Answer:
A) Mach number at Inlet;M1 = 0.292
B) amount of heat received;Q_in = 105.59 KJ/kg
Explanation:
A) The formula for the speed of nitrogen at the inlet is;
C1 = √kRT1
Where;
k is a constant = 1.4
R is the gas constant of nitrogen R = 296.8 J/kg.K
T1 is the temperature at inlet = 10°C = 10 + 273 K = 283K
Thus;
C1 = √(1.4 * 296.8 * 283)
C1 = 342.9 m/s
Formula for mach number at inlet is;
M1 = V1/C1
We are given V1 = 100 m/s
Thus; M1 = 100/342.9
M1 = 0.292
B) We are given mach number at exit; M2 = 0.51
Also; V2 = 200 m/s
Thus;M2 = V2/C2
C2 = V2/M2 = 200/0.51
C2 = 392.16 m/s
Now, we know that;
C2 = √kRT2
So, 392.16 = √(1.4 * 296.8 * T2)
392.16² = 415.52*T2
T2 = 392.16²/415.52
T2 = 370.11 K
Now formula for steady flow balance equation is;
Q_in = =cp(T2 -T1) + [(v2)² - (v1)²]/2
Where Q_in is the amount of heat energy received and cp is the specific heat of nitrogen,= 1.040 KJ/kg.K
Plugging in the relevant values;
Q_in = 1.04(370.11 -283) + [(200)² - (100)²]/2](1KJ/Kg/1000m²/s²)
Q_in = 90.59 + 15
Q_in = 105.59 KJ/Kg