Viscous Drag & Terminal Velocity

Drag force increases with a bigger object

D ∝ r

Drag force will change with type of liquid

Drag force will increase with the velocity of the object

D ∝ V

( Drag will change with the shape of the object)

For a sphere of radius r:

A. Initially:

- There are two forces: weight and upthrust

- W > U (weight > upthrust)

=> resultant force is downwards so it accelerates downwards

B. As speed increases

- Weight and Upthrust are the same but drag force has started to increase

- D = ηrV6π

=> resultant W - U - D is downwards so it is still accelerating downwards

C. At terminal velocity

- Drag + Upthrust = Weight

- no resultant force

- no acceleration

- constant terminal velocity

Volume of a sphere:

V=(4/3)πr^3

D = ηrV6π

is Stokes Law for the Drag on a sphere radiu r moving ar velocity v in a fluid with cofficient of viscosity η

η = D/ 6πvr

η has unit: Nm^-1(ms^-1)^-1 = Nm^-2s = kgms^-2m^-2s = kgm^-1s^-1

=> This is a property of liquid

*It decreases with temperature ( if temperature goes up, viscosity goes down)

If no upthrust (i.e generally in air...)

In air: ρ air << ρ s

=> Upthrust can be neglected

At A. resultant force => mg = ma => a=g=9.81 ms^-2

BVIS HANOI (VV)