find the dimensitions of coefficient of viscocity and its SI unit .
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 = 6πηrv
η = F / (6πrv) …… …… ……… …...(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]
……… ………………… …………………… ....... ...........= [M1 L-1 T-1]
From the dimensional formula, the SI unit of coefficient of viscosity (η) is kg m-1 s-1