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Show
that the Bernoulli’s equation is an alternative statement of the law of
conservation of energy for the motion of fluid flow. Clearly state the
assumptions you have made in your proof. |
6
marks |
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1.5 |
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Assume the fluid flowing in the tube as follows: |
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The fluid is non-viscous. No mechanical energy is converted into internal
energy.
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The fluid is incompressible.
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The fluid is moving with streamlined flow.
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Suppose in a small time interval, Dt,
the mass of fluid transferred is Dm. |
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At position 1,
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At position 2,
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The total work done on the fluid is |
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1 |
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The change in kinetic energy is |
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0.5 |
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The change in gravitational p.e. is |
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0.5 |
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By conservation of energy, the change in k.e.
and p.e. are caused by the work done. |
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1 |
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| b. |
With
the aid of the Bernoulli’s equation, explain how a boat can sail against
the wind by following zig-zag path. |
5
marks |
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2 |
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According to the Bernoulli's equation, when the speed of
flow is high, the pressure is low. |
1 |
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Fig.a shows the sail of a yacht moving against the wind
making a small angle with the wind direction. |
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The windward side of the sail has a faster flow of air
and lower pressure, comparing to the leeward side. |
1 |
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Thus, a propelling force is generated due to the pressure
difference (see Fig.b). |
1 |
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To sail against the wind, a boat must follows a zig-zag
path as shown in Fig.c. |
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| c. |
Describe,
with the help of a labelled diagram, the Pitot tube. Explain how it can
be used to measure the speed of fluid flow. |
5
marks |
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1 |
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A pitot tube consists of a static tube S
and a total tube T. |
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The total tube being filled with liquid stops
the fluid at its mouth. Thus, the speed at the opening of the total tube
is vT = 0. |
0.5 |
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The flow of fluid is unaffected on passing
the mouth of the static tube. The speed of flow is vS = v. |
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Applying the Bernoulli's equation to horizontal
flow, we have |
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The pressure different at the openings of S
and T are indicated by the height of the liquid column: |
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So, the speed of fluid flow is |
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