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