Two‐fluid modelling has recently emerged as a promising approach to representing cumulus convection in weather and climate models. This study applies the two‐fluid model described in Part II to a shallow cumulus convection case study over land (ARM). Large‐eddy simulation data are used to tune the majority of the closures that determine the properties of entrained and detrained air. The two‐fluid model is generally able to reproduce the profiles of the mean and turbulent quantities over all stages of the diurnal cycle. As such, the initiation of shallow convection and the evolution of the cloud layer are well captured. The robustness of the two‐fluid model is verified further using a steady‐state test case (BOMEX), in which the cloud properties are also well modelled.