What is the relationship between wind velocity and drag?

[ponjavic]

Ok so I have a ball tied to a string hanging. I start a fan and the string now forms an angle.

I have heard that there is a relationship between the force on the ball and the wind velocity (obviously)

It should be something like F=kv^2 or something like that, what I need to find out is the magnitude of this constant.

I have a series of angles (enabling me to calculate the drag of the ball). Using this I would like to calculate the velocity of the wind colliding with the ball, any ideas?

 

[brewnog]

Drag is:

Cd*0.5*p*v^2*S

Where Cd is the drag coefficient, p the density of the medium, v the flow velocity, and S the profile area. For a sphere, a typical drag coefficient may range from 0.07 to 0.5, but for practical purposes tends to be around the upper of these two limits.

As always, please excuse the lack of Latex!

 

[Dr.Brain]

Brewnog is right.

Let me put it into latex.

$F_w = dAv^2$

where

d=air density
A= Area of influence
v=Velocity of wind

Though movement of air due to a fan is pretty random , and this is NOT a formula which can give you the true picture of what is really happening with the air molecules.
Anyways , this formula is common for air/Gas/Liquid striking uniformly on a surface . Deriving this formula is pretty easy . Start with Force=change in momentum due to each particle striking the surface and derive it from there.

BJ

 

[geosonel]

Brewnog is right.

Let me put it into latex.

$F_w = dAv^2 \qquad \color{red} \mbox{-------(NOT CORRECT)}$

where

d=air density
A= Area of influence
v=Velocity of wind

dr brain: u forgot the "most interesting" term, namely drag coefficient C_d. The formula for sphere should be:
$$F_w \ = \ \frac{C_{d}dAv^2}{2}$$
where
C_d = Drag Coefficient of sphere
d=air density
A= Area of influence
v=Velocity of wind

in any case, brewnog is also not quite correct. the sphere's drag coeff C_d is a function of the Reynold's Number Re and ranges from about 0.4 for Re > 1000 to values approximated by 24/Re when Re < 1 (so that C_d can be in the thousands).

ponjavic: the "constant" value u are looking for is the Drag Coefficient C_d in the above formula. you can assume C_d is constant for all your wind speeds. draw the 3 forces on the sphere (wind drag, gravity, and string tension) in equilibrium. resolve into horizontal and vertical components. all components must sum to zero when sphere is in equilibrium. Then determine wind drag, and from that, the C_d.