This article demonstrates a new simplified mathematical model developed for an external loop airlift bioreactor, derived from recognised chemical engineering formulae, with the minimum possible reliance on empirical correlations with adjustable parameters. Bubble slip velocity, liquid circulation velocity and gas hold-up are simply estimated based on bubble diameter, gas flow rate, riser diameter and riser height. The model reveals the contribution of bubble diameter to gas hold-up and liquid circulation velocity, filling a gap in the literature. Bubble size is known as an important variable for optimising gas absorption and energy input. Validation of the model is conducted using our own and other experimental data. The current model was found to provide a better estimate of gas hold-up than the literature model compared with, but liquid velocity was overestimated. The impact of using various drag coefficient correlations was also revealed.