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The velocity distribution in a viscous flow over a plate is given by
u = 4y - y2 for y ≤ 2m
where, u = velocity in m/s at a point distant y from the plate. If the coefficient of dynamic viscosity is 1.5 Pa-s, what is the shear stress at y= 1.2 m?
u = 4y - y2 for y ≤ 2m
where, u = velocity in m/s at a point distant y from the plate. If the coefficient of dynamic viscosity is 1.5 Pa-s, what is the shear stress at y= 1.2 m?
- a)1.4 Pa
- b)1.8 Pa
- c)2 Pa
- d)2.4 Pa
Correct answer is option 'D'. Can you explain this answer?
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The velocity distribution in a viscous flow over a plate is given byu ...
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The velocity distribution in a viscous flow over a plate is given byu ...
The velocity distribution u = 4y - y^2 for y < 2="" represents="" the="" laminar="" flow="" over="" a="" flat="" plate,="" where="" u="" is="" the="" velocity="" component="" in="" the="" x-direction="" and="" y="" is="" the="" distance="" from="" the="" plate="" in="" the="" />
The boundary condition for this flow is u = 0 at y = 0, since the fluid is assumed to be at rest at the surface of the plate. At the edge of the boundary layer, y = δ, the velocity approaches the free stream velocity U. This is known as the outer boundary condition.
To determine the thickness of the boundary layer, we can use the momentum integral equation:
δ = 4.91x/Re√(1 - x/Re)
where δ is the boundary layer thickness, x is the distance from the leading edge of the plate, and Re is the Reynolds number.
The Reynolds number is given by:
Re = ρUL/μ
where ρ is the density of the fluid, U is the free stream velocity, L is the length of the plate, and μ is the dynamic viscosity of the fluid.
Using this equation, we can find the velocity profile and boundary layer thickness for a given flow over a flat plate.
The boundary condition for this flow is u = 0 at y = 0, since the fluid is assumed to be at rest at the surface of the plate. At the edge of the boundary layer, y = δ, the velocity approaches the free stream velocity U. This is known as the outer boundary condition.
To determine the thickness of the boundary layer, we can use the momentum integral equation:
δ = 4.91x/Re√(1 - x/Re)
where δ is the boundary layer thickness, x is the distance from the leading edge of the plate, and Re is the Reynolds number.
The Reynolds number is given by:
Re = ρUL/μ
where ρ is the density of the fluid, U is the free stream velocity, L is the length of the plate, and μ is the dynamic viscosity of the fluid.
Using this equation, we can find the velocity profile and boundary layer thickness for a given flow over a flat plate.
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The velocity distribution in a viscous flow over a plate is given byu = 4y - y2 for y ≤ 2mwhere, u = velocity in m/s at a point distant y from the plate. If the coefficient of dynamic viscosity is 1.5 Pa-s, what is the shear stress at y= 1.2 m?a)1.4 Pab)1.8 Pac)2 Pad)2.4 PaCorrect answer is option 'D'. Can you explain this answer?
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