Question

Which of these is the non-conservative differential form of Eulerian x-momentum equation?

(a) \(\frac{\partial(\rho u)}{\partial t}+\nabla.(\rho u\vec{V})=-\frac{\partial p}{\partial x}+\rho f_x\)

(b) \(\rho\frac{Du}{Dt}=-\frac{\partial p}{\partial x}+\rho f_x\)

(c) \(\frac{(\rho u)}{\partial t}=-\frac{\partial p}{\partial x}+\rho f_x\)

(d) \(\rho \frac{\partial u}{\partial t}=-\frac{\partial p}{\partial x}+\rho f_x\)

This question was posed to me during an internship interview.

The query is from Euler Equation in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Right answer is (b) \(\rho\frac{Du}{Dt}=-\frac{\partial p}{\partial x}+\rho f_x\)

To elaborate: Momentum equation excluding the viscous terms gives the Eulerian momentum equation. This can be given by \(\rho\frac{Du}{Dt}=-\frac{\partial p}{\partial x}+\rho f_x\).