Buoyancy and Expansion Power in Gas-agitated Baths

Abstract

The derivation of the energy input to a gas-stirred bath is re-examined. The formula for the work done by the expansion of gas due to pressure decrease as it rises through the bath is found to be different from that given in the literature. According to the previous derivation, this energy input is numerically equal to the work done by the buoyancy force, but the present formula gives a much lower value. The so-called 'buoyancy power', which is conventionally taken to be the sum of this expansion power and the power due to the buoyancy force itself, is therefore approximately half the value given by the previously published formulas. A similar correction applies to the work done by the gas as it expands due to heating in a pyrometallurgical bath: the new formula is smaller than the published one by a factor equal to the ratio of the static pressure drop across the bath to static pressure at the bottom of the bath.