Question

The coefficient of viscosity is equal to the ratio of shear stress to shear strain. True or False?

(a) True

(b) False

I have been asked this question by my school teacher while I was bunking the class.

Origin of the question is Fluids Mechanical Properties topic in division Mechanical Properties of Fluids of Physics – Class 11

Answer 1

The correct choice is (b) False

The best I can explain: Imagine a fluid element with its bottom layer having zero velocity and upper layer, at a height ‘h’, having velocity ‘v’.                                                                                                                                        As the fluid moves, the bottom layer stays as it is, while the other layers will move relative to the bottom layer.                                                                                                                                                                                          So, the strain (=v*Δt/h) continuously increases with time.                                                                                                  So we talk about strain rate (=v*Δt/h*Δt = v/h) and not about strain.                                                                     And we say that stress is proportional to strain rate.                                                                                             Therefore the coefficient of viscosity is the ratio of stress & strain rate.