248 UNIVERSITY OF VIRGINIA PUBLICATIONS 



2g W / 2g 



= (2AR+'-AR^)^-^^- (3) 



Therefore the loss of head in passing from the contraction at A to the 

 next contraction at C, disregarding the negative sign, is 



Ah =f(2AR + ^ ArA ^ J-'- (4) 



\ o) / CO Zg 



The loss of head due to the consumption of energy in overcoming the 

 resistances due to fluid friction throughout the length L = 2n AL of the 

 pipe, or the so called resistance head hr is n Ah or 



In ordinary well formed channels with comparatively smooth bound- 

 aries we may take n to be large and AR to be relatively small compared 

 with R and 



E4 = i. (a) 



where. P is the wetted perimeter of 9. and r therefore the mean hydraulic 

 radius. We take / as unity or regard it as bemg combined with the fac- 

 tor AR/AL. The expression for the resistance head is then 



The coefficient 



AR(\, , AR\ /„x 



is then the "coefficient of resistance." If in (8) we assume AR/AL con- 

 stant and AR = there results Chezy's formula. If AR be assumed 

 constant and not zero there results the second approximation known as 

 Darcy's formula. Neither AR/AL nor AR are constants and we now 

 wish to get some idea of the general forms these functions of r and F should 

 have. There are two terms in the expression for m as given in (8), the 

 first AR/AL we call the mean slope of the resistance, the second AR we 



