H^MODYNAMICS. 65 



velocity which a current would have, with a unit pressure gradient in a tube 

 of unit sectional area. 



Jacobson l passed water through a tube of constant bore, 437 mm. long 

 and 1*147 mm. in radius, with a mean velocity of 802*54 mm. per second. 

 The pressure gradient was 0*5485 mm., and the cross-section of the tube 4*132 

 sq. mm. According to Poiseuille's law, then 



802*54 = C x 4*132 x 0*5485.-. the coefficient (7-353*85. 



Having once found the value of the coefficient, the velocity, if Poiseuille's 

 law be right, can be reckoned in any experiment carried out under the same 

 conditions, where the sectional area and the pressure gradient are known. 

 Jacobson experimentally found that this was so. Let R = the radius of a tube, 

 F=the velocity of any particle at a distance (A) from the centre. Let Z = 

 length of tube, p p the pressures at the two ends of the tube, /u, the coefficient 



of viscosity. Then V=- (R 2 - A 2 ) .*. the velocity varies inversely as the 

 4/xt 



viscosity. The axial velocity = P~P ffi The mean velocity = ~^.-- 



4xt 4x/ 2 



The quantity of fluid which flows through in a given time t =?C-|-. ^ 



The coefficient at one and the same temperature varies for different fluids, 

 and is found to be smaller in proportion to the viscosity of the fluid. Mcolls 

 investigated the viscosity of blood by means of Poiseuille's viscometer. The 

 liquid was allowed to escape from a reservoir through a capillary tube in a 

 horizontal position. The two orifices at the ends were bell-shaped, and at the 

 end where the fluid issued there was a lip to prevent the resistance of surface 

 tension. The viscosity is obtained from the time occupied in emptying the 

 reservoir. 



The viscosity of blood was found by Ewald 2 and by Nicolls to be about five 

 times, by Lewy 3 three and a half times, that of distilled water. A mixture of 

 blood and water is less viscous than blood. The viscosity of blood diminishes 

 rapidly as the temperature rises. Assuming that this is true in the living 

 body, it follows, if the quality of the blood remains unchanged, that the rise 

 of temperature in fever diminishes the resistance, and consequently the heart 

 has less work to do. 



Duncan and Gamgee found that the velocity of flow in glass capillaries of 

 0*9289 to 1*259 mm. diameter was greater for unclotted than for defibrinated 

 blood. 4 The viscosity of the blood is increased by addition of C0 2 , ether and 

 chloral, decreased by laking the blood. 



By experiments upon the flow of distilled water in capillary glass tubes, 

 0*15 to 0*65 mm. in diameter, Poiseuille reached the following conclusions : 



1. That the amount of outflow is proportional to the head of pressure. 



2. That the time spent in the outflow of a certain volume of fluid at a 

 constant pressure is, if the diameter be constant, directly proportional to the 

 length of the tube. 



3. That with the same head of pressure, the time spent in the outflow of a 

 certain volume of fluid through equally long tubes is inversely proportional to the 

 fourth power of the diameter. Thus, if A be the volume of outflow per second, 



AT 4 TT i rr -4 ' kr 2 ^ 



A = -H, and F= ^ = rH, 

 I Tir 2 trl 



where r is the radius, I the length of the tube, H the pressure head, and k 



1 Arch. f. Anat., Pkysiol. u. wissensch. Med., Leipzig, 1860, S. 85. Quoted from Tiger- 

 stedt's "Physiol. des Kreislaufes, " S. 312. 



2 Arch. f. PhysioL, Leipzig, 1877, S. 217. 



3 Arch.f. d. ges. PhysioL, Bonn, 1897, Bd. Ixv. S. 447, 461. 



4 Journ. Anat. and PhysioL, London, 1871, vol. v. p. 155. 



VOL. II. 5 



