Viscocity Stokes' Method

VISCOCITY ‒ STOKES' METHOD

Liquids such as castor oil, honey, glycerine etc., are termed as high viscous liquids. These high viscous liquids will have greater resistance.

Let us discuss about stokes' method to determine the viscosity for a high viscous liquid.

Principle

When a spherical object, like steel ball moves through a high viscous liquid, when the viscous force is equal to the buoyout force it attains the terminal velocity. By finding the termial velocity, the co‒efficient of viscosity shall be determined.

Stokes' formula

Let us consider a high viscous liquid taken in a tall jar as shown in Fig. 2.3. If a steel ball is dropped into the liquid, it begins to move down with acceleration due to gravitational force.

Here, the motion of the ball in the liquid is opposed by the viscous force of the liquid.

However, at one stage, a velocity called terminal velocity is attained, when the apparent weight of the ball is equal to the opposing viscous force acting on the ball.

At this stage, the resultant force on the ball is almost zero. Therefore, the ball will move down continuosly with the same velocity i.e, terminal velocity.

The viscous force (F) depends on the following factors, viz.,

(i) The terminal velocity of the ball (v).

(ii) Radius of the ball (r).

(iii) Co‒efficient of viscosity (η)

The viscous force F ∝ vrη

(or) F= k vrη

Where k is the proportionality constant and is equal to 6π.

The viscous force

F = 6πvrη            …………..(1)

Equation (1) is called Stokes' formula.

Terminal velocity

If ρ is the density of the spherical ball and ρ' is the density of the liquid and if the volume of the sphere is 4/3 πr³, then we can write,

The weight of the ball = 4/3 πr³ρg

Similarly, The weight of the liquid = 4/3 πr³ρ'g

The apparent weight of the ball (or) buoyont force (F_b) = 4/3 πr³ρg ‒ 4/3 πr³ρ'g

Buoyont Force F_b = 4/3 πr³g (ρ‒ρ')             ....... (2)

When the ball reaches the terminal velocity, the viscous force will be equal to the buoyont force.

i.e, At equilibrium,

 Viscous Force (F) = Buoyont Force (F_b)

∴ Equation (1) = Equation (2)

i.e., 6πvrη = 4/3 πr³ g(ρ‒ρ')

Terminal velocity v = [ 4 πr³ g(ρ‒ρ') ] / [ 3×6πrη ]

Thus, by finding the terminal velocity 'v', the co‒efficient of viscosity of the liquid shall be determined.