Orifice Discharge for Gas Flow

Orifice Discharge for Gas Flow The analytic solution for discharge through an orifice of an ideal gas is derived by invoking the equation of state for adiabatic expansion of an ideal gas ... 

For a constant gas flow rate, a decrease in gas density leads to an increase in mean gas velocity and/or average gas flow area. The increases in both these quantities prove to be beneficial to atomization quality. In the former case, it accelerates the liquid flow through the injector orifice so that the liquid is discharged at a higher velocity. In the latter case, it reduces the area available for the liquid flow so that the liquid is squeezed into thinner films and ligaments as it flows through the injector orifice. 

If the puncture occurs on the vessel or on a line shorter than 0.5 m, the discharge is likely to be nonhomogeneous, meaning the gas and liquid velocities are not equal and the phases are not likely to be in equilibrium. For this case, various models have been developed, including some of considerable complexity, accounting for interphase heat, mass, and momentum transfer. These are generally used in the nuclear power industry. For most engineering applications, simpler models suffice. A reasonably simple nonequilibrium model (NEM) is developed here. We also provide an HEM for orifice flow, since it helps to develop the HEM for pipe flow, and its inaccuracies may at times be tolerable. 

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... 

Equation (5-14) is combined with Bernoulli s equation. Assuming flow on a horizontal axis and using a coefficient of discharge to account for friction at the orifice, the mass flow rate of an ideal gas through a thin hole in the containment wall is ... 

Rate of discharge through an orifice meter is given by Eq. (10-8) for either liquids or gases. For the case of subsonic flow of a gas (r < r < 1.0), the expansion factor Y for orifices is approximated by... 

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