128 MOVEMENT THROUGH CAPILLARY TUBES. 



side of the arch and thus encounter a greater resistance to their progress than on 

 the concave side. 



When the tube divides into two or more branches, the propelling force is 

 also diminished on account of the creation of additional resisting forces. When 

 a current is divided into two smaller currents, some fluid-particles will be retarded, 

 while others will be accelerated on account of the unequal velocity of the various 

 layers of the fluid. Many particles that in the main current, as a part of the 

 axial stream, had the greatest velocity will in the secondary currents when situated 

 in the parietal layers move more slowly; while, conversely, many parietal layers 

 in the main current become more centrally situated in the secondary current 

 with increased velocity. As a result of the resistance thus produced a part of 

 the propelling force is naturally lost. The separation of the fluid-particles as the 

 current divides has a similar effect. If, on the other hand, two tubes join to form 

 a single tube, additional resistance acting in a manner opposite to that described 

 must lessen the propelling force. The sum total of the mean velocity in both 

 branches of the current is independent of the angle formed at the point of division. 

 The opening of a lateral branch that forms part of a tube accelerates the main 

 current to the same degree, irrespective of the size of the angle formed by the 

 lateral branch with the main tube. 



MOVEMENT THROUGH CAPILLARY TUBES. 



The movement of fluids through capillary tubes is, in accordance with the 

 capillary attraction prevailing in capillary vessels, and in contravention of the 

 laws that have just been developed, governed by certain rules, for the formulation 

 of which credit is due Poiseuille. These rules are as follows: 



1. The quantity of fluid that escapes from a capillary tube is proportional to 

 the pressure. 



2. The time necessary for the escape of a like quantity of fluid (the pressure, 

 the diameter of the tube, and the temperature remaining the same) is propor- 

 tional to the length of the tube. 



3 . The products of the outflow (all other conditions remaining the same) vary 

 with the fourth power of the transverse diameter. 



4. The velocity of the current is proportional to the pressure-height and to 

 the square of the diameter, and inversely proportional to the length of the tube. 



5. The resistances in the capillary tubes are proportional to the velocities 

 of the current. 



CONTINUOUS AND UNDULATORY MOVEMENT IN ELASTIC TUBES. 



If an uninterrupted, uniform stream of fluid is permitted to flow through an 

 elastic tube, the movement of this current is subject to the same laws that govern 

 its passage through rigid tubes. If the propelling force increases or diminishes, 

 the elastic tubes are either dilated or constricted, and their relation to the column 

 of fluid is, therefore, simply like that of wider or narrower rigid tubes. 



If, however, successive amounts of fluid are introduced at intervals into an 

 elastic tube entirely filled with fluid, the initial portion of the tube will be suddenly 

 distended in accordance with the amount of fluid introduced. The impact imparts 

 to the fluid-particles an oscillatory movement, which rapidly communicates itself 

 to all the fluid-particles from the beginning to the end of the tube ; there results 

 a positive wave, which rapidly propagates itself through the entire tube. If the 

 elastic tube be closed at its peripheral extremity, the positive wave will rebound 

 at the point of closure; it becomes a positive recurrent wave and it may even 

 pass backward and forward repeatedly, becoming gradually smaller and smaller, 

 until it finally subsides. Hence, in a closed tube of such character, the sudden 

 periodic impulsion of a mass of fluid produces only a wave-like movement, that 

 is, merely an oscillatory movement or the movement of a form. 



3. If, however, additional amounts of fluid are at intervals pumped into the 

 initial portion of an elastic tube entirely filled with fluid already in continu- 

 ous movement, the continuous movement is combined with the undulatory 

 movement. In such a case the continuous movement of the fluid, that is, the 

 displacement or movement of the fluid in mass through the tube, must be rigidly 

 distinguished from the undulatory or oscillating movement, the movement of 

 the change in form of the column of fluid. The former is a translatory, the latter 

 an oscillatory movement. The continuous movement is slower in elastic tubes v 

 while the undulatory movement is more rapid. 



