Viscous friction

When a sphere radius r has a velocity v in a liquid .It will has a drag force exerted on the sphere. The drag force is equal to 6$$\pi\eta$$rv (Stoke's law)
where $$\eta$$ is the fluid's dynamic viscosity
Where the drag force comes from ? How does this force occur?

Redbelly98
Staff Emeritus
Homework Helper
Molecules in the fluid are constantly colliding with the sphere. The fluid molecules exert a force on the sphere via these collisions, and collectively these collisions result in the drag force.

The drag force from the colliding with the molecules of the fluid is equal to
$$\rho\pi$$r2v2

This formula come from F$$\Delta$$t = m(v-u).
so, F $$\alpha$$ v2.
but from Stoke's law F $$\alpha$$ v.

$$\rho$$ is the density of fluid.

viscous drag--or friction, proportional to velocity is the drag due to laminar flow around the object. It's not typical that a sphere will experience viscous drag but only at low renyolds numbers.

Redbelly98
Staff Emeritus
Homework Helper
The drag force from the colliding with the molecules of the fluid is equal to
$$\rho\pi$$r2v2

This formula come from F$$\Delta$$t = m(v-u).
so, F $$\alpha$$ v2.
but from Stoke's law F $$\alpha$$ v.

That is true when collisions among the fluid molecules may be neglected, i.e. the viscosity is small.

For significantly large viscosity, the collisions between fluid molecules modify the force expression. In that case the force is proportional to v rather than v2.

In both cases, the force arises from fluid molecules impacting upon the moving object.