We used a mathematical model of O(2) transport and the urine concentrating mechanism of the outer medulla of the rat kidney to study the effects of blood pH and medullary blood flow on O(2) availability and Na(+) reabsorption. The model predicts that in vivo paracellular Na(+) fluxes across medullary thick ascending limbs (mTALs) are small relative to transcellular Na(+) fluxes and that paracellular fluxes favor Na(+) reabsorption from the lumen along most of the mTAL segments. In addition, model results suggest that blood pH has a significant impact on O(2) transport and Na(+) reabsorption owing to the Bohr effect, according to which a lower pH reduces the binding affinity of hemoglobin for O(2). Thus our model predicts that the presumed greater acidity of blood in the interbundle regions, where mTALs are located, relative to that in the vascular bundles, facilitates the delivery of O(2) to support the high metabolic requirements of the mTALs and raises the concentrating capability of the outer medulla. Model results also suggest that increases in vascular and tubular flow rates result in disproportional, smaller increases in active O(2) consumption and mTAL active Na(+) transport, despite the higher delivery of O(2) and Na(+). That is, at a sufficiently high medullary O(2) supply, O(2) demand in the outer medulla does not adjust precisely to changes in O(2) delivery.