Aerodynamics - Velocity Potential Equation Quiz(MCQ)

1 .

What happens to the flow which passes through a curved shock wave?

A)

Creates vorticity upstream

B)

Flow passes by undisturbed

C)

Creates vorticity downstream

D)

Flow moves parallel to the curves shock wave

Correct Answer : Creates vorticity downstream

Explanation : When the fluid flows through a curved shock wave, it undergoes a strong entropy change due to the presence of shock wave. This causes the flow to rotate leading to the formation of vorticity in the downstream region of the shock wave.

2 .

Vorticity is thrice as much as the angular velocity.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : False

Explanation : Vorticity of the fluid is given by the formula ∇ × V which is twice as much as the angular velocity of the fluid.
∇ × V = 2ω
Where, ω is the angular velocity of the fluid.

3 .

What is a velocity potential?

A)

∇?

B)

∇ × ?

C)

– ∇ × V

D)

(∇ × V)?

Correct Answer : ∇?

Explaination : The irrotational flow is given by the curl of velocity vector. If we take a gradient of the scalar function, we get zero as a result.
∇ × (∇?) = 0
Thus the velocity potential is described as the scalar function ∇?. It satisfies the Laplace equations as well.

4 .

According to d�Alember�s paradox, what happens when the flow over a body is irrotational?

A)

Results in zero drag

B)

Results in infinite drag

C)

Results in body forces

D)

Results in formation of vortices behind the body

Correct Answer : Results in zero drag

Explanation : In real life scenario, it is impossible to have only irrotational region over the body. The flow comprises of both rotational and irrotational region. According to d’Alember’s paradox, having irrotational and inviscid flow throughout results in zero drag which is impossible in real life hence it’s a paradox.

5 .

What is the value of angular velocity at a point on the solid surface outside the boundary layer where the velocity becomes equal to free stream velocity?

A)

B)

0.5

C)

1

D)

Infinite

Correct Answer : 0

Explaination : When the fluid flows towards a solid surface, there is a boundary layer formation with zero velocity at its surface and as we proceed normally, it increases to finally become equal to the free stream velocity. At this particular point there is no vorticity i.e. the flow is irrotational. For an irrotational flow the angular velocity is zero.

6 .

According to Euler's equation, what happens to the velocity of the inviscid flow if the pressure increases?

A)

No change

B)

Increases

C)

Decreases

D)

Becomes zero

Correct Answer : Decreases

Explanation : According to the Euler, the relation between velocity and pressure for an inviscid fluid is given by dp = – ρVdV. According to the relation, due to the presence of negative sign, when the pressure increases velocity decreases and vice versa. The same concept is also explained using Bernoulli’s principle.

7 .

What is the value of vorticity for a irrotational flow?

A)

ω

B)

2ω

C)

Zero

D)

Infinite

Correct Answer : 2ω

Explaination : Irrotational flow of a fluid is the one in which the curl of velocity of the fluid element is zero. In real life, this signifies that the fluid element does not undergo any circulation and there’s no formation of vortex.

8 .

Which of these scenarios will lead to formation of vorticity?

A)

Flow over a slender body

B)

Flow over a sharp wedge

C)

Two � dimensional nozzle flow

D)

Flow behind curved shock wave

Correct Answer : Flow behind curved shock wave

Explanation : The flow within the boundary layer and behind curved shock wave is a rotational flow as the curl of velocity vector is not equal to zero. But, flow over a wedge, cone, in a two – dimensional nozzle flow and over a slender body is irrotational since the curl of velocity vector is zero.

9 .

For an irrotational flow, what is the relation for the velocity potential?

A)

V = ∇?

B)

V = ∇ × ?

C)

V = -∇ × V

D)

V = (∇ × V)?

Correct Answer : V = ∇?

Explaination : The irrotational flow is given by the curl of velocity vector. If we take a gradient of the scalar function, we get zero as a result.
∇ × (∇?) = 0
Thus, the velocity potential is describing as the scalar function ∇?.

10 .

Which of these equations is satisfied by the velocity potential equation?

A)

Fano�s equation

B)

Laplace equation

C)

Rayleigh equation

D)

Bernoulli�s equation

Correct Answer : Laplace equation

11 .

What is the nature of the flow having a velocity potential?

A)

Viscous

B)

Inviscid

C)

Rotational

D)

Irrotational

Correct Answer : Irrotational

Explanation : For irrotational flow, curl of velocity vector yields zero. In case the curl of any vector is zero i.e.∇ × V = 0, where V is a vector, it is also expressed in the form of ∇ζ where ζ is a scalar function. In case of irrotational flow, velocity potential ? is the scalar function. Hence if the flow has a velocity potential, it automatically implies that it is irrotational.

12 .

If the Laplace equation is satisfied by the velocity potential, then the fluid flows.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : For the fluid to flow, it is essential for the velocity potential ? to satisfy the Laplace equation. If the condition is not met, the fluid does not flow and has zero velocity.

Thus, the condition for the fluid to flow is :