Question

Water is flowing on a horizontal fixed surface such that its flow velocity varies with y (vertical direction) as v = k((2y²)/(a²) - (y³)/(a³)). If coefficient of viscosity for water is η, what will be the shear stress between layers of water at y = a?

• A. \( \dfrac{\eta k}{a} \)
• B. \( \dfrac{\eta}{ka} \)
• C. \( \dfrac{\eta a}{k} \)
• D. None of these

Hint:

Shear stress in fluids depends on velocity gradient, not velocity itself.

Answer 1

The Correct Option is A

Step 1: Shear stress: τ = η (dv)/(dy)
Step 2: Differentiating velocity: (dv)/(dy) = k((4y)/(a²) - (3y²)/(a³))
Step 3: At y = a: (dv)/(dy) = k((4)/(a) - (3)/(a)) = (k)/(a) τ = (η k)/(a)