Engineering Questions with Answers - Multiple Choice Questions
MCQs on Irrotational Flow
What happens to the flow which passes through a curved shock wave?
a) Creates vorticity downstream
b) Creates vorticity upstream
c) Flow passes by undisturbed
d) Flow moves parallel to the curves shock wave
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.
Which of these equations represent vorticity?
b) ∇ × V
d) (∇.V) × V
Explanation: Vorticity represents the circulation motion of the fluid as it flows. It is given by the curl of the velocity vector (∇ × V). The curl operation determines the circulatory nature. For an irrotational flow vorticity is not equal to zero.
Vorticity is thrice as much as the angular velocity.
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.
What is the value of vorticity for a irrotational flow?
Explanation: 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.
Which of these scenarios will lead to formation of vorticity?
a) Flow behind curved shock wave
b) Flow over a sharp wedge
c) Two – dimensional nozzle flow
d) Flow over a slender body
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.
The special form of Euler’s equation dp = – ρVdV is applicable for rotational flow.
Explanation: The special form of Euler’s equation dp = – ρVdV is applicable for irrotational flow which is derived by adding the x, y, z components of the Euler’s equation for irrotational condition. This would be applicable for rotational flow only along a streamline.
According to Euler’s equation, what happens to the velocity of the inviscid flow if the pressure increases?
a) No change
d) Becomes zero
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.
Which of these conditions is not met at a point for irrotational flow?
Explanation: The Cartesian form of irrotational flow is given by:
∇ × V = ∣∣∣∣∣i∂∂xuj∂∂yvk∂∂zw∣∣∣∣∣
On expanding this we get,
i(∂w∂y–∂v∂z) – j(∂w∂x–∂u∂z) + k(∂v∂x–∂u∂y) = 0
For irrotational flow since vorticity = 0, ∇ × V = 0
∂w∂y=∂v∂z and ∂w∂x=∂u∂z and ∂v∂x=∂u∂y
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?
Explanation: 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.
According to d’Alember’s paradox, what happens when the flow over a body is irrotational?
a) Results in infinite drag
b) Results in zero drag
c) Results in formation of vortices behind the body
d) Results in body forces
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.
What is a velocity potential?
a) ∇ × ϕ
c) – ∇ × V
d) (∇ × V)ϕ
Explanation: 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.
∇ × (∇ϕ) = 0
Thus the velocity potential is described as the scalar function ∇ϕ. It satisfies the Laplace equations as well.