Question

Expand divergence of velocity ∇.\(\vec{V}\) for a one-dimensional flow.

(a) \(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\)

(b) \(\frac{\partial u}{\partial x}\)

(c) \(\frac{du}{dx}+\frac{dv}{dy}+\frac{dw}{dz}\)

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

This question was posed to me at a job interview.

My query is from Governing Equations topic in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

The correct option is (b) \(\frac{\partial u}{\partial x}\)

Explanation: Here,

\(\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{k}\)

\(\vec{V}= u\vec{i} +v\vec{j}+w\vec{k}\)

∇.\(\vec{V}=\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\)

For one-dimensional flow,

∇.\(\vec{V}=\frac{\partial u}{\partial x}\).