Deriving the Formula for Air Resistance and Viscous Drag Using Momentum

[MaximumTaco]

How would one go about proving the formula

D = 1/2C(rho)A(v^2)

I have a suspicion momentum can be used to the show the derivation of this, right ?

 

[Michael D. Sewell]

Drag equals coefficient of aerodynamic drag times one half mass per unit volume times velocity squared times area.

One half mass per unit volume times velocity squared is also called dynamic pressure, and is actually kinetic energy per unit volume.

I hope this helps. -Mike

 

[MaximumTaco]

Originally posted by Michael D. Sewell
Drag equals coefficient of aerodynamic drag times one half mass per unit volume times velocity squared times area.

Yes, i know D = 1/2C(rho)Av^2

C = drag coefficient
rho = fluid density

But how can you show it's proof / derivation

 

[Michael D. Sewell]

By demensional analysis. Kinetic energy is power. Power is work/time.

 

[Clausius2]

In order to calculate the drag force exerted on a slender body, you usually will have to measure the velocity field upstream and downstream of the body. This can be made using a laser velocymeter without intrusion into the flow. With the balance of momentum the drag force is like:

F=1/2*rho*U^2*C(x,y,z,viscosity...);

If U=velocity upstream
u(y)=velocty downstream

then, if you make the calculus, you will have:

C=integral[(1-u^2/U^2)*u/Udy]

this, in boundary layer theory, is the momentum thickness.

Usually, C is an average coefficient along the body.
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I have to claim solidarity and mutually binding between all american and european people against the terrorism. As you can see, I'm writing this from Madrid, where 200 people have been murdered by islamic terrorism or E.T.A.(the vasque ilegal and criminal organization), as we don't know today who has been the infame murderers.
You, american people, have to know what is our daily problem here in Spain. The people murdered were workers and students, that woke up at 6:00 am to go to their jobs and shools and screamed into the train because of the horror of the ingenuity.
Please, uproar there against this bastards.
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Excuse me all this forum because of this change of theme, but I have to say that.

All right, I hope my answer about drag would serve to the requesting.

 

[selfAdjoint]

I have to claim solidarity and mutually binding between all american and european people against the terrorism. As you can see, I'm writing this from Madrid, where 200 people have been murdered by islamic terrorism or E.T.A.(the vasque ilegal and criminal organization), as we don't know today who has been the infame murderers.
You, american people, have to know what is our daily problem here in Spain. The people murdered were workers and students, that woke up at 6:00 am to go to their jobs and shools and screamed into the train because of the horror of the ingenuity.
Please, uproar there against this bastards.

Our hearts and sympathies are with you in this terrible time. Solidarity against the monsters!

 

[Michael D. Sewell]

We are shocked and saddened by your loss. We also know that you are not afraid, and have only been strengthened by this challenge. These people claim to have a cause, they do not. They are sick and perverted murderers who would use any excuse to kill. They would support any cause that involved destruction and death. The cowardly actions of these twisted murderers will only hasten their certain defeat. With each desperate act, they bring us closer together in an alliance that cannot be defeated. The shear weight of our numbers, and strength of our resolve will be a force that will crush them into the dirt, just the way it has always destroyed vermin in the past. We are with you. Fear not.

 

[Clausius2]

Thank you, Michael.