Inputs
Ideal assumes isothermal behavior with Z=1 and Cd=1.
–
n=1 isothermal, n≈k adiabatic.
s
Smaller step → smoother curves, longer compute time.
Results
Total blowdown time
—
seconds
Choked regime time
—
seconds
Unchoked regime time
—
seconds
Mass vented
—
kg
| # | t (s) | P (bar abs) | T (K) | m (kg) | ṁ (kg/s) | Regime |
|---|---|---|---|---|---|---|
| No data yet—press Compute. | ||||||
Regime shown at sample points; integration uses the same regime each step.
Example Data Table
Example computed using defaults: V=0.1 m³, orifice Ø=5 mm, air at 293.15 K, P0=20 bar abs, Pamb=1.01325 bar abs, n=1.2, Cd=0.8, Z=1.
| t (s) | P (bar abs) | T (K) | ṁ (kg/s) | Regime |
|---|---|---|---|---|
| Press Compute to populate the example snapshot. | ||||
Formulas Used
Ideal gas in tank: m = P V / (Z R T)
Polytropic tank process: P ρ-n = const, where ρ = m/V and n∈[1,k]
Critical pressure ratio (choking): r* = (2/(k+1))k/(k-1)
Choked mass flow: ṁ = Cd A P &sqrt;[ k/(Z R T) ] · (2/(k+1))(k+1)/(2(k-1))
Subsonic mass flow: ṁ = Cd A P &sqrt;{ [2k/(Z R T (k-1))] · [ (Pd/P)2/k − (Pd/P)(k+1)/k ] }
State closure (polytropic): with C = P0/ρ0n, at each step P = C · ρn, T = P/(Z R ρ)
Assumes well-mixed tank acting as a single control volume, quasi-steady nozzle flow, constant k and R over the range, and optional Z for real-gas correction.
How to Use
- Select Ideal to fix Z=1 and Cd=1 with n=1.
- Choose a gas or select Custom to set k and R.
- Enter tank volume and orifice (diameter or area).
- Set initial, ambient, and desired final absolute pressures.
- Set the initial temperature and the polytropic exponent n.
- Click Compute. Results and a sampled time-history appear below.
- Use CSV or PDF buttons to export the table and summary.
Safety note: This tool is for educational engineering estimates. Always validate against applicable standards and perform professional review before use in design decisions.
FAQs
Blowdown time is the duration required for a pressurized tank to vent from an initial absolute pressure to a specified lower absolute pressure through an outlet orifice or valve.
Ideal mode assumes Z=1, Cd=1, and isothermal behavior (n=1). Real mode lets you set compressibility Z, discharge coefficient, and a polytropic exponent between isothermal and adiabatic.
The tool compares the downstream-to-upstream pressure ratio with the critical ratio r* = (2/(k+1))k/(k-1). If Pd/P ≤ r*, sonic flow occurs at the orifice and mass flow is limited.
Typical discharge coefficients range 0.6–0.9 for sharp-edged orifices and up to ~0.98 for well-designed nozzles. If unknown, 0.8 is a common preliminary estimate.
Real blowdown is rarely perfectly isothermal or adiabatic. A polytropic model with 1≤n≤k approximates heat transfer with the surroundings, affecting the temperature drop and discharge rate.
Z is the compressibility factor. Z=1 is ideal gas. For higher pressures or certain gases, using Z≠1 can better match real-gas density and mass in the tank.
No. The equations assume single-phase gas. If condensation or flashing can occur, specialized two-phase methods and safety analyses are required.
Always enter absolute pressures. Convert gauge to absolute by adding ambient pressure. The calculator offers units for convenience but treats values internally as absolute.
Small tanks, large orifices, high initial pressure, and choked flow produce high mass flow rates, shortening the duration substantially. Conversely, small orifices or near-ambient conditions lengthen it.
Yes in general. This tool assumes constant k and R over the range. For high accuracy, use properties appropriate to the expected temperature band.
An explicit time-marching scheme updates mass, then uses the polytropic closure to recover P and T. Step size control is available; smaller steps improve fidelity at greater cost.