PHYSICAL CONSIDERATION 349 



it is required to overcome the resistance at the outlet. Obviously, 

 therefore, the formula deduced by Toricelli, holds true only if the 

 resistance to the outflow is so slight that it can justly be neglected. 



Flow of a Liquid Through Rigid Tubes. — Further modifications 

 of the previous contention are made necessary if the orifice of the 

 receptacle is equipped with a round tube of uniform diameter, adjusted 

 in a horizontal direction. It must be evident that this addition places 

 an even greater resistance in the path of the escaping fluid, thereby 

 insuring a still greater reduction in the outflow. It is essential, how- 

 ever, that the size of the tube do not exceed a certain limit, because, 

 if it possesses a very large diameter, the conditions of flow become so 

 complicated that they cannot be brought in accord with our present 

 knowledge pertaining to this matter. Moreover, theoretical specula- 

 tions of this kind seem uncalled for at this time, because channels of 

 exceptional diameter are not encountered in the vascular system. 



A liquid flowing through a tube, always meets with a certain resistance which 

 is dependent, on the one hand, upon the cohesion of its molecules, and, on the 

 other, upon the adhesion of its outer layer to the walls of the vessel. The former 

 constitutes the internal friction or viscosity, and the latter, the external friction. 

 Provided, therefore, that a liquid moistens the vessel wall, an adhesion results, in 

 consequence of which its outermost layers become stationary. The molecules 

 of the layers of fluid situated next to the outermost, are also retarded by cohesion, 

 but they are not stopped altogether. The more centrally situated layers are 

 slowed in quite the same manner until the axial column is reached which, however, 

 is retarded least of all and possesses therefore the greatest speed of flow. When 

 speaking of velocity, we generally refer to the average speed attained by a liquid 

 irrespective of the differences shown by its various layers. Furthermore when 

 dealing with straight tubes which impart a parallel motion to the different particles 

 of the liquid, the general velocity of the flow is only one-half as great as that of 

 the axial stream. Obviously, therefore, the pressure of the liquid in the reservoir 

 is constantly made use of in overcoming the peripheral resistance composed 

 of the forces of adhesion and cohesion. Thus, while a part of the static energy 

 produced by the mere position of the liquid, is consumed in antagonizing this 

 hindrance to the flow, the remainder is converted into kinetic energy, as evinced 

 by the escape of the liquid from the tube. 



The resistance to the flow is betrayed by the lateral or side pressure prevailing 

 at the different points of a system of tubes. Thus, if a number of vertical tubes, 

 or piezometers, are connected in series with the main horizontal channel, some 

 of the liquid escapes from here and enters these branches to a height corresponding 

 to the pressure prevailing at these points. In other words, the level of the liquid 

 in these laterals is accurately adjusted to the peripheral resistance encountered by 

 the liquid as it passes these points. It must be clear that the liquid exerts a certain 

 pressure upon the internal wall of the main tube which is evenly distributed in all 

 directions. Besides, if the main channel is equipped with a branch, the pressure 

 prevailing in the former, is propagated outward through the orifice in its wall in 

 strict agreement with the cross-section of the collateral. Under this condition, 

 the internal pressure is capable of supporting in the side-tube a column of liquid 

 of a certain height or weight. By determining the latter (^), an accurate measure 

 is obtained of the pressure prevailing at the point where the branch joins the main 

 tube. Furthermore, since the resistance in a tube of uniform diameter is pro- 

 portional to its length, and since the resistance still to be overcome diminishes 

 with the proximity of the outlet, the pressure must decrease gradually in a direc- 

 tion from the reservoir to the outlet. For this reason, the occlusion of the latter 



