Boundary Layer Thickness MCQ Quiz - Objective Question with Answer for Boundary Layer Thickness - Download Free PDF

Last updated on May 30, 2025

Latest Boundary Layer Thickness MCQ Objective Questions

Boundary Layer Thickness Question 1:

In incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm, will be

  1. 0.5
  2. 2
  3. 0.25
  4. 4

Answer (Detailed Solution Below)

Option 1 : 0.5

Boundary Layer Thickness Question 1 Detailed Solution

Explanation:

Boundary Layer Thickness in Incompressible Flow

Definition: In fluid dynamics, the boundary layer is the thin region adjacent to a solid surface where the effects of viscosity are significant. For incompressible flow over a flat plate with zero pressure gradient, the boundary layer thickness depends on the Reynolds number and the velocity of the fluid. The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in the flow.

For laminar flow over a flat plate with zero pressure gradient, boundary layer thickness is inversely proportional to the square root of the Reynolds number, i.e.,

δ1Re

Calculation:

Given:

Initial Reynolds number, Re1=1000

Initial boundary layer thickness, δ1=1 mm

Velocity increased by a factor of 4 ⇒ U2=4U1

Reynolds number is directly proportional to velocity, so Re2=4×Re1=4000

Now,

δ2δ1=Re1Re2=10004000=12

δ2=1×12=0.5 mm

Boundary Layer Thickness Question 2:

An incompressible fluid flow over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at location where the Reynolds number is 1000. If the velocity of the fluid alone increased by a factor 4, then the boundary layer thickness at the same location is

  1. 4 mm
  2. 2 mm
  3. 0.25 mm
  4. 0.5 mm

Answer (Detailed Solution Below)

Option 4 : 0.5 mm

Boundary Layer Thickness Question 2 Detailed Solution

Concept: 

For laminar boundary on a flat plate,

The boundary layer thickness at a distance x from leading-edge is given as

δx=5Rexδ=5xρVxμ

⇒ δ1Rex

δ1δ2=Re2Re1

Rex=ρVxμ=Vxν

Re ∝ V

δ1δ2=Re2Re1=V2V1

Calculation:

Given:

δ1 = 1 mm, δ2 = ?, V1 = V, V2 = 4V

δ1δ2=V2V1

1δ2=4VV

1δ2=2

δ2 = 0.5 mm

Boundary Layer Thickness Question 3:

δ*, δE  and θ represents the displacement, Energy and momentum thickness then which of the following relation is correct.

  1. δ* > δE > θ
  2. δ* < δE < θ
  3.  δ* < δE = θ
  4. δ* = δE = θ

Answer (Detailed Solution Below)

Option 1 : δ* > δE > θ

Boundary Layer Thickness Question 3 Detailed Solution

Concept:

In flow over a flat plate, various types of thicknesses are defined for the boundary layer,

(i) Boundary layer thickness (δ): It is defined as the distance from the body surface in which the velocity reaches 99 % of the velocity of the mainstream (U)

(ii) Displacement thickness (δ* or δ+): It is defined as the distance by which the body surface should be shifted in order to compensate for the reduction in mass flow rate on account of boundary layer formation.

The mass flow rate of ideal fluid flow = 0δρudy

The mass flow rate of real fluid flow = 0δρudy

The loss is compensated by displacement layer thickness,

ρδu=0δρudy0δρudy

δ=0δ(1uu)dy

(iii) Momentum thickness (θ): It is defined as the distance from the actual boundary surface such that the momentum flux (momentum transferred per sec) corresponding to mainstream velocity (u) through this distance θ is equal to the deficiency or loss in momentum due to the boundary layer formation.

Given as

θ=0δuu(1uu)dy

(iv) Energy thickness (δE): It is defined as the distance from the actual boundary surface such that the energy flux corresponding to the mainstream velocity u through the distance δis equal to the deficiency or loss of energy due to the boundary layer formation.  

Given as

δE=0δuu(1u2u2)dy

The sequence of the above parameter is given by 

δ > δ* > δ> θ

Boundary Layer Thickness Question 4:

For a liner distribution of velocity profile in the laminar boundary layer on a flat plate given by uU=yδ, the ratio of displacement thickness (δ*) to the boundary layer thickness (δ) is

  1. 15
  2. 12
  3. 13
  4. 14

Answer (Detailed Solution Below)

Option 2 : 12

Boundary Layer Thickness Question 4 Detailed Solution

Concept:

Nominal boundary thickness as δ 

Displacement thickness is given as

δ=oδ(1uU)dy

Calculation:

Given, uu=yδ

δ=oδ(1yδ)dy

δ=δδ2δ2

∴ The ratio of displacement thickness to boundary layer thickness will be ​ = δ2δ=12 

Hence, option 2 is correct.

Boundary Layer Thickness Question 5:

A boundary is known as hydrodyanamically smooth if

  1. kδ=0.3
  2. kδ>0.3
  3. kδ<0.25
  4. kδ=6.0

Answer (Detailed Solution Below)

Option 3 : kδ<0.25

Boundary Layer Thickness Question 5 Detailed Solution

Concept:

Hydro-dynamically smooth:

  • If the average height of irregularities (k) is much lesser than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically smooth.

Hydro-dynamically rough:

  • If the average height of irregularities (k) is much greater than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically rough.
  • According to NIKURDE's Experiment, the boundary is classified as:
  • Hydrodynamically smooth when
  • kδ<0.25
  • Boundary transition condition, when
  • 0.25<kδ<6
  • Hydrodynamically rough when
  • kδ>6
 

Top Boundary Layer Thickness MCQ Objective Questions

The maximum thickness of the boundary layer in a pipe of radius R is

  1. 0
  2. R/2
  3. R
  4. 2R

Answer (Detailed Solution Below)

Option 3 : R

Boundary Layer Thickness Question 6 Detailed Solution

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Explanation:

  • The thickness of the boundary layer represented by δ is arbitrarily defined as that distance from the boundary surface in which the velocity reaches 99% of the velocity of the mainstream.
  • For laminar boundary layers, the boundary layer thickness is proportional to the square root of the distance from the surface. Therefore, the maximum value of the boundary layer thickness occurs at the surface, where the distance is zero.

  • The maximum thickness of the boundary layer in a pipe of radius R is R.

  • For turbulent boundary layers, the boundary layer thickness grows more quickly, but it still has a maximum value of about R/2. This is because, at this point, the turbulence intensity is such that the momentum diffusing effect of the turbulent fluctuations balances the momentum loss due to viscous effects, resulting in a maximum velocity gradient at the edge of the boundary layer.

FM Reported 18Auggg

A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinematic viscosity, v = 30 × 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is _________

Answer (Detailed Solution Below) 5.90 - 6.25

Boundary Layer Thickness Question 7 Detailed Solution

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Concept:

Since in question not any velocity profile is given so we will use Blasius equation.

Calculation:

 Pr = 1, T = 500 K, L = 1.5 m, T = 300 K

(Pr)13=δhyδthδhyδth=1

∴ δhy = δth

Re=ρVDμ=VDv=10×0.530×106=1.66×105 

∵ Re ≤ 5 × 105

∴ Flow is laminar flow

∴ Blasius equation for laminar flow

δhy=5xRex=5×0.51.66×105×1000mm 

δhy = 6.12 mm

δhy = δth = 6.12 mm

Mistake Point: While calculating Reynold number. Calculate the Reynold no. at a point at which hydrodynamic boundary length is required.

A boundary is known as hydrodynamically smooth if: 

  1. Kδ=0.3
  2. Kδ>0.3
  3. Kδ<0.25
  4. Kδ=0.5

Answer (Detailed Solution Below)

Option 3 : Kδ<0.25

Boundary Layer Thickness Question 8 Detailed Solution

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Concept:

Hydro-dynamically smooth:

  • If the average height of irregularities (k) is much lesser than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically smooth.

Hydro-dynamically rough:

  • If the average height of irregularities (k) is much greater than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically rough.
  • According to NIKURDE's Experiment, the boundary is classified as:
  • Hydrodynamically smooth when
  • kδ<0.25
  • Boundary transition condition, when
  • 0.25<kδ<6
  • Hydrodynamically rough when
  • kδ>6

The nominal thickness of the boundary layer is defined when the velocity reaches the velocity of the free stream by

  1. 90%
  2. 99%
  3. 95%
  4. 97%

Answer (Detailed Solution Below)

Option 2 : 99%

Boundary Layer Thickness Question 9 Detailed Solution

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Explanation:

Boundary layer:

When a real fluid flows past a solid body or a solid wall, the fluid particles adhere to the boundary and the condition of no-slip occurs i.e velocity of fluid will be the same as that of the boundary.

Farther away from the boundary, the velocity will be higher and as a result of this variation, the velocity gradient will exist.

Boundary-Layer Thickness:

It is defined as the distance from the boundary of the solid body measured in the perpendicular direction to the point where the velocity of the fluid is approximately equal to 99% or 0.99 times the free stream velocity (U). It s denoted by the symbol (δ).

F2 A.M Madhu 06.05.20 D4

The velocity profile inside the boundary layer for flow over a flat plate is given as uu=sin(π2yδ),Where U is the free stream velocity, δ is the local boundary layer thickness. If δ* is the local displacement thickness, the value of  δδ is

  1. 2π
  2. 12π
  3. 1+2π
  4. 0

Answer (Detailed Solution Below)

Option 2 : 12π

Boundary Layer Thickness Question 10 Detailed Solution

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Concept:

Displacement thickness is given by

δ=0δ(1uU)dy

Where,

u – velocity of the fluid

U - Free stream velocity

Calculations:

Given:

uu=sin(xy2δ)

DisplacementThicknessδ=0δ(1uu)dy

δ=0δ(1sinπy2δ)dy

δ=[y+cosπy2δπ2δ]0δ

δ=δ+2δπ(0)02δπ

δ=δ2δπδδ=12π

The thickness of laminar boundary layer at a distance 'x' from the leading edge over a flat plate varies as:

  1. x12
  2. x13
  3. x12
  4. x

Answer (Detailed Solution Below)

Option 3 : x12

Boundary Layer Thickness Question 11 Detailed Solution

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Thickness of Laminar Boundary layer:

δ=5xRex

Where,

x = distance from the leading edge

Rex = local Reynold's Number = Rex=ρVxμ=Vxν

where, ρ = density of fluid in kg/m3, V = average velocity in m/s

μ = dynamic viscosity in N-s/m2 and ν = kinematic viscosity in m2/s.

δ=5xρVxμxx thus, δ ∝ x1/2

Consider the laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is _______

Answer (Detailed Solution Below) 13.6 - 14.1

Boundary Layer Thickness Question 12 Detailed Solution

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Explanation:

For laminar flow over a flat plate

Blausius equation is:

δx=5(Rex)12δx=5(ρVxμ)12

δx=constantx {∴ δ, v & μ are constant}

δx=constantδ1x1=δ2x2δ2=x2x1δ1δ2=0.750.25×8

⇒ δ2 = 13.86 mm

A fluid is flowing over a flat plate. At a distance of 8 cm from the leading edge, the Reynolds number is found to be 25600. The thickness of the boundary layer at this point is

  1. 1.5 mm
  2. 2.5 mm
  3. 4.0 mm
  4. 5.0 mm

Answer (Detailed Solution Below)

Option 2 : 2.5 mm

Boundary Layer Thickness Question 13 Detailed Solution

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Concept:

The thickness of the boundary layer is given by δ=5xRex

For turbulent flow delta=0.379xRe15

Where δ = Boundary layer thickness, x = Distance of boundary layer from the leading edge, Rex = Reynold’s number at the distance x from the leading edge

Calculation:

Given:

Since in this given case, Reynold’s number is 25600 which is much lesser than the limit for laminar flow (2 × 105), so the flow is laminar.

 x = 8 cm = 0.08 m

δ=5xRex=5×0.0825600=0.4160=1400=0.0025m=2.5mm

An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be

  1. 4
  2. 2
  3. 0.5
  4. 0.25

Answer (Detailed Solution Below)

Option 3 : 0.5

Boundary Layer Thickness Question 14 Detailed Solution

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Concept:

According to the Blasius equation, for a laminar flow

Boundary layer thickness (δ) can be calculated by:

δ=5xRex

where Rex = Reynold's number = ρVxμ {V = Velocity}

δ1V

Calculation:

Given:

δ1 = 1 mm, V2 = 4V1

As,δ1V

δ1δ2=V2V1

1δ2=41=2

 δ2 = 0.5 mm

In incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm, will be

  1. 0.5
  2. 2
  3. 0.25
  4. 4

Answer (Detailed Solution Below)

Option 1 : 0.5

Boundary Layer Thickness Question 15 Detailed Solution

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Explanation:

Boundary Layer Thickness in Incompressible Flow

Definition: In fluid dynamics, the boundary layer is the thin region adjacent to a solid surface where the effects of viscosity are significant. For incompressible flow over a flat plate with zero pressure gradient, the boundary layer thickness depends on the Reynolds number and the velocity of the fluid. The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in the flow.

For laminar flow over a flat plate with zero pressure gradient, boundary layer thickness is inversely proportional to the square root of the Reynolds number, i.e.,

δ1Re

Calculation:

Given:

Initial Reynolds number, Re1=1000

Initial boundary layer thickness, δ1=1 mm

Velocity increased by a factor of 4 ⇒ U2=4U1

Reynolds number is directly proportional to velocity, so Re2=4×Re1=4000

Now,

δ2δ1=Re1Re2=10004000=12

δ2=1×12=0.5 mm

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