\[v_t = \sqrt{\frac{2mg}{\rho C_d A}}\]
Variables
vtterminal velocity (m/s)
mmass (kg)
ggravitational acceleration (m/s²)
rhofluid density (kg/m³)
Cddrag coefficient
Areference area (m²)
Description
What is this formula?
The terminal velocity equation calculates the constant maximum speed reached by a falling object when drag force equals gravitational force.
When to use it
Use this formula when analyzing falling objects, parachutes, atmospheric descent, rain droplets, or aerodynamic resistance problems.
Example
A skydiver with mass 80 kg falls through air with density 1.225 kg/m³, drag coefficient 1.0, and frontal area 0.7 m².
Data:
m = 80 kg
g = 9.81 m/s²
rho = 1.225 kg/m³
Cd = 1.0
A = 0.7 m²
Formula:
vt = √((2*m*g)/(rho*Cd*A))
Substitution:
vt = √((2*80*9.81)/(1.225*1.0*0.7))
Result:
vt ≈ 42.8 m/s
Applications
Parachute design, aerospace engineering, meteorology, sports science, atmospheric physics, and fluid mechanics.