Drag force and maximum velocity

[bang]

Homework Statement

So for my intro engineering class one homework problem is given as follows.
"Considering only aerodynamic drag force, calculate the maximum speed (in mph), that a vehicle would experience with the following specifications."
Horsepower = 330
Mass density of fluid = .077 lbm/ft^3 (ρ)
Reference area = 22 ft^2 (Ap)
Drag coefficient = .29 (Cd)
1 horsepower = 550 ft * lbf / s

Homework Equations

Fd = .5*(Cd)*(Ap)*ρ*V^2

The Attempt at a Solution

The answer is supposed to be given in mph, and the correct answer is 186mph. What I've tried doing is multiplying both sides of the equation by V, therefore making Fd into power, then using the horsepower value and solving for V, but the answer I get is around 60 mph, 1/3rd the value of the correct answer.

Thanks for the help!

 

[PhanthomJay]

The lbm is not the proper unit to use when using the Imperial units if they are still called that. You must convert mass to slugs which perhaps you did, I haven't checked the numbers. Multiplying by v is ok, and is in ft/s.

 

[bang]

Only the mass density of fluid is in lbm, so I would need to convert the mass density of fluid? I don't understand.

 

[PhanthomJay]

Yes. A lbm weighs 1 pound on Earth. Since w = mg, m = ? in slugs.

 

[bang]

So I converted the mass density of the fluid using your equation, but I still get a wrong answer. It's closer but still not correct. I don't see where I could be going wrong.

 

[PhanthomJay]

Show your numbers and I'll check it out. What did you get for the mass density in slugs/ft^3?

 

[SteamKing]

Is V supposed to be in ft/sec or miles per hour?

 

[bang]

The result you get is in ft/sec but I convert it to mph, and the final answer is in mph.

So for the slugs conversion, I used w=mg, which became .077=m*(32.2), and the m=.0024
Then I just plug all the values in and solve
HP = .5*(Cd)*(Ap)*ρ*V^3

330 * 550 = .5(.29)*(22)*(.0024)*V^3
181500 = .0077 * V^3
V=286.7 ft/sec, which converts to 195.5mph, and the answer is supposed to be 186mph.

 

[PhanthomJay]

I just cranked out the numbers and i also get 196 mph or thereabouts, call it 200 mph. Maybe the book slipped a digit somewhere.

 

[bang]

Hm ok, thanks for the help!