THE LAG mo REDUCTION OF 

 RANGE IN TIDE GAGE WELLS 



The following paper first: appeared in limited issue as 

 Tephnical Rfemorandum NOo 14, ,Uo So Tidal Laboratory, 

 Berkeley, California, by Morrough P. O'Brien, Consulting 

 Engineer. The paper is reproduced here to bring the 

 findings to the attention of a larger group of I'esearch 

 workers and others having an interest in tidal phenomena. 



Abstract 



The problem of the lag of high and low water and the reduction of 

 range has been treated by Chapman (Philosophical Magazine, Vol, 4-6, 1923), 

 for the case of a simple orifice connecting a primary tidal basin with a 

 secondary basin on the assumption that the instantaneous rate of flow 

 corresponds to the instantaneous head. In the analysis which follows, the 

 treatment is generalized to include the effect of both laminar and turbu- 

 lent friction and the effect of acceleration. 



General ij]q,uations . - The equation of continuity relating the average 

 velocity in the connecting line and the velocity of rise of the water 

 surface in the well is (for symbol meanings see Appendix I) 



av = A dH' 



(1) 



dt 



At any instant, the elevation of the primary tidal surface is H and that 

 in the gage well is K' o The working head at that instant is 



h = H 



H' = (H - h) 



(2) 



Flow occurs into the well when H>-H', or hs^O, and out of the well when 

 H>H' o The primary tidal surface exhibits periodic variations and for the 

 purpose of this analysis, these variations will be assumed to be sinusoidal, 

 ice o 



H = Hq sin oc t; «. = 2 ^ 



(3) 



The curve of H' will also be a sine curve of lesser amplitude lagging the 

 curve of H but having the same period. Therefore, the equation for the 

 working head may be written as 



h = Hq sin or t - Ho' sine « (t *■ £ ) 

 h = hg sin ex (t + £ ) 

 24 



U) 



