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Industrial MicroHydraulics

# Transient Gas Flow

## Introduction

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

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

 Note: Select K from the appropriate “psia" column of the Volumetric Flow Table here. 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:

## Nomenclature

K L = Units correction factor = Flow resistance, (Lohms) = Initial number of system time constants = Final number of system time constants = Upstream gas pressure = Downstream gas pressure = Temperature factor = Time to charge up or blow down a pressure vessel (sec.) = Pressure vessel volume = System time constant (sec.)