Question

The differential form of continuity equation is __________

(a) ∇.u=constant

(b) Dv/Dt=0

(c) ρ/t + ∇.(ρV)=0

(d) ρ=0

This question was posed to me in final exam.

My query is from Continuity Equation in section Aerodynamics – Fundamental Principles and Equations of Aerodynamics

Answer 1

The correct option is (c) ρ/t + ∇.(ρV)=0

Explanation: ρ-density V-velocity vector t-time

The divergence represents the inflow and outflow whereas the time derivative represents the accumulation of mass inside a body. It states that the amount of mass entering the body is equal to the amount of mass leaving the body.