Drag Force Ratio

  • #1
2,148
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Homework Statement


Calculate the ratio of the drag force on a jet flying at ##1200 km/h## at an atttude of ##15 km## to the drag force on a prop-driven transport flying at half that speed and altitude.The density of air is ##0.38(\frac {kg} {m^3})## at ##10 km## and ##0.67(\frac {kg} {m^3})## at ##5 km##.Assume that the air-planes have the same effective cross-sectonal area and drag coefficient C

Homework Equations


##F_D=\frac 1 2CAρv^2##

The Attempt at a Solution


Here C and A are the same so ## F_D## jet will be ##F_1## and ##F_D## plane will be ##F_2##
##F_1=ρ_1(v_1)^2## and ##F_2=ρ_2(v_2)^2##

The question ask ratio so we dont care about units ( I guess )

##ρ_1## which at 15 km is I found approximately ##0.235 (\frac {kg} {m^3})## ( from Inverse ratio )
##ρ_2## which at 7.5 km is I found ##0.525 (\frac {kg} {m^3})##

So ##\frac {F_1} {F_2}=4 \frac {0.235} {0.525}=1.79##

answer is 3.3

I dont know where I went wrong

Thank you
 

Answers and Replies

  • #2
35,717
12,298
I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.
 
  • #3
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I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.
Yeah...I dont know too.This is all writes in the question.

Thanks
 
  • #4
haruspex
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You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.
 
  • #5
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You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

I know...So I think I just let it go :)
 
  • #6
35,717
12,298
You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.
It wouldn't fit to those values either, but of they might have altered even more values.
 
  • #7
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It wouldn't fit to those values either, but of they might have altered even more values.

What an interesting question....
 

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