THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES

THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES (From the Department of Biology, Bryn Mawr College, Bryn Mawr.) (Accepted for publication, April 1, 1925.) In a recent paper t it has been proposed that the total work involved in the circulation of blood in a section of artery (sufficiently small so that the pulsating changes in the kinetic energy of the blood stream in it can be neglected as compared to the work required to overcome friction) can be expressed b y the equation: E = p f + bvol f~.l.8~ wr 4 + blrrr 2 (1) which embodies Poiseuille's law of flow and a term which covers the cost of maintenance of blood volume, p is the fall in pressure in dynes/cm. ~, b is the cost of blood volume in ergs/cc, sec. (considered constant), vol is the volume, r is the radius of the section of artery, and 71 is the viscosity of whole blood (also taken as "constant"). At constant flow, f (that is, for any given steady state), and at constant length of arterial section, l, the total energy, E, is a minimum when: f~ = ~ r6r~b (2) Substituting forj ~ in the original equation, we obtain: Ell = r2(3rb) Or, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of General Physiology Rockefeller University Press

THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES

The Journal of General Physiology, Volume 9 (6): 835 – Jul 1, 1926

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Publisher
Rockefeller University Press
Copyright
Copyright © 1926 by The Rockefeller University Press
ISSN
0022-1295
eISSN
1540-7748
DOI
10.1085/jgp.9.6.835
Publisher site
See Article on Publisher Site

Abstract

(From the Department of Biology, Bryn Mawr College, Bryn Mawr.) (Accepted for publication, April 1, 1925.) In a recent paper t it has been proposed that the total work involved in the circulation of blood in a section of artery (sufficiently small so that the pulsating changes in the kinetic energy of the blood stream in it can be neglected as compared to the work required to overcome friction) can be expressed b y the equation: E = p f + bvol f~.l.8~ wr 4 + blrrr 2 (1) which embodies Poiseuille's law of flow and a term which covers the cost of maintenance of blood volume, p is the fall in pressure in dynes/cm. ~, b is the cost of blood volume in ergs/cc, sec. (considered constant), vol is the volume, r is the radius of the section of artery, and 71 is the viscosity of whole blood (also taken as "constant"). At constant flow, f (that is, for any given steady state), and at constant length of arterial section, l, the total energy, E, is a minimum when: f~ = ~ r6r~b (2) Substituting forj ~ in the original equation, we obtain: Ell = r2(3rb) Or,

Journal

The Journal of General PhysiologyRockefeller University Press

Published: Jul 1, 1926

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