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# Aerodynamics – Area-Velocity Relation

1 - Question

Sonic flow exists at the throat of an equilibrium chemically reacting nozzle flow?

a) True

b) False

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Answer: aExplanation: According to the area-velocity relation for a quasi one-dimensional flow, the relation is given as:

dAA=(M2-1)duu

For sonic flow, Mach number = 1. Therefore for M=1 we get dAA=0, thus sonic flow does exist for an equilibrium reacting nozzle flow at the throat.

2 - Question

For a subsonic flow, what should be the value of dA to get flow acceleration?

a) Zero

b) Negative

c) Positive

d) One

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Answer: bExplanation: According to the area-velocity relation for a quasi one-dimensional flow, when the flow is subsonic Mach number is less than 1 resulting in the quantity M2-1 being negative. Therefore for achieving accelerated flow, dA has to be negative.

3 - Question

For which of these flows do we need a divergent duct to increase the velocity of the flow?

a) Subsonic flow

b) Supersonic flow

c) Hypersonic flow

d) Sonic flow

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Answer: bExplanation: The area-velocity relation is given by: dAA=(M2-1)duu According to this formula, for supersonic flows the value of M2-1 is positive since M > 1. Thus, with increasing cross-sectional area, the velocity increases. Increasing area is achieved by convergent duct.

4 - Question

What happens to the velocity of the supersonic flow in the convergent duct?

a) Decreases

b) Increases

c) Remains the same

d) Changes periodically

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Answer: aExplanation: Since the supersonic flows have Mach number greater than 1, the value of M2-1 is positive. According to the area-velocity relation, for a convergent duct in which dA is negative, the velocity decreases.

5 - Question

What is the minimum area of a duct known as?

a) Throat

b) Minimum area duct

c) Convergent duct

d) Divergent duct

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Answer: aExplanation: In a nozzle which is designed to achieve supersonic speed, there’s both converging and diverging section which is used to accelerate the flow. There is a minimum area point in the duct where Mach number reaches 1. This minimum area place in a duct is known as the throat.

6 - Question

Which equation is obtained when Mach number is equated to zero in area-velocity relation?

a) Momentum equation

b) Continuity equation

c) Energy equation

d) Bernoulli’s equation

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Answer: bExplanation: The area-velocity relation is given by: dAA=(M2-1)duu In the above equation if we substitute M=0 we get, dAA=−duu On integrating this equation we get: Au=constant This is the continuity equation for incompressible flow in a duct

7 - Question

The trends of velocity change in a duct for both subsonic and supersonic flow are identical.

a) True

b) False

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Answer: bExplanation: For a flow in a duct, both supersonic and subsonic flows show opposite trends. For a subsonic flow (M 1), the flow increases in a divergent duct and decreases in the convergent duct.