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Drag Force Ratio

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  1. Jan 22, 2017 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    ##F_D=\frac 1 2CAρv^2##

    3. 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
     
  2. jcsd
  3. Jan 23, 2017 #2

    mfb

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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.
     
  4. Jan 23, 2017 #3
    Yeah...I dont know too.This is all writes in the question.

    Thanks
     
  5. Jan 23, 2017 #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.
     
  6. Jan 24, 2017 #5
    I know...So I think I just let it go :)
     
  7. Jan 24, 2017 #6

    mfb

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    It wouldn't fit to those values either, but of they might have altered even more values.
     
  8. Jan 24, 2017 #7
    What an interesting question....
     
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