Viscosity

• Stokes’ Law

Viscosity

• Viscosity is the property of a fluid that resists the force tending to cause the fluid to flow.

• It is analogous to friction in solids.

Example:-

• Consider 2 glasses one filled with water and the other filled with honey.

• Water will flow down the glass very rapidly whereas honey won’t. This is because honey is more viscous than water.

• Therefore in order to make honey flow, we need to apply a greater amount of force. Because honey has the property to resist the motion.

• Viscosity comes into play when there is relative motion between the layers of the fluid. The different layers are not moving at the same pace.

Coefficient of Viscosity

• The coefficient of viscosity is the measure of the degree to which a fluid resists flow under an applied force.
• This means how much resistance does a fluid has to its motion.

The ratio of shearing stress to the strain rate.

It is denoted by ‘η’.

Mathematically         

Δt=time , displacement =Δx

Therefore,

`"shearing stress" = (Deltax)/l` where l=length

`"strain rate" =(Deltax)/(lDeltat)` 

`eta="shearing stress"/"strain rate"`

`("F"/"A")/((Delta"x")/("l"Delta"t"))= ("Fl")/("vA")` where `(Deltax)/t="v"`

Therefore `eta=("Fl")/"vA"`

Unit: Poiseiulle (Pl)/Pa/Nsm^-2

Dimensional Formula: [ML^-1T^-1]

Stokes Law

• The force that retards a sphere moving through a viscous fluid is directly ∝to the velocity and the radius of the sphere, and the viscosity of the fluid.
• Mathematically:-F =6πηrv where
  • Let retarding force F∝v where v =velocity of the sphere
    • F ∝ r where r=radius of the sphere
    • F∝η where η=coefficient of viscosity
    • 6π=constant
  • Stokes law is applicable only to laminar flow of liquids.It is not applicable to turbulent law.
  • Example:-Falling raindrops
    • Consider a single rain drop, when rain drop is falling it is passing through air.
    • The air has some viscosity; there will be some force which will try to stop the motion of the rain drop.
    • Initially the rain drop accelerates but after some time it falls with constant velocity.
    • As the velocity increases the retarding force also increases.
    • There will be viscous force F_v and bind force F_bacting in the upward direction.There will also be F_ggravitational force acting downwards.
    • After some time F_g = F_r (F_v+F_b)
    • Net Force is 0. If force is 0 as a result acceleration also becomes 0.