Terminal velocity (derivations)

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Derivations from Terminal velocity.

[edit] Derivation of Terminal Velocity

A falling object experiences two forces: gravitational force, and a large-velocity drag force. The addition of these two forces results in:

F = m g - q A C_d \,

where

m is mass of the object
g is the acceleration due to gravity
q is \frac{1}{2} \rho V^2 , which is commonly known as the dynamic pressure, where
ρ is the fluid density (e.g. density of air)
V is the fluid (or air) velocity
A is the cross-sectional area of the object
Cd is the drag coefficient of the falling object

The terminal velocity is reached when F = 0, so

m g - q A C_d = 0 = m g - \frac{1}{2} \rho V^2 A C_d .

Solving for V to obtain the expression for terminal velocity,

V_t = \sqrt{ \frac{2mg}{\rho A C_d} }


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