Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz with mass δ m and volume δ V) moving along with the flow with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). What is the time rate of change of mass of this element?(a) \(\frac{D(\rho \delta V)}{Dt}\)(b) \(\frac{\partial(\rho \delta m)}{\partial t}\)(c) \(\frac{\partial(\rho \delta V)}{\partial t}\)(d) \(\frac{D(\rho \delta m)}{Dt}\)I got this question in examination.This is a very interesting question from Continuity Equation in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Consider an infinitesimally small fluid element with density ρ (of di

1.	Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz with mass δ m and volume δ V) moving along with the flow with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). What is the time rate of change of mass of this element?(a) \(\frac{D(\rho \delta V)}{Dt}\)(b) \(\frac{\partial(\rho \delta m)}{\partial t}\)(c) \(\frac{\partial(\rho \delta V)}{\partial t}\)(d) \(\frac{D(\rho \delta m)}{Dt}\)I got this question in examination.This is a very interesting question from Continuity Equation in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» RIGHT answer is (a) \(\frac{D(\RHO \delta V)}{Dt}\) EASIEST explanation: Substantial derivative is used as the model is moving. mass = ρ δ V time rate of CHANGE of mass=\(\frac{D(\rho \delta V)}{Dt}\)

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