Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz) fixed in space and fluid is moving across this element with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). What is the final reduced form of net mass flow across the fluid element?

\(\frac{\partial\rho}{\partial t}\)

\(\nabla.(\rho\vec{V})\)dx dy dz

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) fixed in space and fluid is moving across this element with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). What is the final reduced form of net mass flow across the fluid element?
A.	\(\frac{\partial\rho}{\partial t}\)
B.	\(\rho\vec{V} dx \,dy \,dz\)
C.	\(\nabla.(\rho\vec{V})\)
D.	\(\nabla.(\rho\vec{V})\)dx dy dz
Answer» E.

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Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz) fixed in space and fluid is moving across this element with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). What is the final reduced form of net mass flow across the fluid element?

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