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Correct option is (d) The continuity EQUATION by itself has no DIFFUSION term

The explanation is: Diffusion term, in GENERAL, is given by DIV(ΓgradΦ). For the continuity equation, Φ=1. And grad Φ=0. So, the continuity equation by itself has no diffusion term.

The correct answer is (b) Body forces

Explanation: The effect of SURFACE forces are EXTERNAL. They are not produced inside the body. Body forces are created inside the body of conservation. So, the body FORCE term is the SOURCE term.

The correct option is (c) Mass

To explain I would say: Mass of a control volume moving along with the flow will not vary. It is CONSTANT with time. The volume, shape and velocity of the control volume may not be the same at all POINTS of time.

The correct option is (a) INSTANTANEOUS time and instantaneous POSITION

The best EXPLANATION: Current position and time are the variables on which other variables depend on in Eulerian APPROACH. These are the independent variables.

Right choice is (d) Grouping terms related to control volume

The explanation is: ONE term related to control volume is a volume integral. The other term is a surface integral. To group these two terms together, Gauss Divergence Theorem is USED.

Correct option is (a) ISOLATED system

To explain I WOULD say: The PRINCIPLE of CONSERVATION is applicable only to the systems where there will not be any TRANSFER of matter or energy. Isolated system will have these characters.

The correct ANSWER is (c) When control volume is fixed

To explain: LEIBNIZ rule is APPLICABLE to a system only if a system variable is independent. When control volume is fixed, position of the control volume becomes independent. So, Leibniz rule is applicable only to fixed control VOLUMES.

The correct answer is (c) FIRST law of thermodynamics

Easiest explanation: First law of thermodynamics is the physical principle BEHIND the energy equation. This law STATES that “Energy can neither be produced nor be destroyed but can be converted from one FORM into another”.

Right choice is (a) Both Newtonian and non-Newtonian FLUIDS

Explanation: The ENERGY equation given here is in terms of shear stresses. So, no RESTRICTIONS based on the VISCOSITY of the FLUID. It is applicable to both Newtonian and Non-Newtonian fluids.

The correct choice is (b) POTENTIAL flow

Best explanation: AMONG the given FLOWS, only potential flows are in-viscid. So, the EULER equation is applicable to only potential flows among the above.

Correct CHOICE is (a) Γ

Explanation: Γ is the diffusion COEFFICIENT in the GENERAL TRANSPORT equation. Diffusion of any PROPERTY is not included in Eulerian equations. So, Γ=0.

Correct answer is (c) \(div(\VEC{V})=0\)

The best explanation: TAKING the continuity equation,

\(\frac{\PARTIAL\rho}{\partial t}+\nabla.(\rho \vec{V})=0\)

For incompressible flow, ρ is CONSTANT

\(\frac{\partial\rho}{\partial t}+\nabla.(\rho \vec{V})=0\)

The resulting equation is

\(\nabla.(\rho \vec{V})=0\)

\(\rho\nabla.(\vec{V})=0\)

\(\nabla.(\vec{V})=0\)

Thus, for incompressible flow, divergence of \(\vec{V}=0\).

The CORRECT answer is (d) \(\nabla.(\rho\vec{V})\)dx dy dz

The best I can EXPLAIN: Net MASS flow across the element = change in mass flow in x direction + change in mass flow in y direction + change in mass flow in z direction

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

=\(\left[(\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{k})dx \,dy \,dz.((\rho u)\vec{i} + (\rho v)\vec{j} + (\rho w)\vec{k})\right] \)

Net mass flow across the element = \([\nabla.(\rho \vec{V})]dx \,dy \,dz\).

The correct choice is (d) Convection and diffusion

Best EXPLANATION: Convection and diffusion terms are based on a transfer through the BOUNDARIES. The boundaries of a volume are its surfaces which MAKES surface INTEGRALS ideal for convection and diffusion.

The CORRECT option is (B) time-independent position VECTOR

To elaborate: The tag is time-independent so that the tag does not vary along with the FLOW. Position vector is chosen to follow the parcel along its position.

The correct choice is (a) The property is a function of both time and SPACE

To explain: If a property has SUBSTANTIAL derivative, it is DIFFERENTIABLE by both time and space. This MEANS that it is a function (i.e., dependent on) of time and space.

Correct answer is (b) Flow of fluid is through the CONTROL SURFACES

To elaborate: Fluid can ENTER into or exit from the control VOLUME through the control surface. If this flow velocity is integrated ALONG the control surfaces, we can get the net inflow or outflow of fluid to the control volume.

Correct CHOICE is (a) Heat TRANSFER is DIFFERENT in different directions

Easiest explanation: The statement “Heat transfer is different in different directions” is wrong. K is a scalar means that the heat transfer is the same in all directions and the material is isotropic. For different heat transfers in different directions (ANISOTROPIC material), the proportionality constant should be a tensor.

The CORRECT option is (b) The DEPENDENT variables are FUNCTIONS of all of the independent variables

To elaborate: Each dependent variable in the Navier-Stokes equations depends on all of the independent variables. So, partial differentials are used to indicate that the other independent variables should be kept fixed while DIFFERENTIATING.

Right option is (a) λ=\(-\frac{2}{3}\) μ

Easy explanation: The bulk VISCOSITY COEFFICIENT REPRESENTS fluid COMPRESSIBILITY effects. λ=\(-\frac{2}{3}\) μ is the relationship between the bulk viscosity coefficient and the dynamic viscosity coefficient.

Right option is (c) Dynamic viscosity and BULK viscosity

To explain: The TWO viscosities involved in stress train relationship of fluids is dynamic viscosity COEFFICIENT and bulk viscosity coefficient. Bulk viscosity coefficient for DIAGONAL elements respectively.

The CORRECT answer is (b) Vector

To explain: Stress TENSOR is a square MATRIX given by

Τxy = \(\begin{bmatrix}

\tau_{XX} & \tau_{xy} & \tau_{xz} \\

\tau_{yx} & \tau_{yy} & \tau_{yz} \\

\tau_{zx} & \tau_{zy} & \tau_{zz}

\end{bmatrix}\)

The divergence of this will result in a vector

∇. Τ= \(\begin{bmatrix}

\frac{\partial \tau_{xx}}{\partial x}+\frac{\partial \tau_{yx}}{\partial y}+\frac{\partial \tau_{zx}}{\partial Z} \\

\frac{\partial \tau_{xy}}{\partial x}+\frac{\partial \tau_{yy}}{\partial y}+\frac{\partial \tau_{zy}}{\partial z} \\\frac{\partial \tau_{xz}}{\partial x}+\frac{\partial \tau_{yz}}{\partial y}+\frac{\partial \tau_{zz}}{\partial z}

\end{bmatrix}\)

The correct answer is (d) Rate of change term, diffusive term, CONVECTIVE term, source term

The best explanation: Transport equation involves FOUR terms which are rate of change, DIFFUSION, convection and source of properties.

Right OPTION is (c) LAGRANGIAN

The explanation: In Lagrangian fluid flow specification, the fluid is subdivided into many PARTS and each of this part is followed. These parts are CALLED fluid parcels.

Right option is (C) Conservative EQUATION

To EXPLAIN: A stationary model has its POSITION coordinates independent of time. This gives a conservative equation without any SUBSTANTIAL derivative.

The correct answer is (d) YES, the fluid can thermodynamically adjust itself quickly to be in thermodynamic EQUILIBRIUM

To explain: The velocity of fluid FLOW is very high. This may affect their thermodynamic equilibrium. But, the particles are small ENOUGH to thermodynamically adjust themselves to equilibrium so quickly.