Air blow-down, a worked high-velocity example

This worked example is a deliberately aggressive one, a short line dumping high-pressure air to a much lower pressure. It is a built-in network in Fluid Network Studio, and its job is to show what happens when a gas line is pushed near its limit and how the solver flags it. Anyone sizing a blow-down, a vent, or a short high-drop run should see this behaviour before trusting a result.

The scenario

A short pipe connects a point held at high pressure to a point held at much lower pressure. With a large pressure difference across a short, narrow line, the air accelerates hard toward the outlet. The question is not just what flow you get, it is whether the simple steady model is still trustworthy at the velocities involved, because as a gas approaches high speed the isothermal assumptions start to break down.

The real setup

The example uses these parameters exactly as built:

• An inlet boundary at 300 kPa absolute (about 2 bar gauge against the default atmosphere).
• A single pipe, 20 m long, 50 mm internal diameter, roughness 4.6e-5 m.
• An outlet boundary at 120 kPa absolute.
• Working fluid set to the gas phase, air at 15 degrees C, gas constant 287.05 J/kg.K, viscosity 1.81e-5 Pa.s.

The physics and method

The compressible gas kernel solves in absolute pressure, in the pressure-squared variable, using the exact isothermal pipe relation with the acceleration term and the Churchill friction factor. The acceleration term is doing real work here, because as the pressure collapses along the line the density falls steeply and the gas has to keep speeding up to carry the same mass. The solver tracks that and computes the velocity at the outlet end, where it is highest.

The solved result

The 20 m line passes 0.6021 kg/s and the air reaches 211.4 m/s at the outlet:

The mechanism is right there in the table. The mass flow is the same at both ends, and the density falls by a factor of two and a half from 3.627 to 1.451 kg/m3, so the velocity has to rise by exactly that factor, from 84.55 to 211.4 m/s. Nothing accelerates the gas except its own expansion. That is why a short line with a big pressure drop reaches speeds a long line at the same flow never sees.

The advisory is the second half of the result. The threshold for air at 15 degrees Celsius is 102.1 m/s, and the outlet is running at more than twice that, so the isothermal treatment is being stretched well past where it is comfortable. The solver still converges and still reports a mass balance, but the number carries a warning rather than a clean bill of health. This is a case where the honest answer is "here is the result and here is why you should not lean on it", and that is exactly what the advisory says.

Both the figures and the advisory come from the solver. Open the example, press Solve, then widen the pipe and watch the velocity and the advisory fall away together.

What the solver computes and what you learn

Solve it and the gas accelerates to about 210 m/s near the outlet, well past the threshold where the compressibility-limit assumptions hold. The solver raises a high-velocity advisory to tell you so. The model still solves, and the numbers are still produced, but the advisory is the signal that this line is near its compressible capacity and that a simple steady isothermal treatment is being stretched. The lesson is twofold. First, short high-drop lines reach surprising velocities. Second, a good solver does not just hand you a number, it warns you when the assumptions behind that number are getting thin. The advisory threshold is yours to read against your own design intent rather than a hidden pass-or-fail.

Compressible gas is part of the Advanced plan, so solving this example needs that plan.

Take it further

This example sits behind the compressed air system design page, which covers velocity limits and how to colour a network by velocity to spot a hot branch. The glossary explains the terms the solver uses. Fluid Network Studio supports your engineering work and does not replace a qualified engineer, and it makes no claim of compliance with any standard.

Open this example in FNS and widen the pipe to watch the advisory clear.