipe. State the changes that would be observed in the nature of
the flow if the speed of the water is steadily increased from low to high value?
✓ The flow of the water changes from being streamlined to turbulent at a particular speed.
17. Two table Tennis balls are in the same level while suspended from threads a short distance apart. A
stream of air is blown between the balls in a horizontal direction. Explain what happens to the balls.
✓ If two balls are held close to each other and air blown between them, the two balls close in
towards each other. The moving air between the balls lowers the pressure it exerts on their
inner surfaces. The higher atmospheric pressure acting on the outside surfaces causes the
balls s to move closer to each other.
18. When spraying a field of water using a hose pipe, it is common to reduce the pipes opening in order
to spray water furthest. Other than pressure, what other quality is varied in the process?
✓ The cross-sectional area of the horse pipe at the outlet.
19. State how the pressure in a moving fluid varies with the speed of the fluid.
An increase in its speed produces a corresponding decrease in the pressure it exerts while a
decrease in its speed produces a corresponding increase in pressure.
20. It is dangerous to stand close to a road when a fast moving lorry passes. Comment on this statement
(1mk)
✓ The air between you and the lorry moves at a high velocity thus reducing the pressure
between you and the lorry hence you may be pulled into the lorry due to the reduced
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