Question

A commercial jet is flying at a standard altitude of 35,000 ft with a velocity of 550 mph: (a) what is the Mach number? (b) should the flow be treated as incompressible, why or why not?

Answer 1

Mach number = 0.68168

The flow should be treated as compressible.

Step-by-step explanation:

Given that:

The altitude of a commercial jet = 35000

The properties of air at that given altitude are as follows:

Pressure = 24.577 kPa

Temperature T = 50.78176° C

Temperature T = ( 50.78176 + 273 )K = 328.78176 K

`\varphi = 0.38428 \ kg/m^3`

The velocity is also given as: 550 mph = 245.872 m/s

Therefore, the sonic velocity is firstly determined by using the formula:

`a = \sqrt{ \vartheta * R * T\`

`a = \sqrt{1.4 * 287 * 323.78176`

`a = \sqrt{130095.5112`

a = 360.68755 m/s

Then, we can calculate the Mach number by using the expression:

`{Mach \ number = (V)/(a)}`

`Mach \ number = (245.872)/(360.68755)`

Mach number = 0.68168

b) Ideally, all flows are compressible because the Mach number is greater than 0.3, suppose the Mach number is lesser than 0.3, then it is incompressible.