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The velocity distribution in a viscous flow over a plate is given by
u = 4y – y2
where, u = velocity in m/s at a point distanty fromthe plate. If the coefficient of dynamic viscosityis 1.5 pa.s, What is the shear stress at y = 1m?
  • a)
    3 Pa
  • b)
    3.5 Pa
  • c)
    2.5 Pa
  • d)
    3.3 Pa
Correct answer is option 'A'. Can you explain this answer?
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Shear Stress Calculation:

Given:
Coefficient of dynamic viscosity (μ) = 1.5 Pa.s
Velocity distribution equation: u = 4y - y^2
Distance from the plate, y = 1 m

Calculations:
1. Calculate the velocity at y = 1 m using the given velocity distribution equation:
u = 4(1) - (1)^2
u = 4 - 1
u = 3 m/s

2. Calculate the velocity gradient (du/dy) at y = 1 m:
du/dy = d(4y - y^2)/dy
du/dy = 4 - 2y
du/dy = 4 - 2(1)
du/dy = 2 s^-1

3. Calculate the shear stress using the formula for shear stress in a viscous flow:
Shear stress (τ) = μ * du/dy
Shear stress (τ) = 1.5 * 2
Shear stress (τ) = 3 Pa

Therefore, the shear stress at y = 1 m in the viscous flow over a plate is 3 Pa, which corresponds to option 'A'.
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The velocity distribution in a viscous flow over a plate is given byu = 4y y2where, u = velocity in m/s at a point distanty fromthe plate. If the coefficient of dynamic viscosityis 1.5 pa.s, What is the shear stress at y = 1m?a)3 Pab)3.5 Pac)2.5 Pad)3.3 PaCorrect answer is option 'A'. Can you explain this answer?
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