Answer:
The Mach number is 2.866
Total temperature To = 528.524K
Explanation:
[tex] Pressure (P)= 5 * 10^4 N/m^2 [/tex]
[tex] Total pressure (Po) = 1.5 * 10^6 N/m^2 [/tex]
Temperature (T) = 200K
For air, r= 1.4
To find the Mach number we use:
[tex] Po/P = [1 + (r - 1/2) M^2] ^ r^/^r^-^1 [/tex]
[tex] 1.5 * 10^6 / 5 * 10^4 =[ 1 + (1.4 -1 /2) (M^2) ] ^ 1^.^4^/^1^.^4^-^1 [/tex]
[tex] 0.3 * 10^2 = (1 + 0.2M^2) ^3^.^5 [/tex]
[tex] (0.3 * 10^2)^(1/3.5) = 1 + 0.2M^2 [/tex]
[tex] 2.6426 = 1 +0.2M^2 [/tex]
[tex] 2.6426 - 1 = 0.2M^2 [/tex]
1.6426 = 0.2M^2
[tex] M^2 = 1.6426/0.2 [/tex]
[tex]M = sqrt(1.6426/0.2) [/tex]
M = 2.866
To find Total Temperature :
[tex] To/T = (Po/P)^r^-^1^/^8) [tex]
[tex] To/200 = (1.5*10^6 / 5*10^4)^ 1^.^4^-^1^/^1^.^4) [/tex]
[tex] To/200 = (0.3 * 10^2)^0^.^2^8^5^7 [/tex]
To =528.524K
