THE FLOW OF BLOOD THROUGH THE ARTERIES 963 



air, a sudden movement inwards of the piston at A would not be felt imme- 

 diately at B. The propagation of the wave of pressure from A to B would 

 take a finite period of time, its velocity being identical with that of the 

 velocity of propagation of a wave of sound in air, i.e. 1100 feet per second. 



B 



FIG. 418. 



The same retarding effect will be produced if we have an incompressible 

 fluid within a tube whose wall is distensible and elastic. If we imagine 

 (Fig. 419) an elastic tube BC filled and distended with water and connected 

 at B to a rigid tube, which is provided with a piston, the first effect of a 

 rapid movement of fluid driven in by the piston will be a rise of pressure 

 at the point immediately in front of the piston, viz. at a. The wall being 

 distensible, and pressure being propagated along the fluid in every direction, 

 the rise of pressure at a will be spent partly on the particles of fluid in 



FIG. 419. 



front of it, viz. at b, but also on the walls of the tube, so that this is stretched 

 and the cross-section of the tube enlarged. The distended segment at a 

 will then exert a pressure on the contained fluid, driving this backwards 

 and forwards. The fluid on its side towards the piston will tend to come 

 to a stop, while'that towards the distal end of the tube will be accelerated. 

 The distended wall therefore returns to its original diameter, and the next 

 segment at b is stretched in its turn, so that. a wave of increased pressure 

 is propagated along the tubejn the direction of the arrow. 



The velocity with which this wave is propagated depends on the density of the 

 fluid, i. e. its inertia, and on the resistance of the walls of the tube to distension, since 

 this will determine the rapidity of its recovery. The velocity of propagation of the 

 wave of increased pressure, or the wave of expansion of the artery, is expressed by the 

 following formula : 



/gea 



v = k V Dd 

 where v is the velocity per second, 



g, the acceleration due to gravity, 

 e, the elastic coefficient of the wall, 

 a, the thickness of the wall, 

 d, the diameter of the tube, 

 D, the density of the fluid, 

 k y a constant. 



