Salivary fluid secretion is crucial for preventing problems such as dryness of mouth, difficulty with mastication and swallowing, as well as oral pain and dental cavities. Fluid flow is driven primarily by the transepithelial movement of chloride and sodium ions into the parotid acinus lumen. The activation of Cl(-) channels is calcium dependent, with the average elevated calcium concentration during calcium oscillations increasing the conductance of the channels, leading to an outflow of Cl(-). The accumulation of NaCl in the lumen drives water flow by osmosis. We construct a mathematical model of the calcium concentration oscillations and couple this to a model for Cl(-) efflux. We also construct a model governing fluid flow in an isolated parotid acinar cell, which includes a description of the rate of change of intracellular ion concentrations, cell volume, membrane potential and water flow rate. We find that [Ca(2+)] oscillations lead to oscillations in fluid flow, and that the rate of fluid flow is regulated by the average calcium concentration and not the frequency of the oscillations.