ON" THE FLOW OF WATER IN" PIPES, CONDUITS, ETC. 129 



Given a pipe of constant dia meter and straightness and wliose inner 

 surface is a homogeneous heterogeneity (that is "whose inner surface is 

 such that the roughness over anj^ small area of it is the same all over the 

 surface), the conditions of disturbance of interior stream lines under 

 uniform flow may be assumed symmetrical "with respect to the axis of the 

 pipe. It appears that a particle on coming in contact "with the inequality 

 of the bounding surface is reacted upon by that surface and is sent back 

 into the interior of the liquid toward the axis with a motion whose 

 direction is transverse to that of the component direction parallel to the 

 axis of the pipe, and the velocitj'" of this particle compounds with 

 those of others wHch it meets, thereby reducing the resultant velocity 

 of flow in the direction of the discharge parallel to the pipe axis. In the 

 case of the symmetrical pipe, which we are considering, the particles 

 meeting the surface of the pipe simultaneously along the perimeter of a 

 given cross-section are reacted on by the surface with common mean effect 

 such that they form a ring or annulus of particles whose effect on the 

 interior particles is a symmetrical reduction of the effective component 

 of velocity in the direction of the axis and the more rapidly moving 

 particles in the interior moving more in the direction of the axis drive these 

 particles back to the surface of the pipe again whence they are again 

 reflected further on. The result a2>pears to be that something like a 

 vortex ring of particles is rolled along the interior of the pipe surface, the 

 effect of which is to reduce the velocity of flow in a manner analogous to 

 and in effect similar to an actual choking or contraction of the cross-section 

 of the pipe. Grossly exaggerated such a contraction is definitely known to 

 exist in the case of a cylindrical adjutage of leng-th equal to about three 

 diameters. In this case for a flush fitted pipe the actual contraction of 

 the diameter is approximately ten per cent. The converging lines ef flow 

 at the circular entrance contract to an effective cross-section, at mid-length 

 of the pipe, whose area is eightj'-one per cent, of that of the pipe ; the lines 

 then diverge and the flow flUs the pipe on exit. In such a flow if the 

 liquid were perfect there would be a gain of energy between the entrance 

 and the contracted section, while between the contracted section and the 

 exit there would be a corresponding loss equal to that gained, and there 

 would be no loss or gain of energy at exit. But if we assume, which is 

 generally admitted to be true, that the energy which would be gained in a 

 perfect liquid is entirely expended in overcoming the internal "fluid- 

 frictional" resistances, the loss of energy from the contracted section to 

 exit would represent the loss of energy of discharge. Assuming the con- 



