The Michel and Miller (1962) equation is routinely used to estimate the effect of aeration on power consumption in submerged culture fermentation systems. However this correlation was developed for systems that do not contain solid substrates. Since many industrial fermentations use solid substrates, this study developed a modification of the Michel and Miller equation that can be used to predict power consumption when solid substrates are present. A correlation relating power to solids addition was established by adding bran and apple pomace to water, and measuring the power drawn by four separate impeller configurations. This correlation applies to solids content up to 16.7% w/w and bulk densities between 1020 to 1210 kg/m(3). It was found that when aerated the power consumption decreased upon addition of solid substrate. The most likely explanation of this behaviour is that initially the gas hold up increased, decreasing power consumption. At high solid loadings, the power decrease was up to 30% (compared to 66% decrease in power caused by high aeration rates).