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Mach Number and Velocity

  1. Jun 23, 2014 #1
    1. The problem statement, all variables and given/known data
    An object is flying through the air at M=0.5. The free stream temperature is equal to 180 K. At what speed should the object fly when the temperature is 100 K in order to maintain the same Mach number? (therefore ensuring compressibility effects are the same). What was the speed of the first object.


    2. Relevant equations
    [itex]M=\frac{V}{a}[/itex]

    [itex]a=\sqrt{γRT}[/itex]


    3. The attempt at a solution
    I've worked out the speed for the first object which is as follows
    [itex]a=\sqrt{1.4\times287\times180}=268.931m/s[/itex]
    [itex]V=0.5\times268.931=134.465m/s[/itex]

    However when I work out the speed for the second temperature using the exact procedure, I get 100.225 as an answer. The answer that has been given is 88.52m/s.
     
  2. jcsd
  3. Jun 23, 2014 #2
    Please show us your work for the second temperature.

    Chet
     
  4. Jun 25, 2014 #3
    [itex] a=\sqrt{1.4\times287\times100}=200.448[/itex]
    [itex]V=200.448\times0.5=100.224[/itex]
     
  5. Jun 25, 2014 #4
    This calculation looks OK to me.

    Chet
     
  6. Jun 25, 2014 #5
    May be the question has a typo and it meant to ask what happens if the temperature drops 100K (which means it drops to 80K). That brings the answer closer to the answer provided.
     
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