MaximaLabsOpen app

Pressure-Driven Dynamic Networks

Gas vessels of fixed volume carry a molar holdup whose pressure follows the ideal-gas law; valve branches carry a flow driven by the pressure drop across them — flow is an outcome of pressure, not an input, so startup/blowdown/relief dynamics fall out naturally.

dynamicsnetworkrelief
Concept

The tank engine sets each outlet flow directly — it can't represent startup, blowdown, or relief dynamics where flow is an outcome of pressure, not an input. This engine closes that gap: gas vessels of fixed volume carry a molar holdup whose pressure follows the ideal-gas law; valve branches carry a flow driven by the pressure drop across them.

The math
Show the governing equations
P=nRTV(vessel pressure from molar holdup)P = \frac{nRT}{V} \quad \text{(vessel pressure from molar holdup)}
F=Cv⋅opening⋅sign(ΔP)∣ΔP∣(valve_flow)F = C_v \cdot \text{opening} \cdot \text{sign}(\Delta P)\sqrt{|\Delta P|} \quad \text{(valve\_flow)}
A high-pressure vessel pushes gas into a lower-pressure one until they equalize. Fixed-pressure boundary nodes act as infinite reservoirs (supply/relief headers); valve openings can be stepped by disturbances or driven by a PID. Ideal-gas, isothermal, single-species-agnostic — a bounded but honestly pressure-flow-coupled model; a full compressible multicomponent network is the documented follow-up.
Execution

Models an emergency-relief valve opening at a specified time, or a PID-driven pressure- control valve, reusing the same dynamics.pid controller the tank engine uses.