The Hagen Poiseuille's law. Blood, strictly speaking, is not a Newtonian fluid, also blood vessels are not rigid.

Indeed, AC Burton once remarked that, 'most of the (Hagen-Pioseulle) Jaw is common sense'] Hagen - Poiseuille law is also known, simply, as Poiseuille's (pronounced. Pawazee) law Jean Leonard Marie Poiseuille was a Paris based physician and physicist who, in 1842, grasped the fundamental principles as described above in connection wilh his researches on flow of blood through the capillaries It was GHL Hagen. a contemporary of Poiseuille. who worked further with the problem and found out the mathematical expression. It is emphasized, that only, a Newtonian fluid passing through a rigid tube obeys. The Hagen Poiseuille's law. Blood, strictly speaking, is not a Newtonian fluid, also blood vessels are not rigid. Tubes Nevertheless, Hagen Poiseuille's law gives an ides about the major determining factors of law. Resistance against the flow. As the blood flows onwards, it faces a 'resistance' a gainst the flow. The resistance has to be overcome otherwise flow will slop. However, in overcoming resistance, the flowing blood also loses some of its energy (which it received from the heart because of the venmcular contraction). This loss of total energy means that the lateral pressure is also. Tailing (see Bernoulli's principle, earlier in this chapter). As the resistance is ,offered by the vascular tree, which lies peripheral to heart, this is also called the peripheral resistance.The interrelationship between the volume of blood flowing per unit time. Q the resistance. R. the pressure gradient, , m the Hagen - Poiseulle law) is given by the expression (The value of R. there fore is,, putting values of Q from Hagen - Poiseulle equation. R, [This is analogous to the Ohm's law in electricity I= E/R. where, I = quantity of charge flowing in an unit time, i.e current, E = the difference of the potenlial. i.e . the voltage and R = the resistance a gains! the current flow Indeed flow of eleclric current is often visualized as flow of walei in a tube] In our body, as stated above, the Q can be visualized as the cardiac output, n, . the viscosity coefficient of blood, N the total length from the beginning of aorta to the terminal part of vene cave ((in case of systemic circulation) and r .The mean diameter of all the vessels Normally, the 1 does not change in a grown up man, n also does not change frequently. Therefore, it is the r. the radius, which changes readily and frequently (due to such causes like sympathetic stimulation leading to vasoconstriction and so on) Further, the resistance R changes as the 4th power of the r. the radius. "Seat' of the penpheral resistance. Every, segment of the vascular tree (e. g. Windkessel vessels, ariennles, capillaries, capacitance vessels) offers tome resistance. However, the maximum resistance is encountered at the level of the arterioies. Therefore, as explained earlier, the total pressure, P, falls maximally at the level of the artenoles (figure 5.7.4) Further, because of the fact that the arteriolar walls contain heavy investments of smooth muscles and are susceptible to, (i) sympathetic stimulation as well as to the actions of many (ii) vasoaclive agents, the arteriolar diameter alters very frequently (according to the needs of the body) producing alterations of resistance. Therefore, to repeat (i) pressure drop -occurs maximally at the level of artenoles, and (ii) arteriolar resistance varies frequently and very effectively. For all these reasons, arterroles have captured the attention of the physiologists. Fig. 5.7.4 . Blood pressure values in the different segments of the vascular tree. Note the sharpest fall of BP occurs at the level of artenoles. indicating. The alienates offer maximum resistance. The situation changes as the blood enters the zone of capillaries. As the number of capillaries is very great. their total resistance offered a gains! the flow falls. This means the drop of total pressure of the blood due to its passage through the caprllanes is not great (fig. 5.7.4) In the venous system pressure is very low (fig 5.7.4) and hence veins belong To the low pressure syslem' In this connection, it should be remembered that our body is able to constrict, selectively, the artenoles supplying a particular organ. Thus, artenoles supplying the skin undergo selective vasospasm (for example, during early phase of muscular exercise). This causes ischemia of the skin. As artenoles supplying the other organs (e. g .skeletal muscles) remain unaffected or are even dilated, the blood is diverted to these organs. Thus, in this way, the body achieves 'redistribution' of the blood flow Viscosrty. AT the outset, some commonly used terms will be explained Let mn is a tube (fig 5.7. 513) through which water is flowing In such cases, Sir Isaac Newton visualized nearly three centuries agoL that the flowing water may be considered to be consisting of large number of concent ne laminae (like the concentric laminae of an onion) as in A of fig 5 .7.5. Each lamina or 'shell' is in intimate contact with its adjacent laminae When such a liquid (water in this exmple) moves, the Velocity profile' of the laminae takes a paraboloid shape (6 in fig. 5_7S). The lamina adjacent to the wall of the tube, does not move at all. whereas the velocity increases more and more as the amina in question is more and more near the central longitudinal axis. That is, the molecules in the central longitudinal axis has the maximum velocity and it may be visualized that these molecules are 'dragging' the other laminae. This dragging force, that is. the force which causes the velocity gradient in the laminae, is called the shearing force Fig 5.7.5 A cross sectional view of a laminar flow. B. Longiludmal view Note, The velocily is