When cos oi t = 0, Gh^ sin ex £ = h^ cos ©( £ and 



tan ol£ = 1_ 



C (9) 



When cos ex: t = 1, 



C Plo ~ G hp cos ex £■ = hQ sin o<. <£ 



and substitution for G from equation (9) gives 



ho = cos oc £ 



Ho" (10) 



Equations (9) and ^lO) determine the constants necessary for computa- 

 tion of the working head at any instant, t„ The actual elevation H' in the 

 tide gage well is 



H« " H - h = Hq' sin o< ( t - 9) 



Expanding this equation and inserting equations (9) and (10) gives 



2 



= 1 - CO s^ oc £ = sin oC & 



tan oi 9 = - cot ocS (11) 



Herej cx <£■ = tan ( 1^ )o The lag in seconds of events on the H'-curve 



G 

 after the corresponding events on the H-curve is the quantity ©<> 



Both the lag and the reduction in range are seen to be functions of 

 the dimensionless quantity C which may therefore be regarded as the model 

 criterion for the fluctuations in tide gage wells connected to the outside 

 basin by lines which are long in proportion to the maximum velocity head. 



Turbulent Flowo - In completely developed turbulent flow in pipes, 

 the head loss is proportional to the square of the velocity. If this 

 quadratic relationship is tal^n as the definition of "turbulent" flovr, 

 then very short pipe lines connecting two reservoirs may be regarded as 

 being in "turbulent flow", even though the flow may actually be laminar, 

 because the working head is utilized almost entirely in creating velocity 

 head which is proportional to V in both turbulent and laminar flow. In 

 other words laminar flow through an orifice or a very short tube should 

 obey the same type of equation (not the same equation) as turbulent flow 

 in a long pipe o The exact length of tube which divides turbulent and 

 laminar flow as defined here cannot be specified exactly but it will de- 

 pend upon the relationship between the friction head and the velocity 

 heado 



26 



