Choked flow

Choked breeze is a compressible breeze effect. The constant that becomes "choked" or "limited" is the velocity.

Choked breeze is a aqueous activating action associated with the Venturi effect. If a abounding aqueous at a accustomed burden and temperature passes through a brake (such as the throat of a convergent-divergent bill or a valve in a pipe) into a lower burden ambiance the aqueous acceleration increases. At initially subsonic upstream conditions, the attention of accumulation assumption requires the aqueous acceleration to access as it flows through the abate cross-sectional breadth of the restriction. At the aforementioned time, the Venturi aftereffect causes the changeless pressure, and accordingly the density, to abatement after accomplished the restriction. Afraid breeze is a attached action which occurs if the accumulation breeze amount will not access with a added abatement in the after burden ambiance while upstream burden is fixed.

For constant fluids, the concrete point at which the asthmatic occurs for adiabatic altitude is if the avenue even acceleration is at sonic altitude or at a Mach amount of 1.123 At afraid breeze the accumulation breeze amount can be added by accretion the upstream pressure, or by abbreviating the upstream temperature.

The afraid breeze of gases is advantageous in abounding engineering applications because the accumulation breeze amount is absolute of the after pressure, depending alone on the temperature and burden on the upstream ancillary of the restriction. Under afraid conditions, valves and calibrated breach plates can be acclimated to aftermath a adapted accumulation breeze rate.

Choked flow in liquids

If the aqueous is a liquid, a altered blazon of attached action (also accepted as afraid flow) occurs if the Venturi aftereffect acting on the aqueous breeze through the brake decreases the aqueous burden to beneath that of the aqueous breath burden at the prevailing aqueous temperature. At that point, the aqueous will partially beam into bubbles of breath and the consecutive collapse of the bubbles causes cavitation. Cavitation is absolutely blatant and can be abundantly agitated to physically accident valves, pipes and associated equipment. In effect, the breath balloon accumulation in the brake banned the breeze from accretion any further

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

Real Gas Effects

If the upstream altitude are such that the gas cannot be advised as ideal, there is no bankrupt anatomy blueprint for evaluating the afraid accumulation flow. Instead, the gas amplification should be affected by advertence to absolute gas acreage tables, area the amplification takes abode at connected entropy.

Thin-plate orifices

The breeze of absolute gases through thin-plate orifices never becomes absolutely choked. The accumulation breeze amount through the breach continues to access as the after burden is bargain to a absolute vacuum, admitting the accumulation breeze amount increases boring as the after burden is bargain beneath the analytical pressure.8 Cunningham (1951) aboriginal drew absorption to the actuality that afraid breeze will not action beyond a standard, thin, square-edged orifice.

Minimum pressure ratio required for choked flow to occur

The minimum burden ratios appropriate for afraid altitude to action (when some archetypal automated gases are flowing) are presented in Table 1. The ratios were acquired application the belief that 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) , area k is the specific calefaction arrangement of the gas. The minimum burden arrangement may be accepted as the arrangement amid the upstream burden and the burden at the bill throat if the gas is traveling at Mach 1; if the upstream burden is too low compared to the after pressure, sonic breeze cannot action at the throat.

Table 1

Gas k = cp/cv Minimum

Pu/Pd

required for

choked flow

Helium 1.660 2.049

Hydrogen 1.410 1.899

Methane 1.307 1.837

Propane 1.131 1.729

Butane 1.096 1.708

Ammonia 1.310 1.838

Chlorine 1.355 1.866

Sulfur dioxide 1.290 1.826

Carbon monoxide 1.404 1.895

Notes:

Pu = complete upstream gas pressure

Pd = complete after gas pressure

k ethics acquired from:

Perry, Robert H. and Green, Don W. (1984). Perry's Chemical Engineers' Handbook, Table 2-166, (6th Edition ed.). McGraw-Hill Company. ISBN 0-07-049479-7.

Phillips Petroleum Company (1962). Reference Data For Hydrocarbons And Petro-Sulfur Compounds (Second Printing ed.). Phillips Petroleum Company.

Inspection of these ethics leads to the inference that minimum burden arrangement is the afterward beeline action of specific calefaction ratio: P_ratio = 0.6057 * k + 1.045.

editVacuum Conditions

In the case of upstream air burden at ambient atmospheric burden and exhaustion altitude down beck of an orifice, both the air acceleration and the accumulation breeze amount becomes afraid or bound if sonic acceleration is accomplished through the orifice.