Formula & Engineering Reference
Choked (sonic) isothermal flow through the orifice or valve — the same upstream-pressure-proportional choked flow used in the site's Flare System depressuring tab. τ is the inventory divided by the initial mass flow; because choked flow scales with P, the decay is a clean exponential.
What this means: blowdown time is how long the restriction needs to bring the line down to target pressure assuming sonic flow holds the whole way — it's the number operators use to judge whether the relief path is fast enough.
Why it matters / why fast can be dangerous: rapid gas expansion drives severe Joule-Thomson cooling. A line that blows down in seconds can see metal temperatures plunge far below what carbon steel tolerates without becoming brittle — exactly when the system is already stressed by an emergency event.
Operational considerations: size the restriction to API 521's roughly 15-minute fire-case target — fast enough to relieve pressure before a heated vessel weakens, slow enough to avoid extreme cooling and flare/KO-drum surge. Confirm downstream piping and the flare KO drum are rated for the peak instantaneous flow, not just the average.
The time for the choked restriction to bring the line from initial to final pressure, assuming sonic flow holds throughout — an exponential pressure decay.
Severe Joule-Thomson cooling can drop pipe metal temperature below the brittle-fracture threshold for carbon steel within seconds.
It balances fire-exposed vessel weakening (too slow) against extreme cooling and surge loads on the flare system (too fast).
Only while the pressure ratio stays above critical. Near the end of blowdown the flow un-chokes, so the real tail is slightly slower than this estimate.