Question

Which of these equations represent a Euler equation?

(a) \(\rho\frac{Dv}{Dt}=-\nabla p+\rho g\)

(b) \(\rho\frac{Dv}{Dt}=-\nabla p+\mu\nabla^2 v+\rho g\)

(c) ∇p=μ∇^2v+ρg

(d) 0=μ∇^2v+ρg

The question was asked by my college professor while I was bunking the class.

I need to ask this question from Euler Equation topic in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

The correct answer is (a) \(\rho\frac{Dv}{Dt}=-\nabla p+\rho g\)

The explanation: \(\frac{\rho Dv}{Dt}=-\nabla p+\rho g\) represents a Euler equation. All other equations have this term μ∇^2v representing diffusion.