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The velocity distribution for fluid flow over a flat plate is given by u=2y-6y2 in which u is the velocity in metre per second at a distance of y metre above the plate. Determine the shear stress at y=0.15m.Take dynamic viscosity of fluid as 8.6 poise.
- a)0.172 N/m2
- b)0.344 N/m2
- c)0.086 N/m2
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The velocity distribution for fluid flow over a flat plate is given by...
Explanation: for y = 0.15m, velocity gradient = 0.2
viscosity= shear stress/velocity gradient
shear stress = 0.86*0.2 = 0.172N/m2
viscosity= shear stress/velocity gradient
shear stress = 0.86*0.2 = 0.172N/m2
Most Upvoted Answer
The velocity distribution for fluid flow over a flat plate is given by...
To determine the shear stress at a given point on a flat plate, we need to use the velocity distribution equation and apply the formula for shear stress.
Given velocity distribution: u = 2y - 6y^2
Shear stress formula: τ = μ * du/dy
Where:
τ = Shear stress
μ = Dynamic viscosity
du/dy = Velocity gradient
We are given that the dynamic viscosity (μ) of the fluid is 8.6 poise, which can be converted to Pascal-seconds (Pa·s) using the conversion factor: 1 poise = 0.1 Pa·s.
The velocity gradient (du/dy) can be found by differentiating the given velocity equation with respect to y.
Differentiating u = 2y - 6y^2 with respect to y:
du/dy = 2 - 12y
Now, we can substitute the values into the shear stress formula to find the shear stress at y = 0.15m.
τ = μ * du/dy
= 8.6 * 0.1 * (2 - 12(0.15))
= 0.86 * (2 - 1.8)
= 0.86 * 0.2
= 0.172 N/m^2
Therefore, the shear stress at y = 0.15m is 0.172 N/m^2.
Hence, the correct answer is option A) 0.172 N/m^2.
Given velocity distribution: u = 2y - 6y^2
Shear stress formula: τ = μ * du/dy
Where:
τ = Shear stress
μ = Dynamic viscosity
du/dy = Velocity gradient
We are given that the dynamic viscosity (μ) of the fluid is 8.6 poise, which can be converted to Pascal-seconds (Pa·s) using the conversion factor: 1 poise = 0.1 Pa·s.
The velocity gradient (du/dy) can be found by differentiating the given velocity equation with respect to y.
Differentiating u = 2y - 6y^2 with respect to y:
du/dy = 2 - 12y
Now, we can substitute the values into the shear stress formula to find the shear stress at y = 0.15m.
τ = μ * du/dy
= 8.6 * 0.1 * (2 - 12(0.15))
= 0.86 * (2 - 1.8)
= 0.86 * 0.2
= 0.172 N/m^2
Therefore, the shear stress at y = 0.15m is 0.172 N/m^2.
Hence, the correct answer is option A) 0.172 N/m^2.
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Community Answer
The velocity distribution for fluid flow over a flat plate is given by...
U = 2 y - 6 y ^ 2
du / dy = 2 - 12 y
@ y = 0.15 m
du / dy = 0.2
Shear Stress = µ. du / dy
= 0. 86 x 0.2
= 0.172 N/m^ 2
du / dy = 2 - 12 y
@ y = 0.15 m
du / dy = 0.2
Shear Stress = µ. du / dy
= 0. 86 x 0.2
= 0.172 N/m^ 2
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The velocity distribution for fluid flow over a flat plate is given by u=2y-6y2 in which u is the velocity in metre per second at a distance of y metre above the plate. Determine the shear stress at y=0.15m.Take dynamic viscosity of fluid as 8.6 poise.a)0.172 N/m2b)0.344 N/m2c)0.086 N/m2d)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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