The constant velocity with which a body drops down after initial acceleration in a dense liquid or fluid is called terminal velocity. This is attained when the apparent weight is compensated by the viscous force. It is given by
Where ρ and σ are densities of the body and liquid respectively, η is the coefficient of viscosity of liquid and is the radius of the spherical body.
The net force on the sphere becomes zero as the viscous force equals the apparent weight.
Consider a long column of dense liquid-like glycerine. As the ball is dropped in it, the forces experienced are;
1. weight = mg = \(\frac{4}{3}πr^3ρg,\) where ρ is the density of the ball.
2. upthrust = U = \(\frac{4}{3}πr^3ρ_1g,\) where ρ1 is the density of the liquid.
3. viscous force Fv =6πηρv, where v is the terminal velocity.
Net force and the acceleration should be 0.
∴ mg – U – Fv = 0
