When a small sphere moves at low speed through a fluid, the viscous force F opposing the motion, is found experimentally to depend on the radius y, the velocity v of the sphere and the viscosity n of the fluid. Find the force F (Stoke's law)
Answers
Answer:
Stokes' law describes sedimentation of particles in liquids and can be used to measure viscosity. Particles in liquids achieve terminal velocity quickly. One can measure the time it takes for a particle to fall a certain distance and then use Stokes' law to calculate the viscosity of the liquid.
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Consider the movement of a ball inside a viscous fluid:
1) Radius -r
2) Coefficient of Viscosity -η
3) Density of the ball -d
4) Density of the liquid - ρ
5) Acceleration due to Gravity - g
The ball is subjected to the influence of three forces: they are the weight, upthrust and the viscous force - drag or liquid friction.
Weight of the ball = mg =
3
4
πr³dg
Upthrust on the ball by the liquid =
v×
ρ×
g=
3
4
×
πr³×
ρg
.
According to Stokes Law,
Viscous force = 6πηV, (where V is the velocity at a given a time).
At the outset, the downward force, weight, is greater than the combination of the upward forces.
So, initially, the ball accelerates. The viscous force, which depends of the velocity, however, keeps increasing.
As a result, at some point, the net force on the ball becomes zero and the velocity of the ball becomes constant.
It is the Terminal Velocity - Vt
When the balls moves at the terminal velocity,
= >
3πr3d
4
=
3πr3ρg
4
+
6πηVt
=>Vt=
9η
2(d−ρ)gr
2
.