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Aims.  Despite extensive studies carried out since its discovery half a century ago, the nature of supergranulation remains an open question in solar physics. Separability of flow models is a common assumption made in the literature to shed light on the properties of supergranules. This paper studies the ability of separable mass-conserving flow models to reproduce photospheric observations from the Helioseismic Magnetic Imager (HMI) on board of the Solar Dynamics Observatory (SDO) spacecraft corresponding to an average supergranule.   Methods.  For a steady mass-conserving separable flow model to be compatible with the observations, there is an integral relation between the horizontal and vertical components of the flow. We test this relation directly on observations and compare the results with the proportionality relationship for a separable model.   Results.  Observations of an average supergranule do not satisfy the condition for separability. Selecting a narrower range of horizontal scales of supergranules when performing the average does not change this result. Separable models are not consistent with observations of an average supergranule.

SDO/HMI observations of the average supergranule are not compatible with separable flow models