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ThermoLab · Chapters 16 and 17

Chemical equilibrium and compressible flow

Interpolates Kp and solves Mach number, choking, critical area and normal shock in a De Laval nozzle.

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Engineering framework

Theory, equations and conditions of use

Chemical equilibrium minimises Gibbs energy, while compressible flow couples energy, continuity and the speed of sound. Both problems are non-linear.

Fundamento

Equilibrium constant

Kp relates the partial activities of products and reactants at equilibrium.

\(K_p=\prod_i(P_i/P^\circ)^{\nu_i}\)

Fundamento

Stagnation properties

Static temperature falls as enthalpy is converted into velocity.

\(T_0/T=1+(k-1)M^2/2\)

Fundamento

Area–Mach relation

A single A/A* admits both a subsonic and a supersonic solution.

\(\frac{A}{A^*}=\frac{1}{M}[\frac{2}{k+1}(1+\frac{k-1}{2}M^2)]^{\frac{k+1}{2(k-1)}}\)
Base documentalÇengel & Boles, 7th edition · SI appendices A-1 to A-28
USCS conversionA-1E to A-27E, via exact factors from the SI base
AlcancePreliminary design, teaching and independent verification

Engineering FAQ

Preguntas frecuentes

Why are there two Mach numbers?+

The subsonic branch corresponds to a converging duct; the supersonic branch, to expansion after a sonic throat.

When does a shock appear?+

When the back pressure forces the supersonic branch to adapt inside the nozzle.

Does Kp have units?+

It is formulated with normalised activities, so it is dimensionless.

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