THE CIRCULATION OF THE BLOOD AND LYMPH 77 



the energy of position which is transformed into the kinetic energy 

 of the flowing water. H is easily calculated when the mean velocity 

 of efflux is known. For v= J^gti by Torricelli's theorem (since 

 none of the energy corresponding to H is supposed to be used up in 



overcoming friction), or H = . At the second tube the lateral 



^6 



pressure is only h" . The sum of the visible kinetic and potential 

 energy here is therefore mv 2 + mgh". A quantity of energy mg(h' - h"} 

 must have been transformed into heat owing to the resistance caused 

 by fluid friction in the portion of the horizontal tube between the first 

 two vertical tubes. In general the energy of position represented by 

 the lateral pressure at any point is equal to the energy used up in 

 overcoming the resistance of the portion of the path beyond this point. 



Velocity of Outflow. It has been found by experiment that v, the 

 mean velocity of outflow, when the tube is not of very small calibre, 

 varies directly as the diameter, and therefore the volume of outflow 

 as the cube of the diameter. In fine capillary tubes the mean 

 velocity is proportional to the square, and the volume of outflow to 

 the fourth power of the diameter (Poiseuille) . If, for example, the 

 linear velocity of the blood in a capillary of 10 ^ in diameter is \ mm. 

 per sec., it will be four times as great (or 2 mm. per sec.) in a capillary 

 of 20 i* diameter, and one-fourth as great (or mm. per sec.) in a 

 capillary of 5 /* diameter, the pressure being supposed equal in all. 

 The volume of outflow per second is obtained by multiplying the 

 cross-section by the linear velocity. The cross-section of a circular 

 capillary, 10 n in diameter, is TT (5 ~><idoo} 2 = > sav 12500 S( l- mm - 

 The outflow will be 12500 x f = 25000 cub - mm - P er sec - " Tne outflow 

 from the capillary of 20 n diameter would be sixteen times as much, 

 from the 5 /u capillary only one-sixteenth as much. Some idea of 

 the extremely minute scale on which the blood-flow through a single 

 capillary takes place, may be obtained if we consider that for the 

 capillary of 10 n diameter a flow of 050-00 cu b- mm. per sec. would 

 scarcely amount to i cub. mm. in six hours, or to i c.c. in 250 days. 



When the initial energy is obtained in any other way than by means 

 of a ' head ' of water in a reservoir say, by the descent of a piston 

 which keeps up a constant pressure in a cylinder filled with liquid 

 the results are exactly the same. Even when the horizontal tube is 

 distensible and elastic, there is no difference when once the tube has 

 taken up its position of equilibrium for any given pressure, and that 

 pressure does not vary. 



Flow with Intermittent Pressure. When this acts on a rigid tube, 

 everything is the same as before. When the pressure alters, the 

 flow at once comes to correspond with the new pressure. Water 

 thrown by a force-pump into a system of rigid tubes escapes at every 

 stroke of the pump in exactly the quantity in which it enters, for 

 water is practically incompressible, and the total quantity present 

 at one time in the system cannot be sensibly altered. In the 

 intervals between the strokes the flow ceases ; in other words, it is 

 intermittent. It is very different with a system of distensible and 

 elastic tubes. During each stroke the tubes expand, and make 

 room for a portion of the extra liquid thrown into them, so that a 

 smaller quantity flows out than passes in. In the intervals between 

 the strokes the distended tubes, in virtue of their elasticity, tend to 

 regain their original calibre. Pressure is thus exerted upon the 

 liquid, and it continues to be forced out, so that when the strokes of 

 the pump succeed each other with sufficient rapidity, the outflow 



