130 UNIVEBSITY OF VIRGINIA PUBLICATIONS 



traction of the diameter at ten per cent, to be approximately correct, 

 V to be the mean velocity in the contracted section and V that of the 

 discharge, the loss of head equivalent to the change of energy is, 



2g ^ ' ■' 2g 2g 



The observed loss of head is actually about thirty-three per cent, of H. 



In the common laboratory experiment of the formation of vortex smoke 

 rings, when a chamber containing air and smoke receives an impulse 

 discharging through a short tube a vortex ring is ejected; a number of 

 such impulses in rapid succession expel a number of such rings in close 

 proximity and vphich become confused under a steady flow and uniform 

 discharge. Something of similar character takes place in the flow through 

 a long pipe : the dragging of the air along the side walls causes a rolling of 

 such rings of disturbance along the rough boundary and a corresponding 

 interference in the lines of steady flow with retardation of the velocity of 

 discharge. 



We assume therefore that the loss of energy of water flowing in a pipe 

 or canal is due to the geometrical irregularities of the surface over which 

 the water flows, and to the effect of the internal eddies, vortices, disturb- 

 ances of stream lines caused by the deflections and reactions of the rough, 

 irregular surface in contact with water. That in a closed pipe under 

 pressure the effect of these disturbances is equivalent in fact to a choking 

 or contraction of the actual cross-section of the pipe. 



It is well established that if a single solid annular obstruction be 

 placed in a pipe there is a corresponding loss of energy in any actual flow. 

 The actual loss is computed in every text book on this subject and is 

 formulated on the basis of being measured by the change of momentum 

 caused by the impact of an inelastic body of relatively insignificant mass 

 impinging against another of relatively great mass and moving in the same 

 direction — the small mass being the body of water involved in the con- 

 traction moving with higher velocity striking the mass of water in the 

 remainder of the pipe moving with slower velocity. See Weisbach, Applied 

 Mechanics, pp. 675, 884, 887; also Eankine, Civil Engineering, p. 677, 

 where in commenting on the loss of energy due to a contraction in a pipe 

 or canal he says, "It appears that all the energy due to the difference of 

 the velocities is expended in fluid friction, and consequently there is a 

 loss of head." 



