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A n 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
- a)4
- b)2
- c)0.5
- d)0.25
Correct answer is option 'C'. Can you explain this answer?
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Given Information:
- Incompressible fluid flows over a flat plate.
- Zero pressure gradient.
- Boundary layer thickness = 1 mm.
- Reynolds number = 1000.
- Velocity of the fluid is increased by a factor of 4.
Objective:
To find the new boundary layer thickness at the same location when the velocity is increased by a factor of 4.
Solution:
The boundary layer thickness in a laminar boundary layer is given by the Blasius equation:
δ = 5.0 * x / √(Re_x)
Where,
- δ is the boundary layer thickness,
- x is the distance along the plate,
- Re_x is the Reynolds number at that location.
Given that the boundary layer thickness is 1 mm at a location where the Reynolds number is 1000, we can substitute these values into the equation to find the distance along the plate (x).
1 = 5.0 * x / √(1000)
√(1000) = 5.0 * x
31.62 = 5.0 * x
x = 31.62 / 5.0
x = 6.32 mm
When the velocity of the fluid alone is increased by a factor of 4:
The Reynolds number is given by:
Re = ρ * V * L / μ
Where,
- ρ is the density of the fluid,
- V is the velocity of the fluid,
- L is a characteristic length,
- μ is the dynamic viscosity of the fluid.
Since the fluid is incompressible and the pressure gradient is zero, the dynamic viscosity remains constant. Therefore, the Reynolds number is directly proportional to the velocity (V).
When the velocity is increased by a factor of 4, the Reynolds number also increases by the same factor.
Re_new = 4 * Re_old = 4 * 1000 = 4000
We can now use this new Reynolds number to find the new boundary layer thickness (δ_new) at the same location (x = 6.32 mm) by rearranging the Blasius equation:
δ_new = 5.0 * x / √(Re_new)
= 5.0 * 6.32 / √(4000)
= 31.6 / 63.24
≈ 0.5 mm
Therefore, the boundary layer thickness at the same location, when the velocity of the fluid alone is increased by a factor of 4, will be approximately 0.5 mm. Hence, option C is the correct answer.
- Incompressible fluid flows over a flat plate.
- Zero pressure gradient.
- Boundary layer thickness = 1 mm.
- Reynolds number = 1000.
- Velocity of the fluid is increased by a factor of 4.
Objective:
To find the new boundary layer thickness at the same location when the velocity is increased by a factor of 4.
Solution:
The boundary layer thickness in a laminar boundary layer is given by the Blasius equation:
δ = 5.0 * x / √(Re_x)
Where,
- δ is the boundary layer thickness,
- x is the distance along the plate,
- Re_x is the Reynolds number at that location.
Given that the boundary layer thickness is 1 mm at a location where the Reynolds number is 1000, we can substitute these values into the equation to find the distance along the plate (x).
1 = 5.0 * x / √(1000)
√(1000) = 5.0 * x
31.62 = 5.0 * x
x = 31.62 / 5.0
x = 6.32 mm
When the velocity of the fluid alone is increased by a factor of 4:
The Reynolds number is given by:
Re = ρ * V * L / μ
Where,
- ρ is the density of the fluid,
- V is the velocity of the fluid,
- L is a characteristic length,
- μ is the dynamic viscosity of the fluid.
Since the fluid is incompressible and the pressure gradient is zero, the dynamic viscosity remains constant. Therefore, the Reynolds number is directly proportional to the velocity (V).
When the velocity is increased by a factor of 4, the Reynolds number also increases by the same factor.
Re_new = 4 * Re_old = 4 * 1000 = 4000
We can now use this new Reynolds number to find the new boundary layer thickness (δ_new) at the same location (x = 6.32 mm) by rearranging the Blasius equation:
δ_new = 5.0 * x / √(Re_new)
= 5.0 * 6.32 / √(4000)
= 31.6 / 63.24
≈ 0.5 mm
Therefore, the boundary layer thickness at the same location, when the velocity of the fluid alone is increased by a factor of 4, will be approximately 0.5 mm. Hence, option C is the correct answer.
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A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer?
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A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer?.
A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A n incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layerthickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluidalone is increased by a factor of 4, then the boundary layer thickness at the same location, in mmwill bea)4b)2c)0.5d)0.25Correct answer is option 'C'. Can you explain this answer?.
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