Here, S is the time interval by which corresponding tidal events in the 

 tide gage well lag those in the outside basin. The equation of continuity 

 may also be written: 



aV = A d (H-h) 



dt (la) 



Laminar Flow . - For the usual tide gage installation in a tidal model, 

 the flow in the connecting pipe line is probably laminar. The criterion 

 for the occurrence of laminar flow is that 



VD < 2300 (approx.) (5) 



V 

 Since the velocity increases periodically from, zero to a maximum, Vmj the 

 Reynolds number (Vd) increases from zero to a maximum value, Fm, and for 

 the purpose of lirE~ting the present treatm.ent, it will be assuned that for 

 laminar flow 



Hm = Jjr^ <2300 (5a) 



Periodic reversal of flow .introduces some disturbance and tte critical 

 value of thtf Fteynolds number m.ay be slightly lower than 2300 but there are 

 no data available on the magnitude of the reduction. 



Poiseuille's equation for laminar flow in a long tube is 



V = wR^h 



8{LL (6) 



The tube is assumed to be long in order that the velocity head loss at 

 discharge will be negligible as compared with the overall working head, h. 

 The HpaH r-^cessary to accelerate the water in the connecting pipe is 

 neglected. Substituting equation (6) in equation (la), 



Ad (H -h ) = awR^h 



dt SfL L (7) 



Substituting for H and h from equations (3) and (/i) gives 



^r Ho sin oc t - h„ sin oC (t +€)]= awR^h 



Substituting equation (4) in this expression, and differentiating, 



Aoi [Hq cos oc t - hg cos ex (t*-£ )'] = awR*^ . h^ sin(x(t -»■ £ ) 

 *■ 8+J.L 



Inserting the constant C = 8lL_OC__AL 



awR" 



C [ I^ cos oc t - ho (cos ex t cos ex £ - sin oc t sin<*£)J = 



ho (sin oc t cos ot £ f cos oc t + sinoC £ ) (8) 



25 



