Drag force and maximum velocity

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Discussion Overview

The discussion revolves around a homework problem related to calculating the maximum speed of a vehicle considering aerodynamic drag force. Participants explore the application of relevant equations and unit conversions in the context of engineering principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a homework problem involving the calculation of maximum speed using horsepower, fluid density, reference area, and drag coefficient.
  • Another participant suggests that lbm is not the proper unit and that mass should be converted to slugs for consistency in Imperial units.
  • A participant questions whether the mass density of the fluid needs conversion, indicating confusion about the units used.
  • Clarification is provided that a lbm weighs 1 pound on Earth, leading to a discussion about the conversion from lbm to slugs.
  • One participant shares their calculations after converting mass density, but they still arrive at an incorrect answer, prompting further inquiry into their method.
  • Another participant requests to see the calculations to verify the conversion of mass density into slugs per cubic foot.
  • There is a question regarding whether the velocity (V) should be expressed in feet per second or miles per hour, with clarification that the final answer should be in mph.
  • A participant shares their calculations, resulting in a speed of approximately 195.5 mph, which is still not matching the expected answer of 186 mph.
  • Another participant corroborates the calculations, arriving at a similar speed of around 196 mph, suggesting a possible error in the source material.

Areas of Agreement / Disagreement

Participants express differing results for the maximum speed calculation, with some arriving at values around 195-200 mph while the expected answer is 186 mph. There is no consensus on the correct answer, and the discussion remains unresolved regarding the source of the discrepancy.

Contextual Notes

Participants note potential issues with unit conversions and the accuracy of the provided answer in the homework problem. There is uncertainty about the proper handling of mass density and the implications of using different units.

bang
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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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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.
 
Last edited:
Only the mass density of fluid is in lbm, so I would need to convert the mass density of fluid? I don't understand.
 
Yes. A lbm weighs 1 pound on Earth. Since w = mg, m = ? in slugs.
 
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.
 
Show your numbers and I'll check it out. What did you get for the mass density in slugs/ft^3?
 
Is V supposed to be in ft/sec or miles per hour?
 
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.
 
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!
 

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