Question

If \(\vec{f}\) is the body force of an infinitesimally small element (volume dx dy dz and density ρ) moving along with the flow (velocity \(\vec{V}\)), Which term is the work done by the body force?

(a) \(\vec{f}.\vec{V}\)dx dy dz

(b) \(\rho\vec{f}.\vec{V}\)

(c) \(\rho\vec{f}.\vec{V}\)dx dy dz

(d) \(\rho\vec{f}\)dx dy dz

The question was posed to me in a job interview.

I want to ask this question from Energy Equation in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct option is (c) \(\rho\vec{f}.\vec{V}\)dx dy dz

To elaborate: mass = density×volume

mass = ρdx dy dz

rate of work done = force×velocity

rate of work done = \(\rho\vec{f}.\vec{V}\)dx dy dz

\(\rho\vec{f}.\vec{V}\)dx dy dz is the work done by the body force.