3. The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended by the heart in pumping the blood.

4. In particular, this energy is reduced when the resistance of the blood is lowered. One of Poiseuille’s Laws gives the resistance R of the blood as where : L - is the length of the blood vessel, r - is the radius of the blood vessel, C - is a positive constant determined by the viscosity of the blood.

5. Poiseuille's law in medicine Is the law which expresses the relationship between the rate of flow of a liquid in a tube and the pressure gradient in the tube, the radius of the tube, the length of the tube and the viscosity of the liquid. The American Heritage® Medical Dictionary Copyright © 2007, 2004 by Houghton Mifflin Company What exactly is the Poiseuille’s law?

6. Our presentation is based on the pulmonary artery

7. The figure shows a main blood vessel with radius r 1 branching at an angle Ѳ into a smaller vessel with radius r 2

8. We are going to show, using Poiseuille’s Law, that the total resistance of the blood along the path ABC becomes R, where a and b are the distances shown in the figure.

10. Where L - is the length of the blood vessel, (AB & BC ) r1 & r2 - are the radiuses of the vessels C - is a positive constant determined by the viscosity of the blood. Now we are ready to substitute to the formula : With branching R1 and R2

11. Now, we are going to prove that this resistance is minimized when Therefore:

12. R is decreasingR is increasing When theta is 1.15 the resistance of blood is minimized.

13. Now lets see what happens when the radius of the smaller blood vessel is 2/3 the radius of the larger vessel. We just found the optimal branching angle (correct to the nearest degree) r2 r1

14. ∏ The end