Question

When a solid sphere moves through a liquid, the liquid opposes the motion with a force F. The magnitude of F depends on the coefficient of viscosity η of the liquid, the radius r of the sphere and the speed of the sphere. Assuming that F is proportional to different

Answer 1

Question:-

When a solid sphere moves through a liquid, the liquid opposes the motion with a force F. The magnitude of F depends on the coefficient of viscosity η of the liquid, the radius r of the sphere and the speed of the sphere. Assuming that F is proportional to different

Answer:-

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 = (4πr³)/3dg

Upthrust on the ball by the liquid =v×ρ×g=(4×πr³)/3×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,

=>4/(3πr3d) = 4/(3πr3ρg) + 6πηVt

=>Vt=(2(d−ρ)gr2.) / 9n

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