Pollen tube growth is central to the sexual reproduction of plants and is a longstanding model for cellular tip growth. For rapid tip growth, cell wall deposition and hardening must balance the rate of osmotic water uptake, and this involves the control of turgor pressure. Pressure contributes directly to both the driving force for water entry and tip expansion causing thinning of wall material. Understanding tip growth requires an analysis of the coordination of these processes and their regulation. Here we develop a quantitative physiological model which includes water entry by osmosis, the incorporation of cell wall material and the spreading of that material as a film at the tip. Parameters of the model have been determined from the literature and from measurements, by light, confocal and electron microscopy, together with results from experiments made on dye entry and plasmolysis in Lilium longiflorum. The model yields values of variables such as osmotic and turgor pressure, growth rates and wall thickness. The model and its predictive capacity were tested by comparing programmed simulations with experimental observations following perturbations of the growth medium. The model explains the role of turgor pressure and its observed constancy during oscillations; the stability of wall thickness under different conditions, without which the cell would burst; and some surprising properties such as the need for restricting osmotic permeability to a constant area near the tip, which was experimentally confirmed. To achieve both constancy of pressure and wall thickness under the range of conditions observed in steady-state growth the model reveals the need for a sensor that detects the driving potential for water entry and controls the deposition rate of wall material at the tip.