Flow equation for an ideal or viscous gas through a nozzle: application to cascade impactors

Some of the parameters used to express the hydrodynamic equation usually used to describe the flow of an ideal compressible gas through a nozzle do not lend themselves to easy laboratory measurement, and also the equation is not directly applicable to a normal viscous gas. To circumvent these problems, the equation has been modified and simplified. Although the viscous resistance of a normal gas attenuates the flow rate significantly, we have assumed that the attenuation is relatively constant, and does not vary significantly with the ratio of the pressure difference to inlet pressure. Under these conditions the ideal gas equations can be corrected so that they can be applied to a viscous gas. It is shown that the gas flow rate at any pressure difference below choke flow can be determined, if the choke flow, and the inlet and exit pressures are known. Due to the pressure drop across the nozzles preceding the critical nozzle (smallest area) in an impactor, the flow rate vs pressure ratio curve is shifted toward higher pressure ratios as compared to a single nozzle. An equation to calculate the flow rate of a viscous gas through any nozzle in an impactor is also presented. Experiments have been performed which corroborate the new equations. The simplified flow-rate equations have been found to be useful to calculate flow rates through any nozzle in an impactor.