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

I am using an infinitesimally small element of fluid moving along with

1.	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» 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 \(a_x=\frac{Du}{Dt}\).

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