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# MCQs on Boundary Layer Properties

Which of these is not a property of boundary layer?

a) No – slip condition at the surface

b) Temperature of fluid at the surface is equal to wall temperature

c) Flow velocity increases along y – direction

d) Thermal boundary layer is equal to velocity boundary layer

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d

Explanation: When there’s a viscous flow over a flat plate, there’s a boundary layer formation which has certain properties. On the surface, there’s a no slip condition. Apart from this the temperature of the fluid which is immediately at the surface has the same temperature as the surface which is known as the wall temperature. The velocity profile inside a boundary layer increases along the y – direction until it becomes equal to the freestream velocity. The only property that is incorrect is that the thermal boundary layer is equal to the velocity boundary layer.

The boundary of thermal layer is defined as the layer where the outer edge temperature becomes equal to the freestream temperature. Similarly, at the velocity boundary layer, the outer edge velocity is equal to the freestream velocity.

How is the boundary layer thickness defined? (ue is the outer edge velocity)

a) u = 0.99ue

b) u = 0.89ue

c) u = 0.90ue

d) u = 0.50ue

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a

Explanation: Inside the boundary layer, the velocity increases along the y – direction until it becomes equal to the freestream velocity. The thickness of boundary layer δ is defined as the point from the surface where the velocity is 0.99 times the free stream velocity.

What is the thermal boundary layer?

a) T = 0.90Te

b) T = 0.89Te

c) T = 0.99Te

d) T = 0.97Te

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c

Explanation: The flow temperature just like velocity varies within the boundary layer. It is a function of y – direction. The temperature ranges from Tw which is the temperature at the wall (y = 0) to T = 0.99Te at y = δt, where δt is the thermal boundary layer thickness. This variation of temperature is known as temperature profile.

In which case are the velocity and thermal boundary layer equal?

a) Pr = 0

b) Pr = 1

c) Pr > 1

d) Pr < 1

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b

Explanation: In most of the cases the two thermal and velocity boundary layers are not same except in one exceptional case when the Prandtl number = 1, in which case δt = δ. When Prandtl number is greater than 1, δt < δ and when Prandtl number is less than 1, δt > δ. In real life scenario, the Prandtl number is equal to 0.71 thus the thermal boundary layer thickness is greater than the velocity boundary layer thickness.

The displacement thickness is the distance by which, due to the presence of the boundary layer, the flow streamline is displaced.

a) True

b) False

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a

Explanation: Displacement thickness is one of the properties of boundary layer which is the distance by which the external streamline gets displaced due to the presence of the boundary layer.

Without the presence of boundary layer, which is the case of inviscid flow, the streamline would be straight and parallel to the flat surface. But due to the presence of boundary layer in real life scenario having viscous flow, the streamline is displaced.

The formula for the displacement thickness δ* is given by:

δ* = ∫y10(1 – ρuρeue)dy

Which of these relations is applicable for turbulent and laminar boundary layer?

a) δTturbulent < δTlaminar

b) δTturbulent = δTlaminar

c) δturbulent < δlaminar d) δturbulent > δlaminar

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d

Explanation: In case of turbulent flow, there is a high energy and momentum exchange compared to the laminar flow due to the presence of eddies. This leads to the thermal and velocity boundary layer thickness of the turbulent flow to be higher than that of the laminar flow. Thus, δturbulent > δlaminar and δTturbulent > δTlaminar.

According to the y – momentum equation, how does the pressure vary inside the boundary layer normal in the direction normal to the surface?

a) Increases

b) Decreases

c) Remains constant

d) First increases then decreases

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c

Explanation: The y – momentum equation for a boundary layer is given by:

∂p∂y = 0

According to the formula, at any x point in the boundary layer, pressure remains constant in the direction normal to the surface.

When there’s flow over a flat plate, there’s laminar boundary layer at the leading edge followed by turbulent boundary layer.

a) True

b) False

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a

Explanation: When a flat plate is kept in the freestream flow, there’s a formation of a laminar boundary layer at the leading edge. This boundary layer thickness grows to a point where a transition point is reached. Beyond that point, there’s turbulence due to the presence of eddies and there’s turbulent boundary layer formation whose thickness keeps on increasing.

When the Reynolds number approaches infinity, what happens to the boundary layer thickness?

a) Approaches infinity

b) Approaches zero

c) Approaches once

d) Remains same

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b

Explanation: As the Reynolds number increases, the boundary layer thickness decreases when compared to the length of the body. Usually for very large aircrafts, the value of δL is around 0.01 which is a very small value. So hypothetically, as Re ➔ ∞, δ ➔ 0.

What is the value of kinetic energy thickness?

a) δ** = ∫∞0uUe[1 – (uUe)2]dy

b) δ** = ∫∞0uUe[1 – uUe]dy

c) δ** = ∫∞0[1 – uUe]dy

d) δ** = ∫∞0uUe[1 + uUe]dy

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a

Explanation: Kinetic energy thickness is the distance the boundary is displaced by in the perpendicular direction to compensate for the reduced kinetic energy of the fluid due to the formation of boundary layer. It is given by:

δ** = ∫∞0uUe[1 – (uUe)2]dy

Where, u is velocity at some point x on the plate.

Ue is the freestream velocity.

What is the equation for momentum thickness?

a) δ* = ∫∞0uUe[1 – (uUe)2]dy

b) δ* = ∫∞0uUe[1 – uUe]dy

c) δ* = ∫∞0[1 – uUe]dy

d) δ* = ∫∞0uUe[1 + uUe]dy

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b

Explanation: Within the boundary layer, momentum thickness is described in relation to the momentum flow rate. This rate is lower than that which would occur if there were no boundary layer, when the velocity would be equal to the mainstream velocity Ue in the vicinity of the surface considered at the station.

It is given by:

δ* = ∫∞0uUe[1 – uUe]dy

Where, u is velocity at some point x on the plate

Ue is the freestream velocity.

What leads to shear stress between the adjacent layers of fluid inside the boundary layer adjacent to the surface?

a) Aerodynamics drag

b) Viscosity

c) Pressure drag

d) Wave drag

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b

Explanation: There is shear stress between the adjacent layers of fluid in both laminar and turbulent flow inside the boundary layer. This is due to the viscosity and it is given by the relation:

τ = μ∂u∂y

Where, ∂u∂y is the transverse victory gradient.