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.
Correct Answer : Relationship between fluid and thermodynamic properties
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
Explanation : Vorticity is a measure of tendency of the fluid particle to rotate. It is given by :∇ × VThe value of vorticity is twice as much as the angular velocity whose formula is :ω = 1/2 ∇ × V
Correct Answer : 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.
Correct Answer : 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.
Correct Answer : 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∇sWhere, ∇ × V is the vorticity∇h0 is gradient of total enthalpyT∇s is gradient of entropy
