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Mach Number

The Cauchy parameter, after transformation becomes the 'Mach number' subsonic for 'Aair'as ideal gas is derived from Bernoulli equation.

M 2 γ 1 - / (qc p / 1 + (γ 1 - γ /^1 - (* sqrt ≡

In supersonic condition, compressible fluids and past the "choc wave", Mach number is derived from the Rayleigh-Pitot equation with 'qc' = impact pressure past the "choc wave".

M 0.88128485 qc P / 1 + (117 M 2^* / - (2.5^* sqrt * ≡

k 0.88128485 : Pitot constant ≡

P static pressure ≡

qc dynamic pressure ≡

x Pitot dynamic ratio qc/P ≡

x qc P / ≡ supersonic Pitot ratio ≡

x Mach 21.7077 4276.76 x 233.903 + 491.007 x 20.0537 + 16.7228 x 4.31361 + 0.559674 x 0.165479 + / - / - / - / - :

Supersonic Pit k 2 k 022 mat :

x M 0.88128485 x ≤ x Mach M subsonic ≡ if :

Mach x k 15 k 0.025 + (range : i 1 x rows range u i el x i el : m i el x i el M : 21 line for u m augment 31 line :

Mach rows 565

Supersonic Mach Number ... x = qc/P [Dynamic/Static

Mach Pit 1 3 1 sys

k 0.88128485 : Pitot constant ≡

Supersonic solving procedure x f U x 1 + (117 U 2^* / - (2.5^* sqrt / k - 0 ≡ U 1 roots :

A solver is not an option if a good approximation exists. J_fraction is otained from sampled points from the solver. Sampled points are passed to rational fraction "GenfitMatrix".

Smath non-seeded scalar iterative solver

0.88128485 x ≤ x f subsonic if 1 2 1 sys

------- Sanity check .......

..... Explain/Conclude exact solver vs Mach(x) J_Fraction. Conclusion: "Mach(x)" => f(x)± 0.0001 where 'x'=qc/P [supersonic Pitot ratio].

k f k Mach 21 mat 0.9947 0.9948 21 mat

4 f 4 Mach 21 mat 1.87056 1.87058 21 mat

2 f 2 Mach 21 mat 1.3859 1.3859 21 mat

5 f 5 Mach 21 mat 2.06903 2.06905 21 mat

3 f 3 Mach 21 mat 1.6474 1.6474 21 mat

6 f 6 Mach 21 mat 2.24968 2.24971 21 mat

γ 1.4 : Air Isentropic ≡

x Subsonic 0 x ≤ (x 0.88128485 ≤ (& 2 γ 1 - / (x 1 + (γ 1 - γ /^1 - (* sqrt Supersonic if :

speed of sound at sea level = 340.29 m/s

x Supersonic 0.88128485 x ≤ U x 1 + (117 U 2^* / - (2.5^* sqrt / k - 0 ≡ U 1 roots Subsonic if :

x Subsonic x Supersonic 0.88 1 + 20 black 1 5 mat 3 1 sys