To establish a relationship be- 

 tween head difference across the 

 pipes and water discharge through the 

 pipes, simultaneous water level and 

 discharge measurements were conduct- 

 ed on May 30, 1977; June 3, 6, and 

 21, 1977; and April 5, 1978. Water 

 velocity in the canal immediately 

 south of the culverts was determined 

 by timing drogue transits over a 15- 

 m range. Concurrently, water eleva- 

 tions were noted at tide staffs lo- 

 cated at the north and south ends of 

 the culverts. The water elevation 

 at the south staff allowed for 

 determining the cross-sectional 

 area of the open channel flow and 

 therefore for the computation of 

 discharge from velocity measure- 

 ments . 



sectional area of an individual 

 pipe we may express the discharge 

 Q as 



Q - A : V 1 = A 2 V 2 = 3 A p V p 



(2) 



Eliminating V , V , and V p in Eqs . 1 

 and 2 yields 



h = (- 



2 4/3 



k + k + 2 gn L/R ' 

 v e 



1 + 1 



2gA x 2 2gA 2 2 



18 gA p ' 



)« 2 



(3) 



Using Bernoulli's Equation with 

 Manning's friction formulation and 

 expressing quantities in metric 

 units, the head loss across a pipe 

 can be expressed as: 



V T 



h = h. 



h 2 = 



(k + k 



2g 



2 2 

 2 gn Z L V / 



) " + 



4/3 



2g 



V 2 



(l) 



R 



where h. and h are the water eleva- 

 tions at the respective ends of the 

 pipe, V is the average water velo- 

 city through the pipe, g is gravity 



acceleration, k and k are the 



v e 

 entrance and exit loss coefficients, 



respectively, n is Manning's fric- 

 tion coefficient, L is pipe length, 

 and V and V are the water veloci- 

 ties in the open channel at the 



respective pipe ends. Letting A 

 and A be the respective open chan- 

 nel flow cross-sectional areas at 

 the pipe ends and A the cross- 



or Q = K 



where K represents the quantity in 

 Eq. 3 to the -1/2 power. 



For the range of observed val- 

 ues of A and A„ , terms 2 and 3 of 

 Eq. 3 are negligible. The factor K 

 in Eq. 4 then depends only on term 1 

 of Eq. 3. Its value was determined 

 experimentally using 34 field mea- 

 surements of water velocity and 

 tidal elevation differences across 

 the culverts. Values of discharges 

 determined from velocity measurements 

 were plotted on log-log paper versus 

 observations of h (Figure 2). At 

 least squares fit of a line of slope 

 2 drawn thorugh the 34 data points 

 yielded a value of K of 2.56 m /sec 

 with a corresponding standard devia- 

 tion of 0.16 m /sec and correlation 



coefficient r 



0.9, 



Figure 3 shows a comparison of 

 discharges for 6 experiments com- 

 puted from velocity measurements 

 and from Eq. 4. Although individual 

 discharges computed from Eq. 4 do 



2 34 



