The viscosity is analogous to friction in solids. It is the property of a fluid that resists the force tending to cause the fluid to flow.

Consider honey and water flow from one beaker to another. The water flows easily whereas honey is not so. Hence, honey is more viscous than water.

The coefficient of viscosity is the measure of degree to which a fluid resists flow under an applied force. This means how much resistance does the fluid have to its motion. It is denoted by η

In a flowing liquid, the stress is proportional to the rate of change of strain or strain rate.

Let BCDE be the portion of the liquid in between two parallel glass plates and l be the thickness of the liquid. Let A be the area of the liquid in contact with the glass plate. Let F be the tangential force applied to move the upper plate with a constant velocity v.

After a time interval ∆t, the liquid undergoes shear strain of ∆x /l.

The change in shearing strain = ∆x / l

The shearing strain rate (Shearing strain / time interval) = ∆x / l ∆t

The coefficient of viscosity = η = shearing stress / shearing strain = (F/A) / (∆x / l ∆t)

As (∆x / ∆t) = v, we get η = Fl / vA

If dv is the difference in velocity of the two layers of moving liquid distance dx apart, then v/l = dv / dx which is velocity gradient between two layers of liquid

We know η = Fl / vA = F / A(v/l) = F/ A (dv/dx)

Unit The coefficient of viscosity of a liquid is equal to the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid each of area unity. η = F / 1 * 1 = F

and it unit is Poiseuille which is Pascal – second or N/m² or kg/m/s and the dimensional formula is M L^-1 T^-1