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The velocity distribution for flow over a plate is given by u = 0.5y - y2, where u is the velocity in m/s at a distance y m above the plate. If the dynamic viscosity of the fluid is 0.9 Ns/m2, then what is the shear stress at 0.20 m from the boundary?
  • a)
    0.9 N/m2    
  • b)
    1.8 N/m2
  • c)
    2.25 N/m2    
  • d)
    0.09 N/m2
Correct answer is option 'D'. Can you explain this answer?
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Velocity Distribution
The velocity distribution for flow over a plate is given by the equation:
u = 0.5y - y²
Here, u represents the velocity in m/s at a distance y m above the plate.
Dynamic Viscosity
The dynamic viscosity (μ) of the fluid is provided as 0.9 Ns/m².
Shear Stress Calculation
To find the shear stress (τ) at a certain distance from the boundary, we use the formula:
τ = μ * (du/dy)
where du/dy is the velocity gradient.
Finding du/dy
First, we need to differentiate the velocity distribution equation:
- u = 0.5y - y²
- du/dy = d(0.5y - y²)/dy
- du/dy = 0.5 - 2y
Now we can evaluate du/dy at y = 0.20 m:
- du/dy = 0.5 - 2(0.20)
- du/dy = 0.5 - 0.4
- du/dy = 0.1 m/s/m
Calculate Shear Stress
Now, substituting the values into the shear stress formula:
τ = μ * (du/dy)
- τ = 0.9 Ns/m² * 0.1 m/s/m
- τ = 0.09 N/m²
Conclusion
Thus, the shear stress at 0.20 m from the boundary is:
- Correct Answer: 0.09 N/m² (Option D)
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The velocity distribution for flow over a plate is given by u = 0.5y - y2, where u is the velocity in m/s at a distance y m above the plate. If the dynamic viscosity of the fluid is 0.9 Ns/m2, then what is the shear stress at 0.20 m from the boundary?a)0.9 N/m2 b)1.8 N/m2c)2.25 N/m2 d)0.09 N/m2Correct answer is option 'D'. Can you explain this answer?
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