500 



600 



700 



800 



900 



Figure 17. Beach profile adjacent to weir section. 



Determine the wave overtopping rates and the total volume of water 

 carried over the weir by overtopping if wave conditions remain constant 

 over the entire tidal cycle. 



FIND; 



SOLUTION ; The first step is to subdivide the weir into reaches across 

 which the overtopping rate is assumed constant. For brevity, the example 

 weir is divided into only three reaches. The water depth and wave height 

 at the center of each reach are assumed to determine the overtopping rate 

 in the entire reach. The solution is tabulated for five water depths 

 during a tidal cycle in Table 4. Column 1 gives the water depth at the 

 center of the reach at the indicated time. Column 2 is the length of the 

 reach. At low tide (t/T = 0) the shoreline is within reach 2; hence, 

 the length of reach 2 is only 165 feet. Column 3 is the freeboard, the 

 height of the weir at the center of the reach less the water depth. 

 Column 4 is the local wave height. The wave height is depth-limited in 

 most cases and is therefore given approximately by H^ = 0.78d or H, 

 = 3.0 feet, whichever is smaller. Column 5 (obtained from Fig. 7-5 of 

 the SPM) relates breaker height to deepwater wave characteristics 

 assuming a beach slope of 0.07. Columns 6 and 7 are calculated from the 

 tabulated values; column 8 (from Fig. 7-14 of the SPM) was used for the 

 calculations and extrapolated for small values of H^/gT 2 . Column 9 is 

 the relative freeboard computed from columns 3 and 8. The a and Q* 

 values in columns 10 and 11 are empirical coefficients for use in the SPM 

 overtopping equation (Weggel, 1976) and were obtained from Figure 7-24 of 

 the SPM by interpolating between tabulated points. The values of a 

 and Q* are therefore only approximate. The ranges of d g /H' and H'/gT 2 

 were small, thus a and Q* were assumed constant equal to 0.072 and 

 0.04, respectively. Column 12 is the overtopping rate per foot of weir 

 crest given by 



/ 3\l/2 



q = (sQ H o ) ex p - 



0.1085 



log. 



/ R + h - d s \ 

 \R- h+ a) 



(10) 



33 



