Tha criterion for the maximum valus of oc is 



oC = 8 n V 



tan /p /Tt 



(PC) 



(26a) 



If Rj^ exceeds = 2300 and oL from equation (26a) is within reasonable litiits 

 for a particular case, then the analysis of the maximum value of oC must be 

 modified to fit the case of turbulent flow, starting from equation (24.) but 

 using the previous analysis of turbulent flow as the first approximation. Cn 

 the other hand, if Eg ? 2300 and ex given by equation (26a) is far below the 

 value of ex: for the experimental installation, the connection to the tide gage 

 well should be modified or its lag and reduction of range should be determined 

 experimentally. 



Coefficients . - Practically, the case of turbulent flow is important only 

 in very short lines in which the connection is equivalent to an orifice or 

 short tube. Hence the friction coefficient f in turbulent flow probably enters 

 the equation for U in very few cases. Since the Reynolds number is generally 

 small, the flow through the orifice is laminar and the coefficient Cq is 

 nearly unity. The coefficient K is smaller than in truly turbulent flow but 

 not much is known about the correct value. 



Whether a particular problem should be solved by the equations for 

 laminar or turbulent flow depends on the ratio of that portion of the resistance 

 which is proportional to V^ and that proportional to V. Taking the simple 

 case of laminar flow in a short connection, 6 in equation (12) equals 2, C^ = 1. 

 The two components of the head h are then 



-li- and g'l^.V 

 2g wl?^ 



Taking the ratio 



8U V / 2 V'^ ^ ISV 

 wr2 / 2g 2VR2 



Inserting the value of V given by the laminar solution 



V = A dH;_ = oc^Ho sin aS cos « (t - 0) 

 a dt 



a 



At V = V 



max ' 



16' , 8 a -^ 

 2VR^ - oi APoR^sino<r£ 



If this ratio is large as compared with unity, the head necessary to overcome 

 viscous resistance is large as compared with the velocity head and the laminar 

 solution aiDplies, If it turns out to be small as compared with unity, t !:e 



31 



