Engineering Questions with Answers - Multiple Choice Questions

# MCQs on Area-Velocity Relation

1 - Question

Sonic flow exists at the throat of an equilibrium chemically reacting nozzle flow?
a) True
b) False

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.

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

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.

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

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.

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

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.

5 - Question

What is the minimum area of a duct known as?
a) Throat
b) Minimum area duct
c) Convergent duct
d) Divergent duct

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.

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

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

7 - Question

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