In this paper we apply a novel JAVA version of a model on the homeostasis of human red blood cells (RBCs) to investigate the changes RBCs experience during single capillary transits. In the companion paper we apply a model extension to investigate the changes in RBC homeostasis over the approximately 200000 capillary transits during the ~120 days lifespan of the cells. These are topics inaccessible to direct experimentation but rendered mature for a computational modelling approach by the large body of recent and early experimental results which robustly constrain the range of parameter values and model outcomes, offering a unique opportunity for an in depth study of the mechanisms involved. Capillary transit times vary between 0.5 and 1.5s during which the red blood cells squeeze and deform in the capillary stream transiently opening stress-gated PIEZO1 channels allowing ion gradient dissipation and creating minuscule quantal changes in RBC ion contents and volume. Widely accepted views, based on the effects of experimental shear stress on human RBCs, suggested that quantal changes generated during capillary transits add up over time to develop the documented changes in RBC density and composition during their long circulatory lifespan, the quantal hypothesis. Applying the new red cell model (RCM) we investigated here the changes in homeostatic variables that may be expected during single capillary transits resulting from transient PIEZO1 channel activation. The predicted quantal volume changes were infinitesimal in magnitude, biphasic in nature, and essentially irreversible within inter-transit periods. A sub-second transient PIEZO1 activation triggered a sharp swelling peak followed by a much slower recovery period towards lower-than-baseline volumes. The peak response was caused by net CaCl2 and fluid gain via PIEZO1 channels driven by the steep electrochemical inward Ca2+ gradient. The ensuing dehydration followed a complex time-course with sequential, but partially overlapping contributions by KCl loss via Ca2+-activated Gardos channels, restorative Ca2+ extrusion by the plasma membrane calcium pump, and chloride efflux by the Jacobs-Steward mechanism. The change in relative cell volume predicted for single capillary transits was around 10-5, an infinitesimal volume change incompatible with a functional role in capillary flow. The biphasic response predicted by the RCM appears to conform to the quantal hypothesis, but whether its cumulative effects could account for the documented changes in density during RBC senescence required an investigation of the effects of myriad transits over the full four months circulatory lifespan of the cells, the subject of the next paper.