Question

How is the substantial derivative of velocity vector denoted?

(a) \(\frac{D\vec{V}}{Dt}\)

(b) \(\frac{d\vec{V}}{dt}\)

(c) \(\frac{\partial \vec{V}}{\partial t}\)

(d) \(\frac{D\vec{V}}{Dx}\)

The question was posed to me in an interview for internship.

The query is from Governing Equations topic in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

The correct choice is (a) \(\frac{D\vec{V}}{Dt}\)

For explanation: \(\frac{D\vec{V}}{Dt}\) is the substantial derivative. \(\frac{d\vec{V}}{dt}\) is the local derivative. \(\frac{\partial \vec{V}}{\partial t}\) is the partial derivative.