The Drag equation calculator helps you compute a force exerted on a moving object immersed in a fluid. Reading the text below you will discover what the equation for drag force is, how the shape of the object influences the force and what the drag coefficient is.

What is the equation for drag force

If an object moves through a fluid, it experiences a resisting force, the drag force. The value of this force depends on the size and shape of an object, density of the fluid and relative velocity of the object and the fluid. The equation is

Fd = 1/2 * ρ * u² * A * Cd

where

  • Fd is the drag force.
  • ρ is the liquid's density,
  • u is the relative velocity,
  • A is the reference area,
  • Cd is the drag coefficient.

The reference area A for an object of a simple shape is the cross-sectional area orthogonal to the direction of the motion. For example, for a sphere of radius r, we would simply take A = π * r². For an object of a more complicated shape, like a car, the reference area is more difficult to specify, but usually, it's larger than the cross-sectional area.

For an application of the drag force, you can check the free fall with air resistance calculator and the Stokes' law calculator.

Drag coefficient

The drag force equation depends on drag coefficient Cd. What is this? The drag coefficient is a dimensionless number that depends on the shape of the object. If an object has a smooth shape, then Cd is a small number and the resulting drag force is small as well. For example, it's equal to 0.04 for a streamlined body, whereas equals 1.05 for a cube.

The drag coefficient itself depends on the Reynolds number Re. For small enough Reynolds number (of the order of few thousands or smaller) the dependence is mild and the drag coefficient is approximately constant. Check the Reynolds number calculator to learn more about different types of flows and their classification with Reynolds number.

Drag equation calculator

How to use our drag equation calculator? Simply choose a liquid, immersed object and the relative velocity between them. For example for an olive oil the density ρ = 920 kg/m³, with an immersed long cylinder (Cd = 0.82) with cross section A = 1 cm² and the relative velocity u = 0.3 m/s the resulting drag force is Fd = 1.358 N.

Miłosz Panfil, PhD

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