Drag force and maximum velocity

In summary, the homework problem asks for the maximum speed a vehicle would experience if the following specifications were met. Horsepower = 330, mass density of fluid = .077 lbm/ft^3 (ρ), reference area = 22 ft^2 (Ap), and drag coefficient = .29 (Cd). The Attempt at a Solution is to solve for V, which is supposed to be in ft/sec but I get it in ft/sec and mph.
  • #1
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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!
 
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  • #2
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.
 
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  • #3
Only the mass density of fluid is in lbm, so I would need to convert the mass density of fluid? I don't understand.
 
  • #4
Yes. A lbm weighs 1 pound on Earth. Since w = mg, m = ? in slugs.
 
  • #5
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.
 
  • #6
Show your numbers and I'll check it out. What did you get for the mass density in slugs/ft^3?
 
  • #7
Is V supposed to be in ft/sec or miles per hour?
 
  • #8
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.
 
  • #9
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.
 
  • #10
Hm ok, thanks for the help!
 

Related to Drag force and maximum velocity

1. What is drag force and how does it affect an object's maximum velocity?

Drag force is a force that opposes an object's motion through a fluid (such as air or water). It is caused by the friction between the object and the fluid it is moving through. As an object's speed increases, the drag force also increases, ultimately limiting the object's maximum velocity.

2. How is drag force calculated?

Drag force can be calculated using the equation Fd = 0.5 * ρ * v^2 * Cd * A, where Fd is the drag force, ρ is the density of the fluid, v is the velocity of the object, Cd is the drag coefficient, and A is the cross-sectional area of the object.

3. What factors affect the drag force on an object?

The drag force on an object is affected by its velocity, the density of the fluid it is moving through, its shape and size (determined by the drag coefficient and cross-sectional area), and the properties of the fluid (such as viscosity).

4. Can drag force be reduced to increase an object's maximum velocity?

Yes, drag force can be reduced by making changes to the object's shape and size, such as streamlining the object to reduce its drag coefficient and reducing its cross-sectional area. Additionally, using a less dense fluid or altering the properties of the fluid (such as reducing its viscosity) can also help decrease drag force and increase maximum velocity.

5. How does drag force affect different types of objects, such as airplanes and cars?

The effect of drag force on different objects depends on their shape and size. For example, airplanes are designed to be streamlined to reduce drag force and increase their maximum velocity, while cars have a more varied shape and are not designed for optimal aerodynamics. However, both airplanes and cars can benefit from reducing drag force to improve their performance and efficiency.

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