Question

In the equation, ∇.V=1/ v*D (v)/Dt, the term ∇.V is _________

(a) change in velocity

(b) divergence of velocity

(c) volume

(d) velocity as a function of time

This question was addressed to me during a job interview.

This is a very interesting question from Infinitesimal Fluid Element topic in section Aerodynamics – Fundamental Principles and Equations of Aerodynamics

Answer 1

The correct choice is (b) divergence of velocity

Best explanation: Divergence of velocity is physically the time rate of change of the volume of a moving fluid element per unit volume where v is small volume and because of this small volume, ∇.V is same throughout the volume.  Moving control volume is used for the physical interpretation of the divergence of velocity.