Question

In mathematical terms, how can the divergence of a velocity vector \((\vec{V})\) be represented?

(a) \(\nabla.\vec{V}\)

(b) \(\nabla\vec{V}\)

(c) \(\nabla \times\vec{V}\)

(d) \(\vec{V} \times\nabla\)

The question was posed to me by my college professor while I was bunking the class.

The doubt is from Governing Equations in portion Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct option is (a) \(\nabla.\vec{V}\)

Easiest explanation: \(\nabla.\vec{V}\)represents the divergence of a vector. \(\nabla\vec{V}\) is gradient which is not possible for a vector. \(\nabla \times\vec{V}\) is the curl of a vector. \(\vec{V} \times\nabla\) does not represent any property.