Answer:
A) Mach Number = 0.716
B) Speed of Aircraft = 229.64 m/s
Explanation:
Formula for stagnation pressure is given as;
Po = P + ΔP = 54 + 22 = 76 KPa
Also, Po/P = [1 + {((k - 1)m²)/2}]^(k/(k-1))
Where m is mach number and k is specific heat ratio of air.
Specific heat ratio of air = 1.4
Thus we can solve as follows;
76/54 = [1 + {((1.4 - 1)m²)/2}]^(1.4/(1.4-1))
1.407 = [1 + (0.2m²)]^(1.4/0.4)
1.407 = [1 + (0.2m²)]^(7/2)
Now, raise both sides to the power of 2/7 to obtain ;
(1.407)^(2/7) = 1 + 0.2m²
Thus, 1 + 0.2m² = 1.1025
Subtract 1 from both sides;
0.2m² = 1.1025 - 1
0.2m² = 0.1025
m² = 0.1025/0.2
m² = 0.5125
m = 0.716
Now, the speed of sound in air is given as;
C = √KRT
R is ideal gas constant which is 287 J/Kgmol and T is temperature which is 256K
Thus,
C = √(1.4 x 287 x 256) = 320.72 m/s
Thus, Speed of aircraft = Cm
Speed of aircraft = 320.72 x 0.716 = 229.64 m/s
