H^MOD YNAMICS. 6 7 



Now, H decreases uniformly along the tube, and since where the tube 

 widens the velocity becomes less, and li suddenly diminishes, it follows that 

 h 2 increases, and it is conceivable that h 2 in the wide section may become 

 higher than li 2 in the narrow section. In other words, since more of H is 

 spent in maintaining the velocity in the narrow section, the lateral pressure 

 may be lower there than in the succeeding wide section. 



The flow in branching tubes. When a tube branches into a number 

 of smaller tubes, and these collect again into one tube, we have two oppos- 

 ing factors to consider 



1. The increase of sectional area. The velocity is inversely proportional 

 to the sum of the sectional area of the branches. 



2. The increase of resistance, due to the great extent of surface contact 

 between the moving fluid and the fluid that wets the walls of the tubes. The 

 resistance is proportional to the surface area, nearly proportional to the square 

 of the velocity, and inversely proportional to the sectional area. The formula 

 used by engineers for what they call skin 



friction is R = kSv 2 , where R = resistance ; 

 A:, a constant ; S, surface area ; v, velocity. 



On passing from a to b (Fig. 44), 

 the velocity has decreased, but great 

 resistance has been overcome : the total 

 effect therefore will be a much lower 

 lateral pressure at b. On passing from FIG. 44. 



b to c the velocity increases, and a 



further great fall of lateral pressure will have taken place owing to the 

 resistance that has been overcome between b and c. 



The flow in elastic tubes. The same laws which have been discussed 

 in connection with rigid tubes obtain in elastic tubes, if the flow of fluid be 

 continuous. 



If the inflow be intermittent : in the case of the rigid tube the whole 

 column of fluid is driven on, step by step, by each stroke of the pump, and 

 the outflow is also intermittent. In an elastic tube, on the other hand, if the 

 resistance to the output be made great, as by constricting the orifice, the 

 elastic wall of the tube is extended by the input of the pump, and the 

 elasticity of the wall comes into play, and continues the output after the stroke 

 of the pump has ceased. 



By the heart the blood is rhythmically driven into the arteries ; the 

 arterial walls are elastic ; in the small arteries, arterioles, and capillaries, there 

 exists great resistance. All the conditions are present for converting the inter- 

 mittent flow from the heart into the continuous flow through the capillaries. 1 

 If the arteries were rigid tubes, the heart would be required to drive on 

 the whole blood at one and the same time in all the vessels, in place of 

 intermittently forcing a certain small volume of blood into the large arteries. 

 The heart is, on the contrary, saved this large expenditure of work, and after 

 each systole retires into its diastolic rest, leaving the elasticity of the large 

 arteries to continue the circulation. Further, if two tubes be taken, one 

 elastic and the other rigid, and they be chosen so that each delivers the 

 same output when fed by a continuous inflow, then, if the inflow be made 

 intermittent, it is found that the elastic tube now yields the greater output. 2 



Beyond these advantages, due to the intermittent pump and elastic tubes, 

 there is another physiological fact which as yet has received no explanation. 

 It has been found that, if normal saline be artificially circulated by continuous 

 pressure through the vessels of an animal, oedema of the tissue soon arises, and 

 the outflow decreases. If, on the other hand, the inflow be made rhythmic, 

 as in the natural condition, then the oedema is insignificant, and the outflow 

 1 Stephen Hales, "Statical Essays," vol. ii. 

 2 Marey, Ann. d. sc. nat. ZooL, Paris, 1857, tome viii. p. 330. 



