ox THE FLOW OF WATEH IN PJrES, CONDUITS, ETC. 135 



The experiments show that AT? decreases as V increases, and perhaps 

 as r increases. We content ourselves by writing tentatively 

 fi AB _ A 



2 r rPF" 



wherein A, p, and q, are constants to be deteiinined by experiment. 



The expression for the coefficient of resistance can be finally written 



^-| -- 



7-pyq 



(18) 



l + aV<^ + brP ■ (19) 



In this we shall speak of the parameter /x as the coefficient of roughness 

 ivith respect to length. ; it depends almost entirely on the geometrical 

 configuration of the surface of the natural solid boundary over which the 

 water flows. The parameter A is a coefficient of roughness with respect to 

 the cross-section and again depends almost entirely on the geometrical 

 configuration of the surface of the solid boundary. The coefficients a and & 

 appear to be almost absolute constants, while the parameters a and j3 are 

 quite constant within certain narrow limits. The parameters p and q 

 appear to be the same under all conditions and each appears to be equal or 

 nearly so to unity. In the case of the constants p and q the experiments 

 are wanting for very precise determination ; the sequel will show, however, 

 that as far as our present knowledge goes we are justified in taldng each 

 of them equal to unity. The result of comparison with experiments shows 

 that for velocities between zero and twenty feet per second the exponent a 

 of V may be taken as unity. 



6. We shall therefore tentatively write 



m = 



1 + a7 + 6r-/3 • (^*^) 



If H be the total static head, and h^ the head lost at entry, which 

 for a flush fitted pipe is equal to 



^ 2g 



as determined by experiment, then the total head H is equal to the head 

 due to entry plus that due to pipe resistance plus that due to velocity of 

 discharge, or 



(^•^ + "^t)v (^1^ 



