Stoke's law :
when an spherical object moves through a viscous medium (at rest), it creates a relative motion between the different layer of liquid. As a result of which a viscous force comes into action which opposes the motion of falling object. This viscous force is given by ------
F = 6𝛑𝛈rv
Terminal velocity :
If a spherical object of radius r dropped in a liquid, then it will first accelerates and then its acceleration becomes zero and it attains a constant velocity. The maximum constant velocity acquired by the object falling through a viscous medium is called terminal velocity.
In equilibrium-
Fv
+ Fup
= W {Fv = Viscous force & Fup = upthrust force}Fv = W – Fup {m'= mass of liquid displaced}
6πηrV = mg – m’g {m=mass of object}
6πηrV = volume(ρsg) – volume(ρl
g) {ρs= density of solid}
6πηrV = volume g(ρs
- ρl
) {ρl= density of liquid}
6πηrV = 4/3πr3 g (ρs - ρl ) {η= coefficient of viscosity}
6πηrV = 4/3πr3 g (ρs - ρl ) {η= coefficient of viscosity}
V = 2r2
g(ρs
- ρl
) / 9η { V= terminal velocity}
