If p and τ are the net pressure and net shear stress acting on an infinitesimally small element (volume dx dy dz) moving along with the flow (velocity \(\vec{V}\)), what is the net work done on the system?(a) \(\rho (\nabla .(p\vec{V} )+\nabla .(τ.\vec{V}))\)(b) \(((p\vec{V})+(\tau.\vec{V}))dx \,dy \,dz\)(c) \(\rho(\nabla.(p\vec{V})+\nabla.(\tau.\vec{V})) dx \,dy \,dz\)(d) \((\nabla .(p)+\nabla.(\tau))dx \,dy \,dz\)I got this question during an online exam.Origin of the question is Energy Equation topic in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

If p and τ are the net pressure and net shear stress acting on an inf

1.	If p and τ are the net pressure and net shear stress acting on an infinitesimally small element (volume dx dy dz) moving along with the flow (velocity \(\vec{V}\)), what is the net work done on the system?(a) \(\rho (\nabla .(p\vec{V} )+\nabla .(τ.\vec{V}))\)(b) \(((p\vec{V})+(\tau.\vec{V}))dx \,dy \,dz\)(c) \(\rho(\nabla.(p\vec{V})+\nabla.(\tau.\vec{V})) dx \,dy \,dz\)(d) \((\nabla .(p)+\nabla.(\tau))dx \,dy \,dz\)I got this question during an online exam.Origin of the question is Energy Equation topic in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» The CORRECT answer is (c) \(\rho(\NABLA.(p\vec{V})+\nabla.(\tau.\vec{V})) dx \,DY \,DZ\) To elaborate: The RATE of work done is power which is the product of force and velocity. This can be represented by \((\nabla.(p\vec{V})+\nabla.(\tau.\vec{V})) dx \,dy \,dz\).

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