THE CIRCULATION OF THE BLOOD AND LYMPH 73 



reservoir and the lateral pressure at the beginning of the horizontal 

 tube that is, the height at which the straight line joining the 

 menisci of the vertical tubes intersects the column of water in the 

 reservoir. Let H represent the height corresponding to that part of 

 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= A/2^H by Torricelli's theorem (since 

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



gjj| 



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



2 



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

 energy here is therefore %mv z + mgh". A quantity of energy mg (ft - 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 repre- 

 sented 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 /a 

 diameter, and one-fourth as great (or mm. per sec.) in a capillary 

 of 5 p 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 (j. in diameter, is v (5 x y^nnr) 2 = > sav TSTTTO- sc l- mm - The outflow 

 will be jYTTnr x i = ^T^TTTT cu ^ mm - P er sec - The outflow from the 

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

 the 5 p 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 //, diameter a flow of -o-g-^u cub. mm. per sec. would 

 scarcely amount to i cub. mm. in six hours, or to i cc. 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 



