What is the relationship between wind velocity and drag?

In summary, the conversation discusses the relationship between force on a ball and wind velocity. The formula for drag is mentioned as F = kv^2, with the constant needing to be determined. It is also noted that the drag coefficient, air density, area of influence, and wind velocity play a role in this relationship. The formula for a sphere's drag is given as F_w = Cd*dAv^2/2, with Cd being a function of the Reynold's Number. The conversation concludes with the mention of determining the constant value of the drag coefficient in order to calculate wind velocity.
  • #1
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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?
 
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  • #2
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!
 
  • #3
Brewnog is right.

Let me put it into latex.

[itex]F_w = dAv^2[/itex]

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
 
  • #4
Dr.Brain said:
Brewnog is right.

Let me put it into latex.

[itex]F_w = dAv^2 \qquad \color{red} \mbox{-------(NOT CORRECT)}[/itex]

where

d=air density
A= Area of influence
v=Velocity of wind
dr brain: u forgot the "most interesting" term, namely drag coefficient Cd. The formula for sphere should be:
[tex] F_w \ = \ \frac{C_{d}dAv^2}{2} [/tex]
where
Cd = 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 Cd 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 Cd can be in the thousands).

ponjavic: the "constant" value u are looking for is the Drag Coefficient Cd in the above formula. you can assume Cd 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 Cd.
 

1. What is wind velocity?

Wind velocity, also known as wind speed, is the measurement of how fast air is moving in a specific direction. It is typically measured in units of distance per unit of time, such as meters per second or miles per hour.

2. What is drag?

Drag is a force that opposes an object's motion through a fluid, such as air. It is caused by the friction between the object and the fluid and is dependent on the object's shape, size, and velocity.

3. How does wind velocity affect drag?

As wind velocity increases, so does drag. This is because a higher wind velocity means there is more air moving past the object, creating more friction and thus more drag. A higher wind velocity also means that the air molecules are moving faster, which can also increase the force of drag.

4. What factors can affect wind velocity and drag?

Several factors can affect wind velocity and drag, including air temperature, air pressure, and the object's shape and size. Wind velocity can also be influenced by topography, such as mountains or buildings, and the rotation of the Earth.

5. Why is understanding wind velocity and drag important?

Understanding wind velocity and drag is crucial in various fields, such as aviation, engineering, and weather forecasting. It helps determine the performance of objects in the presence of wind, such as airplanes or wind turbines, and can also impact the accuracy of weather predictions and the safety of structures during severe weather events.

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