Transient Gas Flow

This type of flow normally concerns the charging of a volume through a fixed resistance such as an orifice. The use of the Lohm Laws simplifies the calculation of the time required to blow down or charge up a vessel.

The first step is to calculate the system time constant, 𝜏, which takes into consideration the type of gas, the volume of the pressure vessel, the absolute temperature, and the Lohm rate of the orifice. The system time constant is given by:

Where:

K = Volumetric units correction factor
L = Orifice Lohm rate, (Lohms)
f_T = Temperature factor
V = Pressure vessel volume
𝜏 = System time constant (sec.)

Note: Select “K” from the appropriate “psia” column of the table of volumetric flow units on the How To Calculate Flow Resistance for Gases page. Keep the units of pressure vessel volume “V” consistent with the volumetric flow units.

The larger the value of 𝜏, the more sluggish the system.

Once 𝜏 has been calculated, the ratio of upstream pressure to downstream pressure for both the initial and final conditions must be computed. Then, from the pressure-ratio graph, initial and final values for “N” can be found. “N” is the number of system time constants required for the system to reach equilibrium.

If the final condition is equilibrium, where upstream and downstream pressures are equal, the final pressure ratio is 1 and the final value of “N” is 0. With these values, the time for the system to blow down or charge up can be calculated from:

Where:

N_i = Initial number of system time constants
N_f = Final number of system time constants
P₁ = Upstream gas pressure
P₂ = Downstream gas pressure
t = Time to charge up or blow down a pressure vessel (sec.)