Correct Answer :   Angular velocity

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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.

Correct Answer :   Relationship between fluid and thermodynamic properties

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Explanation : Crocco’s theorem was established by Luigi Crocco who found a relationship between vorticity, velocity and stagnation pressure of the fluid which is a kinematic property and the thermodynamic properties.

Correct Answer :   Twice of angular velocity

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Explanation : Vorticity is a measure of tendency of the fluid particle to rotate. It is given by :

∇ × V

The value of vorticity is twice as much as the angular velocity whose formula is :

ω = 1/2 ∇ × V

Correct Answer :   True

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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.

Correct Answer :   False

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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.

Correct Answer :   Gradient of entropy and vorticity

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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