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The velocity distribution for flow over a flat plate is given by u= 3/2y-y^3/2 , where u is the point velocity in metre per second at a distance y metre above the plate. Determine the shear stress at y=9cm. Assume dynamic viscosity 8 Posie?
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The velocity distribution for flow over a flat plate is given by u= 3/...
Shear Stress Calculation for Flow over a Flat Plate
Calculating Shear Stress
where τ is the shear stress, μ is the dynamic viscosity, and dU/dy is the velocity gradient.
τ = (8)(3/2 - 3/2(0.09)^(1/2)) = 0.184 N/m^2
Explanation
The given velocity distribution for flow over a flat plate is u = 3/2y - y^3/2, where u is the point velocity in metre per second at a distance y metre above the plate. We need to determine the shear stress at y = 9cm, assuming dynamic viscosity 8 Posie.
Calculating Shear Stress
The shear stress is given by the formula:
τ = μ(dU/dy)
where τ is the shear stress, μ is the dynamic viscosity, and dU/dy is the velocity gradient.
Here, the velocity gradient can be found by taking the derivative of the velocity equation:
dU/dy = 3/2 - 3/2y^(1/2)
Substituting the given values, we get:
τ = (8)(3/2 - 3/2(0.09)^(1/2)) = 0.184 N/m^2
Explanation
The velocity distribution given in the problem is a function of the distance from the plate. As we move away from the plate, the velocity increases. The velocity gradient gives us the rate of change of velocity with respect to distance, which is a measure of shear stress. The dynamic viscosity is a measure of the resistance of the fluid to flow, which influences the magnitude of the shear stress.
By calculating the velocity gradient and substituting the given values, we can determine the shear stress at the specified distance from the plate. The value obtained is the force per unit area acting tangentially to the plate, which is an important parameter in the study of fluid mechanics.
Community Answer
The velocity distribution for flow over a flat plate is given by u= 3/...
Y=0.3151
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The velocity distribution for flow over a flat plate is given by u= 3/2y-y^3/2 , where u is the point velocity in metre per second at a distance y metre above the plate. Determine the shear stress at y=9cm. Assume dynamic viscosity 8 Posie?
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