348 THE MECHANICS OF THE CIRCULATION, HEMODTNAMICS 



counterbalanced by any factor capable of exerting precisely the same degree of 

 pressure. If wateris used for this purpose, it would have to be 1033 cm. in height, 

 provided its specific gravity is unity. If mercury is employed instead, a column 

 only 76 cm. in height would be required, because the specific gravity of this element 

 is 13.55 times greater than that of water. When a pressure exceeds that of the 

 atmosphere, it is rated as positive, and when it is less than the atmospheric, as 

 negative. Thus, the values of the pressures prevailing in the different channels 

 and cavities of our body, are always rated in accordance with the line of the atmos- 

 pheric pressure (760 mm.). This constitutes the zero line or abscissa. 



Dynamically considered, blood behaves in much the same way as water. 

 It flows through the vascular channels in agreement with certain laws which are 

 derived from those regulating the flow of other practically incompressible liquids. 

 One difficulty, however, is met with and that is the distensible and elastic char- 

 acter of the blood-vessels and spaces. For this reason, it must be admitted that 

 the general physical data given above, may not be ap- 

 plicable to the conditions encountered in a circulatory 

 system built up of living matter. In spite of this prob- 

 ability, however, it seems advisable to give a brief dis- 

 cussion of the factors controlling the flow of a fluid 

 through rigid tubes, because many of the problems con- 

 nected with the circulation of the blood are founded 

 upon them. But as our knowledge regarding the dyna- 

 mics of the movement of liquids, or hydrodynamics, is 

 still very incomplete, the present discussion must be re- 

 stricted to the simplest of the facts known. 



f 



FIG. 181. DIAGRAM 

 ILLUSTRATING Toni- 

 CELLI'S THEOREM. 

 h, height of pressure; R, 

 resistance at orifice. 



Toricelli's Theorem (1643). If a fluid is 

 placed in a receptacle possessing vertical and 

 parallel walls, it exerts a pressure upon the lower 

 surface of this vessel equal to the weight of any 

 other mass of fluid of the same cross-section and 

 height. If a round opening is now made in the 

 bottom of this reservoir, while the quantity of 

 fluid within it is replenished sufficiently to remain at the level (h), the 

 fluid escapes with a velocity (v) which may be expressed by the formula : 

 v = \/2gh, g being the acceleration produced by the gravity. It is a 

 well-known fact that the speed attained by a falling body equals 2gh, 

 and hence, the velocity of a fluid flowing through a hole in the bottom 

 or side of a receptacle, is the same as that attained by the fluid when 

 falling in vacuo through the distance (h) . Thus, it should be possible to 

 determine with accuracy the volume of the fluid escaping in a unit of 

 time, by contrasting the velocity with the cross-section of the outlet. 

 It has been shown, however, that the quantity of fluid which may be 

 expected to escape upon theoretical grounds, does not quite equal the 

 quantity obtained. This discrepancy is caused by the resistance en- 

 countered by the fluid at the brim of the orifice (r) . As only a limited 

 number of columns of fluid lie in straight lines vertically above the open- 

 ing, the others must occupy positions lateral to these. But as the latter 

 tend to escape together with the former, they must converge toward the 

 center of the orifice, so that a conical and not a cylindrical outline is 

 imparted to the entire mass of outflowing liquid. Consequently, the 

 total energy (h) cannot be spent to produce velocity, because some of 



