what is stoke law? also terminal velocity

Dear Student,
When a solid body moves through a fluid,the fluid in contact with the solid is dragged with it. Relative velocities are established between the layers of the fluids near the solid so that the viscous forces start operating. The fluid exerts viscous force on the solid to oppose the motion of the solid.Stokes law states that the magnitude of the viscous force depends on the shape and size of the solid body, Its speed and the coefficient of viscosity of the fluid.

Suppose a spherical body of radius r moves at speed v through a fluid of viscosity ƞ .the viscous force F acting on the body depends on r,v and ƞ . From Stoke's law,
F = 6πƞrv

Terminal velocity:

When a solid is dropped in a fluid, the forces acting on it are.

  • Weight W acting downwards
  • Viscous force F acting upwards
  • Buoyant force B acting upwards

We know from Stokes law that F is proportional to velocity v.

Initially , F=0 and the solid is accelerated due to force W-B

Because of this acceleration, v increases. At a certain instant

F becomes equal to W-B. net force is 0 and solid falls with constant velocity. This is known as terminal velocity. which is given by the following formula:

V0 = (2r2(p-σ)g)/9ƞ

Where v0 is terminal velocity,p is the density of the body, σ is density of the liquid and g is acceleration of the body.
Regards.

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