\(\frac{\partial(\rho\hat{u})}{\partial t}+\nabla.(\rho\vec{V}\hat{u}) = -\nabla.\dot{q_s}-p\nabla.\vec{V}-\tau:\nabla\vec{V}+\dot{q_v}\). This form of the energy equation is applicable to _________

Both Newtonian and non-Newtonian fluids

Let \(\hat{u}\) be the specific internal energy of a system moving along with the flow with a velocity \(\vec{V}\). What is the time rate of change of the total energy of the system per unit mass?

\(\hat{u}+\frac{1}{2}\vec{V}.\vec{V}\)

\(\frac{D}{Dt}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)

\(\frac{\partial}{\partial t}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)

\(\frac{D}{Dt}(\hat{u}+\vec{V}.\vec{V})\)

If \(\vec{f}\) is the body force of an infinitesimally small element (volume dx dy dz and density ρ) moving along with the flow (velocity \(\vec{V}\)), Which term is the work done by the body force?

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

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?

\(\rho (\nabla .(p\vec{V} )+\nabla .(τ.\vec{V}))\)

\(((p\vec{V})+(\tau.\vec{V}))dx \,dy \,dz\)

\(\rho(\nabla.(p\vec{V})+\nabla.(\tau.\vec{V})) dx \,dy \,dz\)

\((\nabla .(p)+\nabla.(\tau))dx \,dy \,dz\)

Explore topic-wise MCQs in Computational Fluid Dynamics Questions and Answers.

This section includes 4 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.	\(\frac{\partial(\rho\hat{u})}{\partial t}+\nabla.(\rho\vec{V}\hat{u}) = -\nabla.\dot{q_s}-p\nabla.\vec{V}-\tau:\nabla\vec{V}+\dot{q_v}\). This form of the energy equation is applicable to _________
A.	Both Newtonian and non-Newtonian fluids
B.	Newtonian fluids
C.	Non-Newtonian fluids
D.	Pseudo-plastics
Answer» B. Newtonian fluids

Discussion

2.	Let \(\hat{u}\) be the specific internal energy of a system moving along with the flow with a velocity \(\vec{V}\). What is the time rate of change of the total energy of the system per unit mass?
A.	\(\hat{u}+\frac{1}{2}\vec{V}.\vec{V}\)
B.	\(\frac{D}{Dt}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)
C.	\(\frac{\partial}{\partial t}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)
D.	\(\frac{D}{Dt}(\hat{u}+\vec{V}.\vec{V})\)
Answer» C. \(\frac{\partial}{\partial t}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)

Discussion

3.	If \(\vec{f}\) is the body force of an infinitesimally small element (volume dx dy dz and density ρ) moving along with the flow (velocity \(\vec{V}\)), Which term is the work done by the body force?
A.	\(\vec{f}.\vec{V}\)dx dy dz
B.	\(\rho\vec{f}.\vec{V}\)
C.	\(\rho\vec{f}.\vec{V}\)dx dy dz
D.	\(\rho\vec{f}\)dx dy dz
Answer» D. \(\rho\vec{f}\)dx dy dz

Discussion

4.	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.	\((\nabla .(p)+\nabla.(\tau))dx \,dy \,dz\)
Answer» D. \((\nabla .(p)+\nabla.(\tau))dx \,dy \,dz\)

Discussion