Sonic flow

Capacity. Pumps deHver a certain capacity, Q, sometimes referred to as flow, which can be measured directly by venturi, orifice plate (11), or magnetic meters (12) (see Flow measurement). The indirect way to determine capacity is often used. Whereas this method is less accurate than applying a flow meter, it often is the only method available in the field. The total head is measured and the capacity found from the pump head—capacity (H— curve (Fig. 2). More recently, sonic flow meters (13) have been used, which can be installed on the piping without the need for pipe disassembly. These meters are simple to use, but require relatively clean single-phase Hquid for reHable measurements. 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

The actual mass flow rate through a pipe, G, in lbs per sec per sq ft is a function of critical mass flow G,-i, line resistance, N, and the ratio of downstream to upstream pressure. These relationships are plotted in Figure 19. In the area below the dashed line in Figure 19, the ratio of G to G,. remains constant, which indicates that sonic flow has been established. Thus, in sizing flare headers the plotted point must be above the dashed line. The line resistance, N, is given by the equation ... 

The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at... 

When the relieving scenarios are defined, assume line sizes, and calculate pressure drop from the vent tip back to each relief valve to assure that the back-pressure is less than or equal to allowable for each scenario. The velocities in the relief piping should be limited to 500 ft/sec, on the high pressure system and 200 ft/sec on the low pressure system. Avoid sonic flow in the relief header because small calculation errors can lead to large pressure drop errors. Velocity at the vent or flare outlet should be between 500 ft/sec and MACH 1 to ensure good dispersion. Sonic velocity is acceptable at the vent tip and may be chosen to impose back-pressure on (he vent scrubber. 

Typical values of y range from 1.1 to 1.67, wliich give rcm values of 1.71 to 2.05. Thus, for releases of most diatomic gases (y = 1.4) to tlie atmosphere, upstream pressures over 1.9 bar absolute will result in sonic flow. Note tliat tlie inverse of rent is occasionally used by industry. 

Critical or sonic flow will usually exist for most (compressible) gases or vapors discharging through the nozzle orifice of a pressure relieving valve. The rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio P2/P1 (exit/inlet) until the linear velocity in the throat of the nozzle reaches the speed of sound in the gas at that location. Thus, the critical or sonic velocity or critical pressures are those conditions... 

Thus, if the dowmstream or backpressure on tlie valve is less than 53%-60% (should be calculated) of the values of P, note above, critical (sonic) flow wll usually exist. If the downstream pressure is over approximately 50% of the relief pressure, P, the actual critical pressure should be calculated to determine the proper condition. Calculation of critical pressure [29] ... 

Steam Rupture disk sonic flow ailical pressure = 0.55 and P2/P1 is less than critical pressure ratio of 0.55. 

Qt = stoichiometric composition of combustible vapor in air expressed as a volume percent Co = sonic flow discharge orifice constant, varying VvTth Reynolds number... 

Six-tenths factor, 47 Yearly cost indices, 47 Critical flow, safety-relief, 438 Back pressure, 440 Sonic flow, 438 Critical flow, see Sonic Cyclone separators, 259-269 Design, 260-265 Efficiency chart, 263 Hydroclones, 265-267 Pressure drop, 263, 264 Scrubber, 269 Webre design, 265 Deflagration venting nomographs,... 

Sizing, 451, 453, 455, 459, 462 Sonic flow, 461 Types, illustrations, 411-421 Rupture disk, liquids, 462, 466 Rupture disk/pressure-relief valves combination, 463 Safely relief valve, 400 See Relief valve Safety valve, 400, 434 Safety, vacuum, 343 Scale-up, mixing, 312, 314—316 Design procedure, 316-318 Schedules/summaries Equipment, 30, 31 Lines, 23, 24 Screen particle size, 225 Scrubber, spray, 269, 270 Impingement, 269, 272 Separator applications, liquid particles, 235 Liquid particles, 235 Separator selection, 224, 225 Comparison chart, 230 Efficiency, 231... 

Sonic flow, safety relief, 438 Rupture disk, 460, 461 Sub-sonic flow, 461 Sonic or critical flow, 115, 125 Calculations, 125 Velocity, 126 Specific speed, 194-197 Impeller designs, 194 Upper limits, chart, 195-197 Specifications,... 

FIGURE 9.4 Quick ampoule sampling of volatiles. Ninety-five percent ampoule filling time as a function of capillary diameter for 3 compounds. Calculation for filling through consecutive Knudsen diffusion into a vacuum, super sonic flow, and laminar flow. 

The choked pressure Pchoked is the maximum downstream pressure resulting in maximum flow through the hole or pipe. For downstream pressures less than Evoked the following statements are valid (1) The velocity of the fluid at the throat of the leak is the velocity of sound at the prevailing conditions, and (2) the velocity and mass flow rate cannot be increased further by reducing the downstream pressure they are independent of the downstream conditions. This type of flow is called choked, critical, or sonic flow and is illustrated in Figure 4-10. 

For vapor flows that are not choked by sonic flow the area is determined using Equation 4-48. The downstream pressure P is now required, and the discharge coefficient C0 must be estimated. The API Pressure Vessel Code4 provides working equations that are equivalent to Equation 4-48. 

In the last 25 years, calculations of the detonation properties of condensed explosives from their chemical compositions and densities have been approached in various ways.2 All have used the necessary conservation conditions for steady flow with the detonation discontinuity satisfying the Chapman-Jouguet hypothesis (minimum detonation velocity compatible with the conservation conditions or sonic flow behind the discontinuity in a reference frame where the discontinuity is at rest). In order to describe the product state and the thermodynamic variables which fix its composition, an equation of state applicable to a very dense state is required. To apply this equation to a mixture of gaseous and solid products, a mixing rule is also needed and the temperature must be explicitly defined. Of the equations of state for high-density molecular states which have been proposed, only three or four have been adapted to the calculation of equilibrium-product compositions as well as detonation parameters. These are briefly reviewed in order to introduce the equation used for the ruby computer code and show its relation to the others. 

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