Question

I am using an infinitesimally small element of fluid moving along with the flow as my model. What is the acceleration of this model in x-direction?

(a) \(a_x=\frac{D\vec{V}}{Dt}\)

(b) \(a_x=\frac{\partial \vec{V}}{\partial t}\)

(c) \(a_x=\frac{Du}{Dt}\)

(d) \(a_x=\frac{\partial u}{\partial t}\)

This question was addressed to me at a job interview.

The question is from Momentum Equation in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Right option is (c) \(a_x=\frac{Du}{Dt}\)

Easy explanation: Acceleration is the rate of change of velocity. Acceleration in the x-direction is the rate of change of velocity in x-direction (u). As the model is moving, rate of change is given by substantial derivative. Thus the acceleration in x-direction is \(a_x=\frac{Du}{Dt}\).