Question

Consider a small control volume V with the surface dS with a normal vector \(\vec{n}\). This moves in a fluid flow in time Δt into another position at a velocity \(\vec{V}\) (V in the diagram). What is the change in volume of this small control volume ΔV?

(a) \([(\vec{V}\Delta t).\vec{n}]\)

(b) \([(\vec{V}\Delta t).\vec{n}]dS\)

(c) \([(\vec{V}\Delta t)]dS\)

(d) \([(\vec{V}).\vec{n}]dS\)

I had been asked this question in a job interview.

The query is from Governing Equations in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

The correct option is (b) \([(\vec{V}\Delta t).\vec{n}]dS\)

The explanation is: The change in control volume can be calculated as the volume of a cylinder with altitude \((\vec{V}\Delta t).\vec{n}\) (product of velocity and time) and base area dS.