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 \(\vec{V} = u\vec{i} + v\vec{j} + w\vec{k}\). The rate of change in mass of the fluid element is given by ____________

\(\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}\)

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

\(\frac{\partial\rho}{\partial t}(dx \,dy \,dz) \)

\([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]dx \,dy \,dz\)

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 \(\vec{V} = u\vec{i} + v\vec{j} + w\vec{k}\). The rate of change in mass of the fluid element is given by ____________
A.	\(\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}\)
B.	\(\frac{\partial \rho}{\partial t}\)
C.	\(\frac{\partial\rho}{\partial t}(dx \,dy \,dz) \)
D.	\([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]dx \,dy \,dz\)
Answer» D.

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