METHOD OF ESTIMATING THE RESISTANCES. 127 



METHOD OF ESTIMATING THE RESISTANCES. 



When a fluid passes through a tiibe of uniform caliber throughout its entire 

 length, the propelling force h diminishes progressively in consequence of the 

 resistances that operate uniformly at every point. The sum of all the resistances 

 in the tube is, therefore, directly proportional to its length. In a tube of uniform 

 caliber the fluid passes through each transverse section at a constant velocity; 

 hence v (and, therefore, F) is the same at any point in the tube. The diminution 

 that takes place in the propelling force h can, therefore, be due only to a diminution 

 of the pressure D, as F remains the same everywhere (and h "= F -f D). The 

 experiment with the pressure- vessel shows, in fact, that the pressure progressively 

 diminishes toward the discharging extremity of the tube. In a tube of uniform 

 width the pressure-height found to prevail in the manometer-tube is the expression 

 of the sum of the resistances that must be overcome by the current in its course 

 from the point examined to the free discharge-opening of the tube. 



Forms of Resistance. The resistances encountered by a stream of fluid 

 reside first of all in the cohesion of the fluid-particles. The outermost parietal 

 layer of the fluid, which is in contact with the tube, remains absolutely quiescent 

 during the passage of the current. All the other layers of the fluid, which may 

 be concerned as a series of concentric cylinders one within the other, move with 

 a progressively increasing velocity from the periphery to the axis of the tube, 

 while the axial thread itself finally represents the most rapidly moving portion of 

 the fluid. In the displacement of these cylindrical layers of fluid at their surfaces 

 of contact, the particles of fluid in juxtaposition must naturally be pulled apart 

 and a portion of the active propelling force will be lost. The degree of resistance 

 depends essentially on the degree of cohesion between the particles of fluid; the 

 more intimate the cohesion between the fluid-particles, the greater will be the 

 resistance; and conversely. It is thus evident that the resistances encountered 

 by the viscous blood in its passage must be greater than those that would be 

 encountered, for example, by water or ether. Four and one-half times as much 

 pressure would be required to drive the same quantity of blood as of water through 

 a tube. 



Heat diminishes the cohesion of the particles and it is, therefore, a means 

 for diminishing the resistance encountered by the current. It is also evident that 

 the resistances are only the result of movement, as the forcible separation of the 

 fluid-particles does not begin until the column is set in motion. It is, further, 

 obvious that the greater the velocity of the current the greater the number 

 of fluid-particles that are torn apart in a unit of time the greater will be the 

 sum of the resistances. The parietal layer of fluid in contact with the surface of 

 the tube remains, as has been said, in absolute quiescence; it follows, therefore, 

 that the material composing the walls of the tube has no influence on the resistances. 



INFLUENCE OF INEQUALITIES IN THE SIZE OF THE TUBE. 



When the velocity of the current remains the same, the intensity of the 

 resistances depends on the diameter of the tube; the smaller the diameter the 

 greater the resistance, and the larger the diameter the less the resistance. The 

 resistances, however, increase more rapidly in narrower tubes than the diameter 

 of the tubes increases. This has been proved by experimental investigation. 



In tubes that exhibit inequality in size in their course, the velocity of the 

 current varies, being naturally slower in the wide portions and more rapid in the 

 narrower portions. In general the velocity of the current in tubes of unequal 

 caliber is inversely proportional to the transverse section of the different portions 

 of the tube, that is, if the tubes are cylindrical inversely proportional to the square 

 of the diameter of the circular transverse section. 



While in tubes of uniform size the propelling force of the moving fluid dimin- 

 ishes uniformly section by section, the diminution is not uniform in tubes of 

 unequal width; for since, as has just been shown, the resistance is greater in a 

 narrow than in a wide tube, the diminution in the propelling force must naturally 

 be greater in the narrow places than in the wide places. At the same time, i't 

 has been shown that the pressure in the wider places is greater than the sum of 

 the resistances still to be overcome; while, on the other hand, at the narrower 

 places it is smaller than the sum of these resistances. 



Curvature and tortuosity of the vessels give rise to new resistances. In con- 

 sequence of centrifugal force the fluid-particles cling more closely to the convex 



