01 / READ THE CHANGE
Pressure and speed exchange
An expansion fan turns supersonic flow around a convex corner. Static pressure falls as Mach number rises.
TURN THE FLOW. CHANGE ITS STATE.
Oblique Shocks & Expansion Fans
Drag a compression or expansion corner. See the wave geometry and thermodynamic change emerge from the same solution.
INTERACTIVE CALCULATED DIAGRAMB · LIVE
Diagram · drag background to pan
Drag the turquoise handles, or focus a handle and use arrow keys. The sliders provide the same controls.
Preparing the calculation…
A · no saved reference
02 / READ THE CHANGE
Total pressure tells another story
An ideal expansion conserves total pressure. A shock generates entropy and loses total pressure even while static pressure rises.
03 / READ THE CHANGE
Respect the attached limit
Beyond the maximum turning angle, the attached-shock solver stops. A detached bow shock cannot be represented by extending the straight shock line.
THE SAME MODEL, CONNECTED VIEWS
Follow the calculation
B · solid turquoise A · dashed amber
Compare A and B
| Quantity | A · saved | B · live | B − A | Unit |
|---|
A remains fixed until saved again. Export includes the model version, settings and plotted data.
Equations, assumptions & sources
Read the balance, then connect each symbol to the model. Open a symbol key for definitions and units. Long equations can be scrolled sideways.
01 · Attached compression turn
The θ–β–M relation supplies the weak or strong attached-shock branch.
Symbols & units
- Flow-turn angle and shock angle, rad; controls display degrees.
- Upstream Mach number; ratio of specific heats γ = 1.4.
02 · Expansion turns use a different relation
The model uses negative turn angles for expansion and solves the Prandtl–Meyer relation.
Symbols & units
- Prandtl–Meyer expansion angle, rad; ν is an angle here, not kinematic viscosity.
- Downstream Mach number.
03 · Total enthalpy is conserved
Conserved total enthalpy does not imply conserved total pressure across a shock.
Symbols & units
- Upstream/downstream stagnation specific enthalpy, J/kg.
- Static temperature, K; flow speed, m/s. Constant cₚ is used.
Steady two-dimensional inviscid calorically perfect gas, γ = 1.4. Upstream static state is 101325 Pa and 288.15 K. One corner only; no boundary-layer interaction, shock reflection, detached shock shape or real-gas chemistry. Curves contain gaps where attached solutions do not exist.
NASA · oblique shocks ↗NASA · Prandtl–Meyer angle ↗Physical relations and teaching sources support the stated concepts. Generic coefficients are explicitly illustrative; they are not measured manufacturer data. Numerical verification is separate from experimental validation. Model version: applied-labs-v1.1.