# Drag Formula

Drag force is the resistance of a fluid, the force that it applies acting opposite to the motion of an object that is moving submerge in a certain fluid.

Drag = (density) * (square of the velocity) * (Drag coefficient) *(transversal area)

The equation is written

F_{D} = ½ ρ * v^{2} * C_{D} * A

We have:

F_{D}: Drag force

ρ: fluid density

v: Relative velocity between the fluid and the object

C_{D}: Drag coefficient

A: Transversal area or cross sectional area

Drag Formula Questions:

1) A car travels with the speed of 90 km/h have a drag coefficient of 0.32.

If the area of cross section is 5 m^{2}, what is the drag force? The air density is 1.2 Kg/m^{3}.

Answer: Using the formula for drag force, we can substitute directly,

F_{D} = ½ ρ * v^{2} * C_{D} * A

F_{D} = ½ (1.2 Kg/m^{3})*(25 m/s)^{2} * 0.32 * 5 m^{2} = 600 Kg*m/s^{2} =600 N

2) what is the drag coefficient of an object moving in water and that feels a drag force of 500 N? The sectional area is 2 m^{2} and is moving at 30 m/s.

Answer: From the formula of drag we can find the drag coefficient,

C_{D} = 2 * F_{D} / (ρ * v^{2} * A)

Substituting the values in the formula above, with the density of the water 1 Kg/L,

C_{D} = 2 * 500 N / (1 Kg/L * (30 m/s)^{2} * 2 m^{2})=

C_{D} = 2 * 500 N / (1000 Kg/m^{3} * (30 m/s)^{2} * 2 m^{2})= 0.00055

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