The heart pumps blood throughout the body, the arteries are the blood vessels carrying
blood away from the heart, and the veins return blood to the heart. Close to the heart, arteries
are very large. The smallest blood vessels are capillaries
Precise measurements demonstrate that the flux (rate of flow) of fluid through the capillary
wall is not constant over the length of the capillary. Fluids in and around the capillary are
subjected to two forces. The hydrostatic pressure, resulting from the heartís pumping, pushes
fluid out of the capillary into the surrounding tissue. The oncotic pressure drives absorption
in the other direction. Along the length of
the capillary, the hydrostatic pressure decreases while the oncotic pressure is approximately
Along a cylindrical capillary of length L = 0.1 cm and radius r = 0.0004 cm, the hydrostatic
pressure, ph, varies from 35 mm Hg at the artery end to 15 mm Hg at the vein end. (mm
Hg, millimeters of mercury, is a unit of pressure.) The oncotic pressure, po, is approximately
23 mm Hg throughout the length of the capillary
(a) Find a formula for The hydrostatic pressure as a function of x, the distance in centimeters from the artery end of the capillary, assuming that The hydrostatic pressure is a linear function of x.
(b) Find a formula for p, the net outward pressure, as a function of x.
(c) The rate of movement, j, of fluid volume per capillary wall area across the capillary wall is
proportional to the net pressure.We have j = k*p where k, the hydraulic conductivity, has
Check that j has units of volume per time per area.
(d) Write and evaluate an integral for the net volume flow rate (volume per unit time) through
the wall of the entire capillary.