Choked flow of a fluid is a fluid dynamic condition caused by the Venturi effect. When a flowing fluid at a certain pressure and temperature flows through a restriction (such as the hole in an orifice plate or a valve in a pipe) into a lower pressure environment, under the conservation of mass the fluid velocity must increase for initially subsonic upstream conditions as it flows through the smaller cross-sectional area of the restriction. At the same time, the Venturi effect causes the static pressure to decrease. Choked flow is a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed.
For homogeneous fluids, the physical point at which the choking occurs for adiabatic conditions is when the exit plane velocity is at sonic conditions or at a Mach number of 1. The mass flow rate can still be increased by increasing the upstream stagnation pressure, or by decreasing the upstream stagnation temperature.
The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, depending only on the temperature and pressure on the upstream side of the restriction. Under choked conditions, valves and calibrated orifice plates can be used to produce a particular mass flow rate.
If the fluid is a liquid, a different type of limiting condition (also known as choked flow) occurs when the Venturi effect acting on the liquid flow through the restriction decreases the liquid pressure to below that of the liquid vapor pressure at the prevailing liquid temperature. At that point, the liquid will partially flash into bubbles of vapor and the subsequent collapse of the bubbles causes cavitation. Cavitation is quite noisy and can be sufficiently violent to physically damage valves, pipes and associated equipment. In effect, the vapor bubble formation in the restriction limits the flow from increasing any further.
All gases flow from upstream higher stagnation pressure sources to downstream lower pressure sources. There are several situations in which choked flow occurs, such as: change of cross section (as in a convergent-divergent nozzle or flow through an orifice plate), Fanno flow, isothermal flow and Rayleigh flow.
Assuming ideal gas behavior, steady state choked flow occurs when the ratio of the absolute upstream pressure to the absolute downstream pressure is equal to or greater than [ ( k + 1 ) / 2 ] k / ( k - 1 ), where k is the specific heat ratio of the gas (sometimes called the isentropic expansion factor and sometimes denoted as γ ).
For most gases, k ranges from 1.09 (e.g. butane) to 1.67 (monatomic gases), and therefore [ ( k + 1 ) / 2 ] k / ( k - 1 ) ranges from 1.7 to about 2.1 ... which means that choked flow usually occurs when the absolute source vessel pressure is at least 1.7 to 2.1 times as high as the absolute downstream pressure.
where the terms are defined in the table below. If the density
ρ is not known directly, then it is useful to eliminate it
using the Ideal gas
law corrected for the real gas compressibility:
so that the mass flow rate is primarily dependent on the cross-sectional area A of the hole and the upstream pressure P, and only weakly dependent on the temperature T. The rate does not depend on the downstream pressure at all. All other terms are constants that depend only on the composition of the material in the flow. Although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow rate can still be increased if the upstream pressure is increased.
|= mass flow rate, kg/s|
|C||= discharge coefficient, dimensionless|
|A||= discharge hole cross-sectional area, m²|
|k||= cp/cv of the gas|
|cp||= specific heat of the gas at constant pressure|
|cv||= specific heat of the gas at constant volume|
|ρ||= real gas stagnation density at P and T, kg/m³|
|P||= absolute upstream stagnation pressure of the gas, Pa|
|M||= the gas molecular mass, kg/mole (also known as the molecular weight)|
|R||= Universal gas law constant = 8314.5 (N·m) / (kmole·K)|
|T||= absolute upstream stagnation temperature of the gas, K|
|Z||= the gas compressibility factor at P and T, dimensionless|
The above equations calculate the steady state mass flow rate for the stagnation pressure and temperature existing in the upstream pressure source.
If the gas is being released from a closed high-pressure vessel, the above steady state equations may be used to approximate the initial mass flow rate. Subsequently, the mass flow rate will decrease during the discharge as the source vessel empties and the pressure in the vessel decreases. Calculating the flow rate versus time since the initiation of the discharge is much more complicated, but more accurate. Two equivalent methods for performing such calculations are explained and compared online.
The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant R which applies to any ideal gas or whether they are using the gas law constant Rs which only applies to a specific individual gas. The relationship between the two constants is Rs = R / M.
The flow of real gases through thin-plate orifices never becomes fully choked. The mass flow rate through the orifice continues to increase as the downstream pressure is lowered to a perfect vacuum, though the mass flow rate increases slowly as the downstream pressure is reduced below the critical pressure. Cunningham (1951) first drew attention to the fact that choked flow will not occur across a standard, thin, square-edged orifice. 
The minimum pressure ratios required for choked conditions to
occur (when some typical industrial gases are flowing) are
presented in Table 1. The ratios were obtained using the criteria
that choked flow occurs when the ratio of the absolute upstream
pressure to the absolute downstream pressure is equal to or greater
than [ ( k + 1 ) / 2 ] k / ( k - 1 ) ,
where k is the specific heat ratio of the gas. The
minimum pressure ratio may be understood as the ratio between the
upstream pressure and the pressure at the nozzle throat when the
gas is traveling at Mach 1; if the upstream pressure is too low
compared to the downstream pressure, sonic flow cannot occur at the
|Gas||k = cp/cv||Minimum