Question

Using Newton's law of viscosity for streamline flow, derive an expression for the coefficient of viscosity.

Answer 1

According to Newton’s law of viscosity, for a streamline flow, viscous force (f) acting on any layer is directly proportional to the area (A) of the layer and the velocity gradient `((dv)/dx)` i.e.,

`f ∝ A((dv)/dx)`

∴ `f = ηA((dv)/dx)`   .....(1)

where η is a constant, called the coefficient of viscosity of the liquid. From Eq. (1) we can write,

`η = f/(A((dv)/dx))`  .....(2)

The coefficient of viscosity can be defined as the viscous force per unit area per unit velocity gradient. The S.I. unit of viscosity is Ns/m².