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.
Expand 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
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Drag Force
021. Optimizing for Drag
047. Stop at the Sign
362. Terminal Velocity
363. Drag Force
420. Drag Coefficient
436. Reynolds Number Drag
442. Re Drag
462. Basketball Hoop
Similar Problems from FE Section: Consequences of Fluid Flow
021. Optimizing for Drag
047. Stop at the Sign
362. Terminal Velocity
363. Drag Force
368. Elevated Storage Tank
420. Drag Coefficient
436. Reynolds Number Drag
442. Re Drag
462. Basketball Hoop