description
 Stokes’ Law
notes
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^{1}T^{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_{b}acting in the upward direction.There will also be F_{g}gravitational 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.
 Let retarding force F∝v where v =velocity of the sphere