At a given point in the high-speed flow over an airplane wing, the local Mach number, pressure and temperature are 0.7,0.9 atm, and 250 K, respectively. Calculate the values of p,, To, p*, T*, and a* at this point.

a) p₀ = 1.2484 atm

b) T₀ = 274.5 K

c) p* = 0.6595 atm

d) T* = 228.74 K

e) a* = 303.16 m/s  

Explanation:

Given that;

Local Mach number M = 0.7

Pressure P = 0.9 atm

Temperature T = 250 K

First we obtain the following ratios corresponding to Mach Number 0.7 from Appendix(A) table { ISENTROPIC FLOW PROPERTIES }

For M = 0.7; Pressure→ P/P₀ = 0.7209, Temperature; T/T₀ = 0.91075

Now we calculate;

a)  value of p₀

we that; P/P₀ = 0.7209

p₀ = p / 0.7209

we substitute

p₀ = 0.9 / 0.7209

p₀ = 1.2484 atm

b) value of T₀

we know that;  

T/T₀ = 0.91075

T₀ = T / 0.91075

we substitute

T₀ = 250 / 0.91075

T₀ = 274.5 K

c) value of p*

To obtain value of p*, we say;

(p* / p₀) = 0.52828

p* = 0.52828 × 1.2484

p* = 0.6595 atm

d) value of T*

To obtain value of T*, we say;

(T* / T₀) = 0.8333

T* = 0.8333 × 274.5

T* = 228.74 K

e) value of a*

we know that;

a* = √(γRT*)

so

a* = √(1.4 × 287 × 228.74)

a* = √(91907.732)

a* = 303.16 m/s  

the clapeyron equation (also called the clausius-clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties.

explanation: