 # Drag Force Formula

Drag Force (D) is defined as the force that resists the motion of a body with fluid. If the motion of the body exists in the fluid-like air it is known as aerodynamic drag. And, if the fluid is water it is known as hydrodynamic drag. The drag force always acts in the opposite direction to the flow of fluid.

## Drag Coefficient Formula

Following is the formula used to calculate the drag coefficient:

 $$\begin{array}{l}D=\frac{C_{d}*\rho *V^{2}A}{2}\end{array}$$

Where,

• Cd is the drag coefficient
• ρ is the density of the medium in kg.m-3
• V is the velocity of the body in km.h-1
• A is the cross-sectional area in m2

### Solved Examples

Question 1. A car travels with a speed of 80 km.h-1 with a drag coefficient of 0.25. If the cross-sectional area is 6 m2, calculate the drag force.

Solution:
Given:
Velocity, V= 80 km.h-1

Drag coefficient, Cd= 0.25

Cross-sectional area, A= 6 m2

Density of fluid, ρ =1.2 kg.m-3

The drag force is given as:

$$\begin{array}{l}D=\frac{C_{d}*\rho *V^{2}A}{2}\end{array}$$
$$\begin{array}{l}D=\frac{0.25*1.2*6400*6}{2*3600}\end{array}$$

D=1.6 N

Question 2. A plane moves with the velocity of 600 km.h-1 with a drag coefficient of 0.25. If the cross-sectional area of the plane is 110 m2, calculate the drag force.
Solution:
Given:
Velocity, V=600 km.h-1

Drag coefficient, Cd= 0.25

Density of fluid, ρ=1.2 kg.m-3

Cross-sectional area, A=110 m2

The drag force is given as:

$$\begin{array}{l}D=\frac{C_{d}*\rho *V^{2}A}{2}\end{array}$$
$$\begin{array}{l}D=\frac{0.25*1.2\frac{kg}{m^{2}}360000\frac{m}{km}110m^{2}}{2*3600}\end{array}$$

D=1650 N