Discharge mass flux

Example 7 Flow through Frictionless Nozzle Air at po and temperature To = 293 K discharges through a frictionless nozzle to atmospheric pressure. Compute the discharge mass flux G, the pressure, temperature, Mach mimher, and velocity at the exit. Consider two cases (1) po = 7 X 10 Pa absolute, and (2) po = 1.5 x 10 Pa absolute. 

FIG. 26-63 Discharge mass flux for highly suhcooled water (20 C) from orifice and4-mm pipe of various lengths. (Data of Uchida and Narai, 1966 reproduced hy peimission of ASME.)... 

Propane is stored in a vessel at its vapor pressure of 95 bar gauge and a temperature of 298 K. Determine the discharge mass flux if the propane is discharged through a pipe to atmospheric pressure. Assume a discharge coefficient of 0.85 and a critical pipe length of 10 cm. Determine the mass flux for the following... 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

Full-Bore and Punctured Pipe Discharge With a pipe puncture, the mass flux at the discharge point is larger than the mass flux in the pipe G,p, by the puncdure-to-pipe area ratio A j/Ap, or (D/Dp) , denned as C. Specifically ... 

HEM for Two-Phase Pipe Discharge With a pipe present, the backpressure experienced by the orifice is no longer qg, but rather an intermediate pressure ratio qi. Thus qi replaces T o iri ihe orifice solution for mass flux G. ri Eq. (26-95). Correspondingly, the momentum balance is integrated between qi and T o lo give the pipe flow solution for G,p. The solutions for orifice and pipe now must be solved simultaneously to make G. ri = G,p and to find qi and T o- This can be done explicitly for the simple case of incompressible single-phase (hquid) inclined or horizontal pipe flow The solution is implicit for compressible regimes. 

FIG. 26-68 Ratio of mass flux for horizoutal pipe flow to that for orifice discharge for flashing liquids hy the homogeueoiis eqiiilihriiim model, (Leung and Gmlmes, AIChE J, 33 (3), pp. 524-527, 1987 reproduced by permission of AIChE. copy-right 1987. All rights reseroed.)... 

FIG. 26-69 Ratio of mass flux for inclined pipe flow to that for orifice discharge for flashing liquids by the homogeneous equilibrium model. Leung, J. of Loss Prev. Process Ind. 3 pp. 27-32, with kind peimission of Elsevier Science, Ltd, The Boulevard, Langford Lane, Kidlington, 0X5 IGB U.K., 1990.)... 

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

A storage tank contains ethylene at 80°F and has a relief valve that is set to open at a pressure of 250 psig. The valve must be sized to relieve the gas at a rate of 85 lbm/s when it opens. The valve has a discharge coefficient (the ratio of the actual to the theoretical mass flux) of 0.975. 

Search with values of Pi until G is maximized. The choke pressure, PcU is the value of Pi that produces a maximum value of mass flux Gmax. The discharge rate w is given from the mass flux, a discharge coefficient CD, and the orifice cross-sectional area A as... 

The accuracy of the energy balance method for discharge of flashing liquids through orifices and horizontal pipes is illustrated in Figs. 23-42 and 23-43. The ratio of predicted to observed mass flux is plotted for saturated water data by Uchaida and Narai and by Sozzi and... 

Lakes and oceans are often vertically stratified. That is, two or more fairly homogeneous water layers are separated by zones of strong concentration and density gradients. In Chapter 21, two- and multibox models will be developed to describe the distribution of chemicals in such systems. In these models, volume fluxes, Qex, are introduced to describe the exchange of water and solutes between adjacent boxes (Fig. 19.5). Qex has the same dimension as, for instance, the discharge of a river, [L3TT ]. The net mass flux, LFnet, from box 1 into box 2 is given by ... 

If we consider only chemical and hydraulic processes, the equations (1) for specific discharge q and solute mass flux relative to the solution Jd, in terms of gradients of pressure p and salt mass fraction uts reduce to [1]... 

The safety system design is often poor as very few experimental validation with liquefied gases/supercritical fluids have been published until now. We did operate some measurements of flash discharge of liquid/supercritical CO2 from pressure vessels and proposed a simple model for mass flux evaluation [1] these results can be used for safety systems design. 

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