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# Computational Fluid Dynamics – Navier Stokes Equation

1 - Question

What are the independent variables in the Navier-Stokes equations?

a) x, y, z, ρ

b) x, y, z, τ

c) x, y, z, t, ρ

d) x, y, z, t

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Answer: dExplanation: There are four independent variables in Navier-Stokes equations. Three spatial variables (x, y, z) and one time variable (t).

2 - Question

What are the dependent variables in the Navier-Stokes equations?

a) τ,T,p,ρ

b) p,ρ,T

c) u,v,w,T,p,ρ

d) u,v,w,T,p

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Answer: cExplanation: There are six dependent variables in the Navier-Stokes equations. They are pressure (p), temperature (T), density (ρ) and three components of the velocity vector (u,v,w).

3 - Question

The Navier-Stokes equations are all partial differential equations. What will be the best reason behind this?

a) Ordinary differentials are not present in the Navier-Stokes equations

b) The dependent variables are functions of all of the independent variables

c) Each dependent variable depends on only one of the independent variables

d) Partial differentials are only present in the Navier-Stokes equations

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Answer: bExplanation: 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.

4 - Question

Turbulence problems particularly depend on this term of the Navier-Stokes equations. Which is that term?

a) Rate of change term

b) Convection term

c) Diffusion term

d) Source term

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Answer: cExplanation: Turbulence is caused by abrupt changes in velocities perpendicular to the flow. This, in turn, can be given in viscosity terms. Diffusion term of the Navier-Stokes equations holds the viscosity terms. So, without diffusion terms, we cannot model turbulence.

5 - Question

The Navier-Stokes equations are ____ system of equations.

a) coupled

b) uncoupled

c) exponential

d) radical

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Answer: aExplanation: Navier-Stokes equations are called a coupled system of equations because all of the equations should be solved to get the dependent variables. Equations cannot be solved separately to get the unknowns.

6 - Question

The diffusion term in the general transport equation is div(Γgradφ). While equating this with the Navier-Stokes equations, what is Γ?

a) k

b) λ

c) μ

d) V⃗

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Answer: cExplanation: The diffusion term in the Navier-stokes equations is div(μ gradu) for the x-momentum equation. Comparing this with the general transport equation, Γ is μ- dynamic viscosity coefficient.

7 - Question

The viscosity terms in x-momentum equation is ∂τxx∂x+∂τyx∂y+∂τzx∂z. In a more general form, this becomes div(μ gradu). Which of these relations is used for this transformation?

a) Thermodynamic relations

b) Stress-strain relations

c) Fluid flow relations

d) Geometric relations

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Answer: bExplanation: Stress-strain relationship states that “the shear stresses are proportional to the gradient of velocities”. This relationship is used for the transformation.

8 - Question

Which is the diffusion terms of the y-momentum equation?

a) ∂τxy∂x+∂τyy∂y+∂τzy∂z

b) ∂τyx∂x+∂τyy∂y+∂τyz∂z

c) ∂τxx∂x+∂τyx∂x+∂τzx∂x

d) ∂τxy∂y+∂τyy∂y+∂τzy∂y

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Answer: aExplanation: ∂τxy∂x+∂τyy∂y+∂τzy∂z are the diffusion terms of the y-momentum equation. It involves all the shear stress tensors which are in the y-direction.

9 - Question

The major difference between the Navier-Stokes equations and the Euler equations is the dissipative transport phenomena. The impact of this phenomena in a system is ____

a) They decrease entropy

b) They increase entropy

c) They increase internal energy

d) They decrease internal energy

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Answer: bExplanation: Dissipation is the process where energy is transformed from one form into another. This transformation increases the entropy of the system.

10 - Question

Diffusion terms are not included in ____ of the Navier-Stokes equations.

a) continuity equation

b) y-momentum equation

c) z-momentum equation

d) energy equation

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Answer: cExplanation: Mass diffusion of the continuity equations are in general not included in the Navier-Stokes equations. This is because most of the fluid flow and thermodynamic processes do not include any change in concentration which is mass diffusion.