Question

At a given point in a supersonic wind tunnel, the pressure and temperature are 5×104 N/m2 and 200 K, respectively. The total pressure at this point is 1.5×106 N/m2. Calculate the local Mach number and total temperature.

Answer 1

The Mach number is 2.866

Total temperature To = 528.524K

Step-by-step explanation:

`Pressure (P)= 5 * 10^4 N/m^2`

`Total pressure (Po) = 1.5 * 10^6 N/m^2`

Temperature (T) = 200K

For air, r= 1.4

To find the Mach number we use:

`Po/P = [1 + (r - 1/2) M^2] ^ r^/^r^-^1`

`1.5 * 10^6 / 5 * 10^4 =[ 1 + (1.4 -1 /2) (M^2) ] ^ 1^.^4^/^1^.^4^-^1`

`0.3 * 10^2 = (1 + 0.2M^2) ^3^.^5`

`(0.3 * 10^2)^(1/3.5) = 1 + 0.2M^2`

`2.6426 = 1 +0.2M^2`

`2.6426 - 1 = 0.2M^2`

1.6426 = 0.2M^2

`M^2 = 1.6426/0.2`

`M = sqrt(1.6426/0.2)`

M = 2.866

To find Total Temperature :

`To/T = (Po/P)^r^-^1^/^8) [tex]</p><p></p><p>[tex] To/200 = (1.5*10^6 / 5*10^4)^ 1^.^4^-^1^/^1^.^4)`

`To/200 = (0.3 * 10^2)^0^.^2^8^5^7`

To =528.524K