What is the Relationship Between Mach Number and Velocity in Compressible Flow?

[LaReina]

Homework Statement

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.

Homework Equations

$M=\frac{V}{a}$

$a=\sqrt{γRT}$

The Attempt at a Solution

I've worked out the speed for the first object which is as follows
$a=\sqrt{1.4\times287\times180}=268.931m/s$
$V=0.5\times268.931=134.465m/s$

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.

 

[Chestermiller]

Homework Statement

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.

Homework Equations

$M=\frac{V}{a}$

$a=\sqrt{γRT}$

The Attempt at a Solution

I've worked out the speed for the first object which is as follows
$a=\sqrt{1.4\times287\times180}=268.931m/s$
$V=0.5\times268.931=134.465m/s$

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.

Please show us your work for the second temperature.

Chet

 

[LaReina]

Please show us your work for the second temperature.

Chet

$a=\sqrt{1.4\times287\times100}=200.448$
$V=200.448\times0.5=100.224$

 

[Chestermiller]

This calculation looks OK to me.

Chet

 

[dauto]

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.