What does the curl of velocity field give us?

Moment

Angular velocity

Moment of Inertial

Angular acceleration

Correct Answer : Angular velocity

Explanation : If the translation velocity of the fluid particle is given by V, then the angular velocity ω is given as the curl of velocity field. It tells us the measure of rotation for the fluid particle at a particular point.

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Crocco's theorem gives a relation between which of the following?

Entropy and flow velocity

Flow velocity and enthalpy

Gradient of entropy and vorticity

Gradient of angular acceleration and enthalpy

Correct Answer : Option (C) : Gradient of entropy and vorticity

Explanation : According to the Crocco’s theorem, there is a relationship established between vorticity, gradient of enthalpy and gradient of entropy.

V × (∇ × V) = ∇h0 – T∇s

Where, ∇ × V is the vorticity

∇h0 is gradient of total enthalpy

T∇s is gradient of entropy

According to Crocco's theorem, the vorticity behind the curved shockwave is zero.

True

False

Can Not Say

None of the above

Correct Answer : Option (B) : False

Explanation : Across a stationary shock wave, the change in enthalpy is zero therefore ∇s = 0. But for a curved shockwave, the enthalpy does not remain constant making ∇s ≠ 0. This results in V × (∇ × V) ≠ 0 according to the Crocco’s theorem. Therefore the vorticity behind a curved shock wave is not zero and the flow behind the curved shock wave is rotational.

Flow passing through curved shock creates vorticity in the downstream.

True

False

Can Not Say

None of the above

Correct Answer : Option (A) : True

Explanation : A fluid while passing through a curved shock wave, experiences a strong entropy change due to the presence of shock wave. This leads to a rotational fluid causing vorticity behind the shock wave and the gradient in entropy change is non zero.