Choked flow

Choked flow is a compressible flow effect. The parameter that becomes 'choked' or 'limited' is the fluid velocity. Choked flow is a compressible flow effect. The parameter that becomes 'choked' or 'limited' is the fluid velocity. Choked flow is a fluid dynamic condition associated with the Venturi effect. When a flowing fluid at a given pressure and temperature passes through a constriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases. At initially subsonic upstream conditions, the conservation of mass principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the constriction. At the same time, the Venturi effect causes the static pressure, and therefore the density, to decrease at the constriction. Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment for a fixed upstream pressure and temperature. For homogeneous fluids, the physical point at which the choking occurs for adiabatic conditions, is when the exit plane velocity is at sonic conditions; i.e., at a Mach number of 1. At choked flow, the mass flow rate can be increased only by increasing density upstream and at the choke point. The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, and depends only on the temperature and pressure and hence the density of the gas on the upstream side of the restriction. Under choked conditions, valves and calibrated orifice plates can be used to produce a desired 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 causes a decrease of the liquid pressure beyond the restriction to below that of the liquid's 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 prevents the flow from increasing any further. All gases flow from upstream higher pressure sources to downstream lower pressure sources. There are several situations in which choked flow occurs, such as the change of cross section in a de Laval nozzle or flow through an orifice plate. Here the most important part is where to calculate choked velocity: at upstream or downstream of a nozzle or orifice. The choked velocity is always observed at upstream of an orifice or nozzle and this velocity is usually less than speed of sound in Air. Another important aspect is this is the actual velocity for upstream fluid. Hence, upstream actual volumetric flow rate, when expanded to downstream pressure, will result in more actual volumetric flow for the downstream condition. Thus, overall leakage rate when measured at downstream conditions needs to take care of this fact. When this choked velocity has reached the mass flow rate from upstream to downstream, it can still be increased if upstream pressure is increased. However, this value of choked velocity will keep actual volumetric flow rate (Actual Gas Flow rate, and hence velocity) the same irrespective of upstream pressure, provided choked flow conditions prevail. Assuming ideal gas behaviour, steady-state choked flow occurs when the downstream pressure falls below a critical value p ∗ {displaystyle p^{*}} . That critical value can be calculated from the dimensionless critical pressure ratio equation where γ {displaystyle gamma } is the heat capacity ratio c p / c v {displaystyle c_{p}/c_{v}} of the gas and where p 0 {displaystyle p_{0}} is the total (stagnation) upstream pressure. For air with a heat capacity ratio γ = 1.4 {displaystyle gamma =1.4} , then p ∗ = 0.528 p 0 {displaystyle p^{*}=0.528p_{0}} ; other gases have γ {displaystyle gamma } in the range 1.09 (e.g. butane) to 1.67 (monatomic gases), so the critical pressure ratio varies in the range 0.487 < p ∗ / p 0 < 0.587 {displaystyle 0.487