Lab Manual Experiment : To determine the co-efficient of viscosity of four

different liquid by falling sphere resistance method using stoke’s law

Submitted by- Abhishek kumar Mishra

Abhishek Pathak

Anurag Bajpai

Pooja Singh

Prachi Gupta

Juhi Tyagi

Object : To determine the co-efficient of viscosity of four

different liquid by falling sphere resistance method using stoke’s law

Apparatus Required : Cylindrical tube ( length = 75 cm , diameter = 5 cm ) , stopwatch

Theory : This method on based on stoke’s law , according to which the drag force , F on a small sphere moving wth a constant velocity , U through a viscous fluid of viscosity, µ for a viscous condition is given by –

F = 3πµUd

Where , d = diameter of sphere

U = velocity of sphere

When the sphere attain a constant velocity U , the drag force is the difference between the weight of sphere and buoyant force acting on it .

Let L = distance travelled by the sphere in viscous fluid ,

T = time taken by sphere to cover distance l ,

ρs = density of sphere

ρf = density of fluid

W = weight of sphere

and Fa = buoyant force acting on the liquid

then constant velocity of sphere , U = L/t

weight of liquid , W = volume*density of sphere*g

= (π/6)*d3*ρs*g

And buoyant force Fb = weight of fluid displaced

= vol. of liquid displaced*density of fluid*g

= (π/6)*d3*ρf*g

For equilibrium,

Drag force = weight of sphere – buoyant force

F = W - Fb

Substituting the value of F , W and Fb , we get

µ = gd3*[ρs – ρf]/18U

hence from above equations the value of d ,U , ρs and ρf are known and hence the viscosity of liquid can be determined .

Method : Thus this method consists of a tall vertical transparent cylindrical tank , which is filled with a liquid whose viscosity is to be determined . This tank is surrounded by another transparent tank to keep the temperature of the liquid in the cylindrical tank to be constant .

A spherical ball of diameter ‘d’ is placed on the surface of liquid . Provision is made to release this ball .After a short distance of travel , the ball attains a constant velocity . time to travel a known vertical distance between two fixed marks on the cylinder tank is noted to calculate the constant velocity U of the ball . Then with the known values of d , ρs , ρf the viscosity µof the fluid is calculated using the equation

µ = g*d3*[ρs – ρf]/18U

Observations : d = diameter of sphere =

ρs = density of sphere =

ρf = density of fluid =