Question

What happens to the shear stress if the thickness between the two plates is increased in a Couette flow?

(a) Increases

(b) Decreases

(c) Remains same

(d) Becomes infinite

This question was posed to me during an interview.

My question is from Couette Flow in portion Numerical Techniques for Nonlinear Supersonic Flow, Elements of Hypersonic Flow, Couette and Poiseuille Flow of Aerodynamics

Answer 1

Right choice is (b) Decreases

To explain: The relation between the shear stress and the viscous shear layer is given by:

τ = μ(\(\frac {u_e}{D}\))

Where, ue is the velocity at y = D that is at the upper plate.

τ is the shear stress

D is the thickness of the vicsous shear layer/distance between the two parallel plates

As peer the formula, then the thickness of the viscous shear layer increases, the shear stress decreases provided the other properties remain the same.