Question

Consider a model of finite control volume (volume V and surface area) fixed in space with elemental volume dV, vector elemental surface area d\(\vec{S}\), density ρ and flow velocity \(\vec{V}\). What is the mass inside the control volume?

(a) \(\iint_s\rho \vec{V}.d\vec{S}\)

(b) \(\iiint_V\rho dV\)

(c) ρdV

(d) \(\frac{\partial}{\partial t} \iiint_V\rho dV\)

The question was asked in an interview.

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

Answer 1

Correct answer is (b) \(\iiint_V\rho dV\)

To elaborate: Mass=density × volume

mass inside dV=ρdV

mass inside \( V=\iiint_V\rho dV\).