The correlation of slot‐opening with flow rate for air bubbling into water

Abstract

AbstractWhen air flows through a slot in a vertical diaphragm into a tank full of water, the level on the air‐inlet side is depressed below the apex of the slot. This depression, defined as the slot‐opening, has been correlated with the air rate. Some 300 determinations have been made at air rates between 0·01 and 800 cu. ft. per min. for one rectangular and one triangular slot. A few further measurements have been made with slots of varied dimensions.All these measurements are shown to fit with the simple hydrodynamic theory (Rogers & Thiele, 1934) when this is modified to take account of surface tension effects. The new theory requires that below a critical air rate the slot opening should be determined by surface tension effects alone, whereas above this rate the original hydrodynamic equations would apply. The values now found for the constants of these equations are significantly different from those proposed by the previous workers. In particular, the exponent of h (the slot opening) now corresponds with the theoretical values to within the limits of experimental accuracy. The larger values obtained in the earlier work (Roger & Thiele, 1934: Spells & Bakowski, 1950) were probably due to the inclusion of measurements below the critical rate.