ESTIMATION OF RESISTANCE. 117 



presence of RESISTANCES, which oppose the current in the tube, i.e., part of the 

 energy is transformed into heat. As the propelling power at b is represented only 

 by F, while in the vessel it is h, the difference must be due to the sum of the 

 resistances, D ~ h - F ; hence it follows that h F -f D (Donders). 



Estimation of Resistance. 



Estimation Of the Resistance. When a Huid flows through a tube of 

 uniform calibre the propelling force, k, diminishes from point to point on account 

 of the uniformly acting resistance, hence the sum of the resistances in the whole 

 tube is directly proportional to its length. In a uniformly wide tube, fluid flows 

 through each sectional area with equal velocity, hence v and also F are equal in 

 all parts of the tube. The diminution which h ("propelling force) undergoes can 

 only occur from a diminution of pressure D, as F remains the same throughout 

 (and h = F + D). Experiment with the pressure-cylinder shows, that as a matter 

 of fact, the pressure towards the outflow end of the tube becomes gradually 

 diminished. 



In a uniformly wide tube, the height of the pressure in the manometers expresses the 

 resistances opposed to the current of fluid, which it has to overcome in its course 

 from the point investigated to the free orifice, of efflux. 



Nature Of the Resistance. The resistance opposed to the flow of a fluid, 

 depends upon the cohesion of the particles of the fluid amongst themselves. During 

 the current, the outer layer of fluid which is next the wall of the tube, and which 

 moistens it, is at rest (Girard, Poiseuille). All the other layers of fluid, which 

 may be represented as so many cylindrical layers, one inside the other, move more 

 rapidly as we proceed towards the axis of the tube, the axial thread or stream 

 being the most rapidly moving part of the liquid. On account of the movement of 

 the cylindrical layers, one within the other, a part of the propelling energy must 

 be used up. The amount of the resistance greatly depends upon the amount of the 

 cohesive force which the particles of the fluid have for each other ; the more firmly 

 the particles cohere with each other, the greater will be the resistance, and vice 

 versa. Hence, the sticky blood-current experiences greater resistance than water 

 or ether. 



Heat diminishes the cohesion of the particles, hence it also diminishes the resistance 

 to the flow of a current. These resistances are first developed by, and result from, 

 the movement of the particles of the fluid, they being, as it were, torn from each 

 other. The more rapid the current, therefore, i.e., the larger the number of 

 particles of fluid which are pulled asunder in the unit of time, the greater will he 

 the sum of the resistance. As already mentioned, the layer of fluid lying next the 

 tube, and moistening it, is at rest, hence the material which composes the tube 

 exerts no influence on the resistance. 



Effect of Tubes of Unequal Calibre, 



Unequal Diameter. When the velocity of the current is uniform, the resis- 

 tance depends upon the diameter of the tube the smaller the diameter, the greater 

 the resistance ; the greater the diameter, the less the resistance. The resistance in 

 narrow tubes, however, increases more rapidly than the diameter of the tube 

 decreases, as has been proved experimentally. 



In tubes of unequal calibre, at different parts of their course, the velocity of the 

 current varies it is slower in the wide part of the tube and more rapid in the 



