Question

Viscous force acting on a body is given byF=6πηrv here r is radius v is velocity.Obtain the dimension of coefficient of viscosity​ η.

Answer 1

Dear Student,

According to Stoke 's Law, a body of radius r moving with velocity v through a medium of coefficient of viscosity η experiences a viscous force given by:

F = 6π η rv

η = F / (6π rv ) …… …… ……… …...(i)

Now, dimension of force ( F ) = [M¹ L¹ T^-2]

Dimensions of radius ( r ) = [L¹]

Dimensions of velocity ( v ) = [L¹ T^-1]

6π is a dimensionless factor

therefore, dimensions of coefficient of viscosity (η) = [M¹ L¹ T^-2] / [L¹] [L¹ T^-1]

dimensions of coefficient of viscosity (η) = [M¹ L^-1 T^-1]

Regards