Force of air resistance in wind tunnel

[hover]

Homework Statement

I am working on making a small wind tunnel using a 20" fan. What i want to figure out is the force generated by the movement of air. I want to make the size of the tunnel shrink to help induce more velocity in the air (see picture).

Homework Equations

Bernoulli's Equation-
p1*v1=p2*v2

p being the air pressure in the tube
v being the air velocity in the tube

air friction equation (from http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html" )-
F=(-1/2)*C*p*A*v^2

F= force
C=numerical drag coefficient
p=density
A=area
v=velocity

Newtons second law(duh..)-
F=ma

F=force
m=mass
a-acceleration

The Attempt at a Solution

The equation that will help the most with this is the second equation- F=(-1/2)*C*p*A*v^2

F= force
C=numerical drag coefficient
p=density
A=area
v=velocity

First off, HyperPhysics doesn't tell me any of the units for F, C, p, A and v. Second, what is the numerical drag coefficient? Since this is a fan moving air at a distance, I'm going to suspect that there will be some inverse square law to add to this equation. Not to mention that because the shape of the tube narrows down, it will likely alter the equation.

Thanks for helping out

 

[Astronuc]

F= force
C=numerical drag coefficient
p=density
A=area
v=velocity

Well what does one expect the units of velocity, area, density and force to be? Pick SI / MKS units, e.g. velocity in m/s, area in m², . . .

then C must have units of Force/(density*area*velocity²).

Basically one must measure F, p, A and v to find C.

 

[hover]

F= force
C=numerical drag coefficient
p=density
A=area
v=velocity

Well what does one expect the units of velocity, area, density and force to be? Pick SI / MKS units, e.g. velocity in m/s, area in m², . . .

then C must have units of Force/(density*area*velocity²).

Basically one must measure F, p, A and v to find C.

Well that's pointless then. I have no way to measure the velocity, force or the numerical drag coefficient. How can i find out the force effectively?

 

[Astronuc]

In a wind tunnel, one could attach a spring (with a know spring constant) to the object being tested and the measure the deflection of the spring in tension or compression depending on whether the object is pulling or pushing the spring. Or one could use a spring scale.

Air (gas) flow or velocity could be measure by a Pitot tube - http://en.wikipedia.org/wiki/Pitot_tube

Density should be available from tables, one is probably starting with air at atmospheric pressure. I don't think the pressure in the smaller section will be much greater than 1 atm, but rather the air velocity will increase.

Continuity of mass applies here, and I expect there will be little compression of the air, especially at low air speeds.

 

[hover]

In a wind tunnel, one could attach a spring (with a know spring constant) to the object being tested and the measure the deflection of the spring in tension or compression depending on whether the object is pulling or pushing the spring. Or one could use a spring scale.

Air (gas) flow or velocity could be measure by a Pitot tube - http://en.wikipedia.org/wiki/Pitot_tube

Density should be available from tables, one is probably starting with air at atmospheric pressure. I don't think the pressure in the smaller section will be much greater than 1 atm, but rather the air velocity will increase.

Continuity of mass applies here, and I expect there will be little compression of the air, especially at low air speeds.

Thanks, I'll look into those. I, particularly, like the idea of measuring the force using a spring.

I just need to know one more thing. Since I'm using a fan, the air will be turning and twisting a lot, due to the way the fan pushes the air. I need some way to straighten out the air so it flows smoothly (or more smoothly). If i can remember correctly, I think that one episode of Mythbusters, they made a wind tunnel and used a bunch of straws to help stabilize the air. They used a ton of straws. I suppose i could too, but are there any other alternatives i could use to help stabilize the air in my wind tunnel?

 

[Astronuc]

I just need to know one more thing. Since I'm using a fan, the air will be turning and twisting a lot, due to the way the fan pushes the air. I need some way to straighten out the air so it flows smoothly (or more smoothly). If i can remember correctly, I think that one episode of Mythbusters, they made a wind tunnel and used a bunch of straws to help stabilize the air. They used a ton of straws. I suppose i could too, but are there any other alternatives i could use to help stabilize the air in my wind tunnel?

Most wind tunnels use a set of foils to 'straighten' the flow, but there is some pressure drop associated with that.

Cyrusabdollahi built a wind tunnel.