The differentiation of mesenchymal stromal cells has been shown to be af- fected by many parameters such as morphogens, flow rate, medium viscosity, and shear stress when exposed to fluid flow. The mechanism by which these cells sense their environment is still under intense discussion. In particular, during flow chamber experiments, it is difficult to interpret the interplay of the above-mentioned parameters in the process of cell differentiation. In this work, we tested the hypothesis that the competition between diffusion and advection of paracrine morphogens could explain the dependency of the cell differentiation to the above-mentioned parameters. To evaluate this hy- pothesis, we developed a numerical model simulating a simplified version of the advection-diffusion-reaction of morphogens secreted by the cells within a flow chamber. The model predicted a sharp transition in the fraction of receptors bound to the morphogen. This transition was characterized by a new dimensionless number depending on flow rate, flow viscosity, flow chamber dimensions, and morphogen decay rate. We concluded that the competition between diffusion and advection of paracrine morphogens can act as a probe for the cells to sense their peri-cellular environment.