Compressible flow, solved in the direction you actually need

Which one do I need?

• Isentropic flow

  A nozzle or a diffuser with no shock in it. Type into any quantity, not just Mach number — and get both roots of the area ratio at once.

• Normal shock

  A pitot probe, a shock tube, the shock swallowed by a supersonic inlet. Solves from either Mach number, any jump ratio, or the stagnation pressure reading you can actually take in a tunnel.

• Oblique shock

  A wedge, a compression ramp, an inlet cowl. Both the weak and the strong root, the detachment limit as a number rather than an error, and the Mach number from two measured angles — which is what a schlieren photograph gives you.

• Prandtl–Meyer expansion

  An expansion corner, a nozzle wall opening out, the shoulder of a wedge. Solves ν → M as well as M → ν, and says how much turning is left before the flow can no longer follow the wall.

• de Laval nozzle

  A rocket engine or a blowdown tunnel. The answer here is a regime before it is a number — not choked, a shock standing inside the bell, over- or underexpanded — so it names the regime, says where the shock is, and draws the waves past the lip at the angles it solved for them.

• Fanno flow

  A long duct where friction dominates. How much duct is left before it chokes, both of the flows a given length can carry, and the ceiling on how long a supersonic one can be.

• Rayleigh flow

  A combustor or a heat exchanger. Heat to choking from either side, and the temperature peak below sonic where adding heat starts cooling the gas.

• Conical flow — Taylor–Maccoll

  A missile nose or an inlet spike. A cone is not a wedge of the same half-angle: the flow relieves sideways, so the shock sits closer in and is weaker — and it keeps turning behind the shock, so the surface state and the post-shock state are both reported.