Critical flow

Critical flow occurs when a compressible fluid velocity approaches the speed of sound about 1000 ft/s. Process piping handling vapor is typically designed to work at a velocity of 100 ft/s. 

The velocity of water flowing from the tub through the drain is 20 ft/s. The pressure drop, in psi, of the water as it escapes from the tub, is 

The pressure at is now the 1-psi static head minus the 5-psi nozzle exit loss or negative 4 psig (or positive 10.7 psia). That is, the pressure at the drain is a substantial partial vacuum, or a negative pressure, meaning that it is below atmospheric pressure (atmospheric pressure at sea level is 14.7 psia). 

This suggests that the pressure in a water drain can get so low that air could be sucked out of the bathroom and down the drain. Of course, we all see this happen several times a day— typically when we flush a toilet. So much air is drawn into the water drainage piping that we install vents on our roofs to release this air. The only requirement, then, for vapors to be drawn into a flowing nozzle is for the nozzle exit loss to be larger than the static head of liquid above the nozzle. 

Incidentally, if a bird builds its nest on top of one of our roof toilet vents, we find the toilet will no longer flush properly. The 

But how about the liquid at point B Is this liquid also at its boiling or bubble point It is the same liquid, having the same temperature and composition as the liquid at point A. But the pressure at point B is slightly higher than the pressure at point A. 

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Consider the case of the simple Bunsen burner. As the tube diameter decreases, at a critical flow velocity and at a Reynolds number of about 2000, flame height no longer depends on the jet diameter and the relationship between flame height and volumetric flow ceases to exist (2). Some of the characteristics of diffusion flames are illustrated in Eigure 5. 

This equation is cubic in hquid depth. Below a minimum value of Ejp there are no real positive roots above the minimum value there are two positive real roots. At this minimum value of Ejp the flow is critical that is, Fr = 1, V= V, and Ejp = (3/2)h. Near critical flow conditions, wave motion ana sudden depth changes called hydraulic jumps are hkely. Chow (Open Channel Hydraulics, McGraw-Hill, New York, 1959), discusses the numerous surface profile shapes which may exist in nommiform open channel flows. 

Critical Flow Nozzle For a given set of upstream conditions, the rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio po/pi until the linear velocity in the throat reaches that of sound in the gas at that location. The value of po/pi for which the acoustic velocity is just attained is called the critical pressure ratio r. The actual pressure in the throat will not fall below even if a much lower pressure exists downstream. 

Under critical flow conditions, only the upstream conditions pi, Vi, and T need be known to determine flow rate, which, for P < 0.2, is given by... 

Discharge coefficients for critical flow nozzles are, in general, the same as those for subsonic nozzles. See Grace and Lapple, Trans. Am. Soc. Mech. Fug., 73, 639-647 (1951) and Szaniszlo, ]. Eug. Power, 97, 521-526 (1975). Arnberg, Britton, and Seidl [J. Fluids Eug., 96, 111-123 (1974)] present discharge-coefficient correlations for circular-arc venturi meters at critical flow. For the calciilation of the flow of natural gas through nozzles under critical-flow conditions, see Johnson,/. Ba.sic Eng., 92, 580-589 (1970). 

Opening a manual valve. Manual valves which are normally closed to isolate two or more pieces of equipment or process streams can be inadvertently opened, causing the release of a high-pressure stream or resulting in vacuum conditions. Other effects may include the development of critical flows, flashing of liquids, or the generation of a runaway chemical reaction. 

When the pressure relief device is set to open at greater than 15 psig (critical flow will result), it is normally not uecessaiy to be concerned about the pressure drop in the separator. If the hquid is to be drained from the separator during the emergency blowdown, a vortex breaker and false bottom should be used (Fig. 26-18, view BB). 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

When the bracketed quantity in the equations equals or exceeds 90 degrees, critical flow is indicated. The quantity must be limited to 90 degrees. This then becomes unity since sin 90° = 1. 

For comparison, the outlet temperature for gas at critical flow accross an orifice is given by... 

The main flare header should not be designed for critical flow at the entrance to the flare stack, or else noise and vibration will result. 

A reading below Mi = 1 on Figure 1 also indicates critical flow. In such a case, read the graph at M2 = 1. 

As normally designed, vapor flow through a typical high-lift safety reliefs valve is characterized by limiting sonic velocity and critical flow pressure conditions at the orifice (nozzle throat), and for a given orifice size and gas composition, mass flow is directly proportional to the absolute upstream pressure. 

Back pressure reduces the pressure drop across the orifice of any type of PR valve. This results in reduced discharge rates in the case of vapors, if the back pressure exceeds the critical flow pressure. For liquids, any back pressure reduces the pressure drop and results in a lower discharge rate. 

If the superimposed back pressure is less than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is unaffected and back pressure is not a factor. However, builtup back pressure on a conventional pressure relief valve will affect its flow capacity and operating characteristics, and should not exceed 100% of its set pressure. If total back pressure (superimposed plus built-up) is greater than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is affected, and total back pressure is incorporated into the sizing procedure. Any back pressure reduces the capacity of a conventional PR valve in liquid service, and... 

Critical and Subcritical Flow - The maximum vapor flow through a restriction, such as the nozzle or orifice of a pressure relief valve, will occur when conditions are such that the velocity through the smallest cross-sectional flow area equals the speed of sound in that vapor. This condition is referred to as "critical flow" or "choked flow . 

In the above equation, is the critical velocity (m/s), K is the ratio of specific heats (Cp/C ) at inlet conditions, P is the pressure in the restriction at critical flow conditions (KPa, absolute - Note that this term is known as the critical flow pressure ), and p, is the density of the fluid at the critical flow temperature and pressure (kg/m ). 

The pressure drop which corresponds to critical flow is called the "critical pressure drop", i.e., P,-Px. where P, is the absolute upstream pressure. 

If the pressure Pj downstream of the restriction is less than the critical flow pressure, then the maximum obtainable flow which occurs at critical velocity is a function of P, and P but is unaffected by Pj. If Pj is greater than P , however, then the flow is termed "subcritical," and the rate is a function of P, and Pj. There are thus two equations for sizing PR valves in vapor service, depending on whether the flow is critical or subcritical. 

In PR valve design, it is desirable to select a PR valve discharge location at a low enough pressure to permit designing for critical flow conditions, so that the relieving rate will be independent of minor back pressure fluctuations. 

The first step in sizing a PR valve for vapor flow is to determine the critical flow pressure P from the following equation ... 

Gas Specific Heat Ratio K = Cp/C, Critical Flow Pressure Ratio, P,/P,... 

For critical flow conditions (i.e., when total superimposed plus built-up back... 

For the exceptional cases of subcritical flow (e.g., where a PR valve is designed for a low set pressure and the total superimposed plus built-up back pressure exceeds the critical flow pressure), the following equation may be used applied ... 

For steam flow under critical flow conditions, the following equation is obtained by substituting the appropriate constants in Equation (4) ... 

We shall first consider the case of non-flashing liquids. In this situation, there is no critical flow pressure limiting the flow of liquid through a PR valve orifice, as opposed to the case of vapor flow. The discharge rate is a function of the pressure drop across the valve and can be estimated by the following expression ... 

By trial and error procedure, determine the amount of liquid which flashes by an isoenthalpic (constant enthalpy) expansion to the critical flow pressure (or actual pressure if greater than critical) for the flashed vapor. 

Calculate individually the orifice area required to pass the flashed vapor component, using Equation (5a), (3b), (4), (5), or (6), as appropriate, according to service, type of valve and whether the back pressure is greater or less than the critical flow pressure. 

Calculate individually the orifice area required to pass the unflashed hquid component, using Equation (8). The pressure drop term Pj should be made equal to the set pressure minus the total back pressure developed by the vapor portion at critical flow pressure, except when the critical flow pressure is less than the calculated total back pressure (superimposed plus built-up), considering the combined liquid and vapor flow. In the latter case, P should be made equal to set pressure minus the calculated total back pressure. 

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