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# MCQs on Area-Velocity Relation

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

a) True

b) False

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a

Explanation: 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.

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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b

Explanation: 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.

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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b

Explanation: 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.

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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a

Explanation: 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.

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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a

Explanation: 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.

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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b

Explanation: 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

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

a) True

b) False

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b

Explanation: For a flow in a duct, both supersonic and subsonic flows show opposite trends. For a subsonic flow (M < 1), the velocity increases in a convergent duct and decreases in the divergent duct. On the other hand, for a supersonic flow (M > 1), the flow increases in a divergent duct and decreases in the convergent duct.