Fluid flow sonic velocity

The flow velocity is thus proportional to the difference in transit time between the upstream and downstream directions and to the square of the speed of sound in the fluid. Because sonic velocity varies with fluid properties, some designs derive compensation signals from the sum of the transit times which can also be shown to be proportional to C. 

For the situations covered here, compressible fluids might reach sonic velocity. When this happens, further decreases in downstream pressure do not produce additional flow. Sonic velocity occurs at an upstream to downstream absolute pressure ratio of about 2 1. This is shown by the formula for sonic velocity across a nozzle or orifice. 

A relief device should be installed vertically and preferably on a nozzle at the top of the equipment (for example, vessel) or on a tee connected to a pipeline. When discharging a gas or vapor, the fluid reaches sonic velocity when passing through a relief device. Thus, the gas flow rate or AP can be determined by a method as described in Chapter Three. 

When the ratio of AP/Fi exceeds 0.02, the gas is undergoing compression. Critical flow occurs when the flow is not a function of the square root of the pressure drop across the valve, but only of the upstream pressure. This phenomenon occurs when the fluid reaches sonic velocity at the vena contracta. Since gas cannot travel faster than sonic velocity, critical flow is a flow-limiting condition for gas. It has been found that critical flow occurs at different APIP ratios, depending on whether the valve is high or low recovery. 

Figures 2-38A and 2-38B are based on the perfect gas laws and for sonic conditions at the outlet end of a pipe. For gases/vapors that deviate from these laws, such as steam, the same application will yield about 5% greater flow rate. For improved accuracy, use the charts in Figures 2-38A and 2-38B to determine the dowmstream pressure when sonic velocity occurs. Then use the fluid properties at this condition of pressure and temperature in ...

It will now be shown from purely thermodynamic considerations that for, adiabatic conditions, supersonic flow cannot develop in a pipe of constant cross-sectional area because the fluid is in a condition of maximum entropy when flowing at the sonic velocity. The condition of the gas at any point in the pipe where the pressure is P is given by the equations ... 

The temperature or enthalpy of the gas may then be plotted to a base of entropy to give a Fanno line.iA This line shows the condition of the fluid as it flows along the pipe. If the velocity at entrance is subsonic (the normal condition), then the enthalpy will decrease along the pipe and the velocity will increase until sonic velocity is reached. If the flow is supersonic at the entrance, the velocity will decrease along the duct until it becomes sonic. The entropy has a maximum value corresponding to sonic velocity as shown in Figure 4.11. (Mach number Ma < 1 represents sub-sonic conditions Ma > 1 supersonic.)... 

For the flow of a compressible fluid, conditions of sonic velocity may be reached, thus limiting the maximum flowrate for a given upstream pressure. This situation can also occur with two-phase flow, and such critical velocities may sometimes be reached with a drop in pressure of only 30 per cent of the inlet pressure. 

Barclay, F. J., T. J. Ledwidge, and G. C. Cornfield, 1969, Some Experiments on Sonic Velocity in Two-Phase Critical Flow, Symp. on Fluid Mechanics and Measurements in Two-Phase Flow Systems, Proc. Inst. Mech. Eng. 184(Part 3C) 185-194. (3)... 

Mach number M V c fluid velocity sonic velocity Compressible flow... 

With a ratio between storage pressure and ambient pressure of about 2 or greater (for air), the flow rate is limited to the sonic velocity of the fluid at the end of the flow restriction (choked flow). At this point, the fluid pressure can be greater than the ambient pressure. The remaining expansion occurs beyond the flow restriction, where the release accelerates both radially and axially. 

This is identical to the equation derived in physics for the speed of so in the fluid. Therefore, the maximum fluid velocity obtainable in a pipe of const cross-sectional area is the speed of sound. This does not imply that higt velocities are impossible they are, in fact, readily obtained in converg diverging nozzles (Sec. 7.3). However, the speed of sound is the maximum val that can be reached in a conduit of constant cross section, provided the entran velocity is subsonic. The sonic velocity must be reached at the exit of the pi-If the pipe length is increased, the mass rate of flow decreases so that the so velocity is still obtained at the outlet of the lengthened pipe. 

When the fluid flowing through the valve is a compressible gas or a vapor, then the design must consider whether critical flow is achieved in the nozzle of the valve. The critical flow rate is the maximum flow rate that can be achieved and corresponds to a sonic velocity at the nozzle. If critical flow occurs, then the pressure at the nozzle exit cannot fall below the critical flow pressure Pcf, even if a lower pressure exists downstream. The critical flow pressure can be estimated from the upstream pressure for an ideal gas using the equation... 

When flow is subsonic, < 1 all terms on the right in these equations are then positive, and dP/dx < 0 and du/dx > 0. Pressure therefore decreases and velocity increases in the direction of flow. The velocity increase is, however, limited, because these inequahties would reverse if the velocity were to become supersonic. This is not possible in a pipe of constant cross-sectional area, and the maximum fluid velocity obtainable is the speed of sound, reached at the exit of the pipe. Here, dS/dx reaches its limiting value of zero. For a discharge pressure low enough, the flow becomes sonic and lengthening the pipe does not alter this result the mass rate of flow decreases so that the sonic velocity is still obtained at the outlet of the lengthened pipe. 

Two-fluid nozzle atomization In two-fluid nozzle atomizers, the liquid feed is fed to the nozzle under marginal or no pressure conditions. An additional flow of gas, normally air, is fed to the nozzle under pressure. Near the nozzle orifice, internally or externally, the two fluids (feed and pressurized gas) are mixed and the pressure energy is converted to Kinetic energy. The flow of feed disintegrates into droplets during the interaction with the high-speed gas flow which may have sonic velocity. 

Determining the maximum fluid flow rate or pressure drop for process design often has the dominant influence on density. As pressure decreases due to piping and component resistance, the gas expands and its velocity increases. A limit is reached when the gas or velocity cannot exceed the sonic or critical velocity. Even if the downstream pressure is lower than the pressure required to reach sonic velocity, the flow rate will still not increase above that evaluated at the critical velocity. Therefore, for a given AP, the mass discharge rate through a pipeline is greater for an adiabatic condition (i.e., insulated pipes, where heat transfer is... 

The flow rate of a compressible fluid in a pipe with a given upstream pressure will approach a certain maximum rate that it cannot exceed even with reduced downstream pressure. The maximum velocity is limited by the velocity of propagation of a pressure wave that travels at the speed of sound in the fluid. The maximum velocity that a compressible fluid can attain in a pipe is known as the sonic velocity, V, and can be expressed as ... 

Shock waves occur in nature in the air surrounding explosions (the shock wave causes much of the destruction of buildings, etc., in an atomic bomb blast) and in the sudden closing of a valve in a duct with high-velocity flow. Sonic booms are shock waves. Shock waves can be produced in the laboratory in a duct or nozzle with supersonic flow. In such cases the shock wave will stand still in one place while the fluid flows through it. The latter is the easier to analyze mathematically, so we use it as a basis for calculations. The nomenclature for a shock wave is shown in Fig 8.13. 

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