H&MOD YNAMICS. 



the curve formed by a plane section through the axis of a main artery and its 

 branches is approximately a parabola, and this is found by experiment to be 

 the best shape. Hence there is no energy lost when blood passes from a main 

 artery into its branch. 1 



If a tube be fixed to the orifice, then the mean velocity of outflow through 

 such a tube leading from the bottom of the vessel is found to be less than 

 through the simple orifice. This is due to the resistance to the flow in the 

 tube, owing to viscosity of the fluid ; that is, in a simple case, where the fluid 

 wets the inner wall of the tube. Now, " rigid mathematical calculation can 

 only be applied to the motion of actual fluids, as long as it is not turbulent ; 

 when a certain limit of velocity is exceeded the motion is disturbed." 



By introducing a small stream of coloured liquid into transparent tubes, in 

 which water was moving with a velocity nearly equal to that of the blood, 

 Nicolls found the motion not turbulent in tubes of different diameters. We 

 may assume, therefore, that the flow in the blood vessels is not turbulent. 



Plow of fluid in cylindrical tubes. In a cylindrical tube, the fluid 

 particles, flowing under constant pressure, move parallel with the axis, but 

 with varying velocity. In the axial layer the velocity is at its greatest, at the 

 wall it is practically nil. The material of which the wall is made has no 

 influence on the velocity, the whole friction lies between the particles of fluid. 

 In any two tubes, equally long and wide, it is only the chemical and physical 

 qualities, i.e. the viscosity of the circulating fluid, which influence the relative 

 velocity of flow. Since the threads of fluid which are at the same distance 



^ Y 



c^*- 



FIG. 42. 



from the axis will move at the same velocity, the fluid may be considered as 

 consisting of an infinite number of concentric cylindrical surfaces, which glide 

 over one another, and move the more rapidly, tlie smaller their radius. The 

 velocity which is reckoned from the outflow per second per sectional area of 

 the tube, yields us the mean velocity of all these cylinders of fluid. 



The mean velocity in such tubes as we are considering, where the motion is 

 steady, is equal to half the axial velocity. 2 " It is the friction between the par- 

 ticles of fluid, or the viscosity, that causes the outflow from a tube to be less in 

 a given time than from a free opening of the same bore. Part of the head of 

 pressure is spent in overcoming this viscosity. The amount of head so lost 

 in overcoming fluid friction is in a uniform tube proportional to the length 

 of tube which has been traversed by the fluid. This may be shown experi- 

 mentally by means of the apparatus sketched in Fig. 42'. 



In the figure, A is a vessel filled with fluid to the level shown ; BC is a 

 uniform tube attached horizontally to A; D, E, F, H, M, K", are vertical 

 tubes (piezometers) to indicate the lateral pressure at different points along 



1 Nicolls, Journ. PhysioL, Cambridge and London, 1896, vol. xx. p. 416. 



2 v. Kries, Arb. a. d. physiol. Anst. zu Leipzig, 1887, S. 101. 



