FLOW OF WATER IN CLEAN PIPES 



247 



R — Ai2. Consider the change of energy A^ in a mass M in passing 

 from A through B to C. If there were no losses from fluid friction, or 

 the fluid were perfect, the mean velocity in passing from A to B would 

 be diminished resulting in a corresponding loss of energy but in passing 

 from 5 to C the mean velocity would be increased again, under the law 

 of continuity, to the same value which it had at A with a corresponding 

 gain of energy thus restoring exactly the energy lost between A and B, 

 with the final result that there would be neither loss nor gain of energy. 

 But on account of fluid friction there is a resultant loss of energy. There- 

 fore the whole or part of the energy which otherwise would be gained 

 between B and C is consumed in doing the work of overcoming the fluid 

 friction. According to Rankine it is almost wholly consumed. If —hE 

 is the loss of energy in passing from A to B then the gain of energy in 

 passing from B to C is 



il-f)^E 



where / is some fraction nearly or quite equal to unity. Hence the whole 

 change of energy in passing from A to C is equal to the loss 



■f^E 



(1) 



In order to form some idea of the mechanical equivalent of this loss 

 we make use of the principle of continuity which states that the product 

 of the normal component of mean velocity by the area of the cross section 

 is constant. Let v be the mean velocity at o and V that at Q,. Let p 

 represent a mean perimeter such that 



7? AR = fi — CO 



(2) 



The loss of pressure head in passing form one contraction, say at A 

 to an adjacent expansion, at B is for a unit mass 



