Isentropic flow of a calorically perfect gas. Enter any one of the tabulated quantities, the Mach number, a total-to-static ratio, or the area ratio on the subsonic or supersonic branch, and the others follow from the closed-form relations, in place of the tables in Anderson’s Appendix A. The γ in the top bar applies to every value on the page.

Appendix A · Isentropic flow properties

Calculator

Enter one known quantity
p/p0ρ/ρ0T/T0A*/A

Reference

Relations used

Total-to-static ratios

Each ratio increases monotonically with M, so a known ratio gives the Mach number directly by solving the relation for M.

Area–Mach number relation

A/A* has its minimum, 1, at M = 1, so every A/A* > 1 has two solutions: one subsonic and one supersonic. The branch must be chosen from the flow; the calculator finds the chosen root by bisection.

Background

Where these relations come from