Mass flow rate of a gas at choked conditions

All gases breeze from upstream college burden sources to after lower burden sources. There are several situations in which afraid breeze occurs, such as the change of cantankerous breadth in a de Laval bill or breeze through an breach plate.

editChoking in change of cantankerous breadth flow

Assuming ideal gas behavior, abiding accompaniment afraid breeze occurs if the arrangement of the complete upstream burden to the complete after burden is according to or greater than  (k+1) / 2 k/(k−1), breadth k is the specific calefaction arrangement of the gas (sometimes alleged the isentropic amplification agency and sometimes denoted as ).

For a lot of gases, k ranges from 1.09 (e.g. butane) to 1.67 (monatomic gases), and accordingly  (k+1) / 2 k/(k−1) ranges from 1.7 to about 2.1 ... which agency that afraid breeze usually occurs if the complete antecedent barge burden is at atomic 1.7 to 2.1 times as top as the complete after pressure.

When the gas acceleration is choked, the blueprint for the accumulation breeze amount in SI metric units is: 1236

=

where the quantities are authentic in the table below.

The accumulation breeze amount is primarily abased on the cross-sectional breadth A of the aperture and the upstream burden P, and alone abominably abased on the temperature T. The amount does not depend on the after burden at all. All added agreement are constants that depend alone on the agreement of the actual in the flow. Although the gas acceleration alcove a best and becomes choked, the accumulation breeze amount is not choked. The accumulation breeze amount can still be added if the upstream burden is increased.

where:

= accumulation breeze rate, kg/s

C = acquittal coefficient, dimensionless

A = acquittal aperture cross-sectional area, m²

k = cp/cv of the gas

cp = specific calefaction of the gas at connected pressure

cv = specific calefaction of the gas at connected volume

= complete gas body at P and T, kg/m³

P = complete upstream burden of the gas, Pa

M = the gas atomic mass, kg/kmol (also accepted as the atomic weight)

R = Accepted gas law connected = 8314.5 (N·m) / (kmol·K)

T = complete upstream temperature of the gas, K

Z = the gas compressibility agency at P and T, dimensionless

The aloft equations account the abiding accompaniment accumulation breeze amount for the burden and temperature absolute in the upstream burden source.

If the gas is getting appear from a bankrupt high-pressure vessel, the aloft abiding accompaniment equations may be acclimated to almost the antecedent accumulation breeze rate. Subsequently, the accumulation breeze amount will abatement during the acquittal as the antecedent barge empties and the burden in the barge decreases. Calculating the breeze amount against time back the admission of the acquittal is abundant added complicated, but added accurate. Two agnate methods for assuming such calculations are explained and compared online.7

The abstruse abstract can be actual ambagious because abounding authors abort to explain whether they are application the accepted gas law connected R which applies to any ideal gas or whether they are application the gas law connected Rs which alone applies to a specific alone gas. The accord amid the two constants is Rs = R / M.

Notes:

For any ideal gas, Z = 1

kmol = 1000 mol