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The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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?
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The cross section area of the other position which supports an object ...
Solution:
Given data:
Mass of the object (m) = 2000 kg
Boundary layer thickness (δ) = 1 mm
Reynolds number (Re) = 1000
Velocity of the fluid (v) is increased by a factor of 4
Reynolds number:
Reynolds number is a dimensionless quantity that determines the type of flow (laminar or turbulent) in a fluid. It is given by the formula:
Re = ρvd/μ
Where,
ρ = density of the fluid
v = velocity of the fluid
d = characteristic length
μ = dynamic viscosity of the fluid
Bernoulli's equation:
Bernoulli's equation describes the conservation of energy in fluid flow. It is given by the formula:
P + 0.5ρv^2 + ρgh = constant
Where,
P = pressure of the fluid
ρ = density of the fluid
v = velocity of the fluid
g = acceleration due to gravity
h = height above a reference point
Boundary layer thickness:
Boundary layer thickness is the distance between the solid surface and the point where the flow velocity reaches 99% of the free-stream velocity. It is influenced by factors such as Reynolds number and surface roughness.
Effect of increased velocity:
When the velocity of the fluid alone is increased by a factor of 4, the Reynolds number will also increase by the same factor. This is because Reynolds number is directly proportional to the velocity of the fluid.
Calculation:
1. Given that the Reynolds number (Re) is 1000, we can find the characteristic length (d) using the formula:
Re = ρvd/μ
1000 = ρv(1)/μ
2. Assuming the density (ρ) and dynamic viscosity (μ) of the fluid to be constant, we can rewrite the formula as:
v = Reμ/(ρd)
v = 1000μ/(ρd)
3. Let the initial velocity be v1 and the final velocity be v2. According to the given information, v2 = 4v1.
4. Substituting the values of v1 and v2 in the equation obtained in step 2, we get:
v2 = 1000μ/(ρd)
4v1 = 1000μ/(ρd)
5. Rearranging the equation, we can solve for v1:
v1 = (1000μ/(ρd))/4
v1 = 250μ/(ρd)
6. Since the Reynolds number is directly proportional to the velocity, we can write:
Re2 = Re1 * (v2/v1)
Re2 = 1000 * (4v1/v1)
Re2 = 4000
7. Now, let's calculate the boundary layer thickness at the same location using the new Reynolds number (Re2).
Re2 = ρv2d/μ
4000 = ρv2(1)/μ
8. Assuming the density (ρ) and dynamic viscosity (μ) of the fluid to be constant, we can rewrite the formula as:
v2 = Re2μ/(ρd)
v2 = 4000μ/(ρd)
9. Substituting the values of v2 in
Given data:
Mass of the object (m) = 2000 kg
Boundary layer thickness (δ) = 1 mm
Reynolds number (Re) = 1000
Velocity of the fluid (v) is increased by a factor of 4
Reynolds number:
Reynolds number is a dimensionless quantity that determines the type of flow (laminar or turbulent) in a fluid. It is given by the formula:
Re = ρvd/μ
Where,
ρ = density of the fluid
v = velocity of the fluid
d = characteristic length
μ = dynamic viscosity of the fluid
Bernoulli's equation:
Bernoulli's equation describes the conservation of energy in fluid flow. It is given by the formula:
P + 0.5ρv^2 + ρgh = constant
Where,
P = pressure of the fluid
ρ = density of the fluid
v = velocity of the fluid
g = acceleration due to gravity
h = height above a reference point
Boundary layer thickness:
Boundary layer thickness is the distance between the solid surface and the point where the flow velocity reaches 99% of the free-stream velocity. It is influenced by factors such as Reynolds number and surface roughness.
Effect of increased velocity:
When the velocity of the fluid alone is increased by a factor of 4, the Reynolds number will also increase by the same factor. This is because Reynolds number is directly proportional to the velocity of the fluid.
Calculation:
1. Given that the Reynolds number (Re) is 1000, we can find the characteristic length (d) using the formula:
Re = ρvd/μ
1000 = ρv(1)/μ
2. Assuming the density (ρ) and dynamic viscosity (μ) of the fluid to be constant, we can rewrite the formula as:
v = Reμ/(ρd)
v = 1000μ/(ρd)
3. Let the initial velocity be v1 and the final velocity be v2. According to the given information, v2 = 4v1.
4. Substituting the values of v1 and v2 in the equation obtained in step 2, we get:
v2 = 1000μ/(ρd)
4v1 = 1000μ/(ρd)
5. Rearranging the equation, we can solve for v1:
v1 = (1000μ/(ρd))/4
v1 = 250μ/(ρd)
6. Since the Reynolds number is directly proportional to the velocity, we can write:
Re2 = Re1 * (v2/v1)
Re2 = 1000 * (4v1/v1)
Re2 = 4000
7. Now, let's calculate the boundary layer thickness at the same location using the new Reynolds number (Re2).
Re2 = ρv2d/μ
4000 = ρv2(1)/μ
8. Assuming the density (ρ) and dynamic viscosity (μ) of the fluid to be constant, we can rewrite the formula as:
v2 = Re2μ/(ρd)
v2 = 4000μ/(ρd)
9. Substituting the values of v2 in
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The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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?
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The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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?.
The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cross section area of the other position which supports an object having a mass 2000 kg is an incompressible fluid flows over a flat plate with zero pressure gradient the boundary layer thickness 1mm at a location where the Reynolds number is 1000if 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?.
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