Follow one fluid parcel through a kidney tubule: Starling filtration, reabsorption in every segment, hormones, and the urine that is left.
Educational model with textbook-typical numbers. Not medical advice, not a diagnostic or dosing tool, and not a model of any real patient or disease course.
The science
Blood flow. RBF = (MAP − Pv)/(Raff + Reff + Rother) with Pv = 5 mmHg and resistances chosen so RBF ≈ 1100 mL/min at 93 mmHg. Plasma flow RPF = RBF (1 − Hct). Glomerular capillary pressure PGC = MAP − RBF Raff (about 55 mmHg at rest). Autoregulation (myogenic response plus tubuloglomerular feedback) is a limited-range P-controller on the afferent resistance, so RBF and GFR stay nearly flat between roughly 80 and 150 mmHg and follow pressure outside that range; the exact limits are a simplification.
Starling filtration. Along the capillary (coordinate x from 0 to 1) dQf/dx = Kf (PGC − PBS − π(x)). As plasma is filtered the proteins stay behind, so plasma protein concentration c(x) = cA RPF/(RPF − Qf) rises, and the oncotic pressure follows the Landis-Pappenheimer fit π = 2.1c + 0.16c² + 0.009c³ (c in g/dL, cA = 7 g/dL gives πA ≈ 26 mmHg). GFR = Qf(1); Kf is calibrated so GFR = 125 mL/min (about 180 L/day) in the baseline state. The filtration fraction is FF = GFR/RPF (about 0.2).
Tubule. A steady one-dimensional march along five segments (PCT, descending limb, thick ascending limb, DCT, collecting duct) with RK4 per cell: dF/ds = −k F. Water: PCT 65 % of the filtered volume, descending limb 43 % of what enters, distal tubule 30 %, collecting duct 0.15 + 0.835·ADH/(ADH + 0.03) of what enters. Sodium: PCT 65 % and ascending limb 25 % of the filtered load; distal parts take 1 − 0.5a and 1 − 0.12a of what enters, where a is the aldosterone factor. Constant fractions give glomerulotubular balance: urine volume scales with GFR. Inulin is filtered and not reabsorbed, so its concentration rises as water leaves: TF/P = 1/Π(1 − f) and clearance U V / P = GFR.
Glucose. Load = GFR · cglu; reabsorption saturates with an effective Tm of 300 mg/min and splay: R = L / (1 + (L/Tm)6)1/6. Glucose appears in urine only when blood sugar is clearly high (here above about 150 mg/dL).
Urine. Osmolar excretion is held at 0.5 mOsm/min, so Uosm = 0.5/V (bounded to 1200 mOsm/L, which sets a minimum obligatory volume).
Simplifications. Steady state (no pulsation or transients), one averaged nephron scaled to about two million per kidney pair, no tubular transport kinetics (Michaelis-Menten except for the glucose curve), no potassium, acid-base or urea handling, ADH and aldosterone are dimensionless inputs. Typical textbook sources: Guyton and Hall, Boron and Boulpaep, OpenStax Anatomy and Physiology. This is not a diagnostic or treatment tool. Models built with Blender, scene by Three.js.