## Aerodynamic Drag

Consider a round ball with a diameter of 20 cm is kicked such that it travels 40 m/s. If the drag coefficient is 1.5, what is the ball’s drag force? Assume the density of air is 1.22 kg/m^3.

##
__
__**Hint**

**Hint**

The drag force on objects immersed in a large body of flowing fluid or objects moving through a stagnant fluid:

$$$D=\frac{1}{2}\rho U^{2}C_{D}A$$$

where
$$C_D$$
is the drag coefficient,
$$U$$
is the flowing fluid or moving object’s velocity,
$$\rho$$
is the fluid density, and
$$A$$
is the projected area of blunt objects with axes perpendicular to the flow.

##
__
__**Hint 2**

**Hint 2**

$$$A=\frac{\pi}{4}d^2$$$

where
$$d$$
is the diameter.

The drag force on objects immersed in a large body of flowing fluid or objects moving through a stagnant fluid:

$$$D_f=\frac{1}{2}\rho U^{2}C_{D}A$$$

where
$$C_D$$
is the drag coefficient,
$$U$$
is the flowing fluid or moving object’s velocity,
$$\rho$$
is the fluid density, and
$$A$$
is the projected area of blunt objects with axes perpendicular to the flow. For a round object, the cross section of the projected area is:

$$$A=\frac{\pi}{4}d^2$$$

where
$$d$$
is the diameter.

Thus,

$$$D_f=\frac{1}{2}(1.22\frac{kg}{m^3})(40m/s)^{2}(1.5)(\frac{\pi}{4}(.2m)^2)$$$

$$$D_f=\frac{1}{2}(1.22\frac{kg}{m^3})(1,600m^2/s^2)(1.5)(\frac{\pi}{4}(.04m^2))$$$

$$$D_f=(1,464kg\cdot m/s^2)\pi(.01)=46\:N$$$

46 N