G. H. KNIBBS. XXXYV, 
mum for a given fall of pressure. If the motion be tur- 
bulent, there is less translational flow for the given fall of 
pressure, for the energy is exhausted,—(a) partly in motion 
of translation, (b) partly in rotational motion. 
2. Flow in capillaries.—In large tubes fluids flow 
steadily only with great difficulty, and fora given velocity 
it is practicably impossible to maintain steadiness when 
they are above a certain dimension, which has some rela- 
tion to the viscosity of the fluid. The laws of steady and 
turbulent flow are discussed in treatises on hydrodynamics, 
and have been previously reviewed in this Society.’ 
In an elliptical tube, for example, the velocity of steady 
flow v of an incompressible fluid of viscosity 7, is expressed 
by the equation 
gehaseaee! cao? 
in which p is the fall of pressure in the length 1 of the tube 
of semi-diameters a and b. 
Should the flow be turbulent, as it would be both in 
underground fissures, and in the artesian bore itself, then 
the flow will be, writing i for p/l 
v=k° 5 Te RO | ERM ED 
ay 
in which c and d, and n are functions of the roughness of 
the channel, and ec depends upon its absolute dimensions, 
(7 is unity for steady flow, and is probably never less than 
+). It may be noted here, that the fall of pressure in the 
artesian tube can be roughly calculated for any definite 
? History, theory and determination of the viscosity of water by the 
efflux method, G. H. Knibbs—Journ. Royal Soc., xx1x., 1895, pp. 77 — 146. 
Recent determinations of the viscosity of water by the efflux method, 
G. H. Knibbs—Journ. Royal Soc., xxx., 1896, pp. 186-198. Steady flow 
of water in uniform pipes and channels, G. H. Knibbs—Journ. Royal Soc. 
Xxx., 1896, pp. 314 - 355. 
2 Journ. Royal Society, N.S.W., 1895, p. 112. 
* Journ. Royal Society N.S.W., 1897, pp. 348-9, etc. 
