The rising gas bubbles that are generated in an electrolyser cause electrolyte to flow upwards. By adding a downcomer after separating the gas, the electrolyte will recirculate through natural convection without a pump. We measured the resulting flow rate as a function of current density and electrode–wall distance in a zero-gap alkaline water electrolysis cell. Next, we developed a simple but surprisingly accurate fully analytical model to describe this flow rate as a function of various geometrical and operational parameters. From this model, we derive fully explicit expressions for the optimal electrode–wall distance. For our setup of 0.4 m height we find that values of 1.5–1.9 mm maximise mass transfer, velocity, or minimise the ohmic drop. The electrolyte flow rate is maximised for larger distances, around 6 mm. The accuracy, simplicity, and generality of our analytical model will be useful for the design and optimisation of a variety of gas-evolving electrolysers, including lab-scale as well as industrial reactors.