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# Computational Fluid Dynamics – Euler Equation

1 - Question

The general transport equation is ∂(ρΦ)∂t+div(ρΦu⃗ )+div(ΓgradΦ)+S. For Eulerian equations, which of the variables in the equation becomes zero?

a) Γ

b) ρ

c) Φ

d) u⃗

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Answer: aExplanation: Γ is the diffusion coefficient in the general transport equation. Diffusion of any property is not included in Eulerian equations. So, Γ=0.

2 - Question

Euler equations govern ____________ flows.

a) Viscous adiabatic flows

b) Inviscid flows

c) Adiabatic and inviscid flows

d) Adiabatic flows

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Answer: cExplanation: Euler equations constitute the governing equations of flow for adiabatic and inviscid flows. Here, the dissipative transport of flow properties is neglected.

3 - Question

Which of these is the non-conservative differential form of Eulerian x-momentum equation?

a) ∂(ρu)∂t+∇.(ρuV⃗ )=−∂p∂x+ρfx

b) ρDuDt=−∂p∂x+ρfx

c) (ρu)∂t=−∂p∂x+ρfx

d) ρ∂u∂t=−∂p∂x+ρfx

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Answer: bExplanation: Momentum equation excluding the viscous terms gives the Eulerian momentum equation. This can be given by ρDuDt=−∂p∂x+ρfx

4 - Question

Eulerian equations are suitable for which of these cases?

a) Compressible flows

b) Incompressible flows

c) Compressible flows at high Mach number

d) Incompressible flows at high Mach number

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Answer: dExplanation: Eulerian equations are best suited for examining incompressible flows at high Mach number. They are used to study flow over the whole aircraft.

5 - Question

Euler form of momentum equations does not involve this property.

a) Stress

b) Friction

c) Strain

d) Temperature

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Answer: bExplanation: Euler form of equations is for inviscid flows. For inviscid flows, viscosity is zero. So, there are no friction terms involved.

6 - Question

There is no difference between Navier-Stokes and Euler equations with respect to the continuity equation. Why?

a) Convection term plays the diffusion term’s role

b) Diffusion cannot be removed from the continuity equation

c) Its source term balances the difference

d) The continuity equation by itself has no diffusion term

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Answer: dExplanation: 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

7 - Question

Which of these equations represent a Euler equation?

a) ρDvDt=−∇p+ρg

b) ρDvDt=−∇p+μ∇2v+ρg

c) ∇p=μ∇2v+ρg

d) 0=μ∇2v+ρg

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Answer: aExplanation: ρDvDt=−∇p+ρg represents a Euler equation. All other equations have this term μ∇2v representing diffusion.

8 - Question

Which of the variables in the equation ρDuDt=−∂p∂x+∂τxx∂x+∂τyx∂y+∂τzx∂z+ρfx will become zero for formulating Euler equation?

a) fx, τyx, τzx

b) τxx, τyx, u

c) τxx, τyx, τzx

d) τxx, p, τzx

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Answer: cExplanation: τxx, τyx, τzx represent shear stresses due to viscous effects; u is the x-velocity; fx is the body force and p is the pressure. τxx,τyx,τzx should become zero for the flow to be in-viscid and the equations to be Eulerian.

9 - Question

In Euler form of energy equations, which of these terms is not present?

a) Rate of change of energy

b) Heat radiation

c) Heat source

d) Thermal conductivity

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Answer: dExplanation: As the flow considered by Euler equations is adiabatic, heat cannot enter or exit the system. So, the thermal conduction is omitted.

10 - Question

To which of these flows, the Euler equation is applicable?

a) Couette flow

b) Potential flow

c) Stokes Flow

d) Poiseuille’s flow

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Answer: bExplanation: Among the given flows, only potential flows are in-viscid. So, the Euler equation is applicable to only potential flows among the above.