Question

Why a surface integral is used to represent flow of B into and out of the control volume?

(a) Control volume is moving

(b) Flow of fluid is through the control surfaces

(c) Fluid only on the control surfaces

(d) Control volume is stationary

This question was addressed to me in an online interview.

This intriguing question comes from Governing Equations topic in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct answer is (b) Flow of fluid is through the control surfaces

To elaborate: Fluid can enter into or exit from the control volume through the control surface. If this flow velocity is integrated along the control surfaces, we can get the net inflow or outflow of fluid to the control volume.