The height of the free surface above the bottom y , when the wave crest and 

 trough are at the structure, may be determined from equations (7-73) and 

 (7-74) as follows: 



y = d + h + ( ^ t ^ ) H. 



and 



y =d + h - 1±-X H. 



■'t o \ 2 I t 



y = 3 + 1.00 + (1)(1.5) = 5.50 m (18.1 ft) 



y = 3 + 1.00 - (1)(1.5) = 2.50 m (8.2 ft) (T = 6 s) 



A similar analysis for the 10-second wave gives 



y = 5.85 m (19.2 ft) 



y, = 2.85 m (9.4 ft) (T = 6 s) 



The wall would have to be about 6 meters (20 feet) high if it were not to be 

 overtopped by a 1 .5-meter- (5-foot-) high wave having a period of 10 seconds. 



The horizontal wave forces may be evaluated using Figure 7-91. Entering the 

 figure with the computed value of H-/gT , the value of F/wd can be 

 determined from either of two curves of constant H'/d . The upper family 

 of curves (above F/wd = Q) will give the dimensionless force when the 

 crest is at the wall: F/wd ; the lower family of curves (below F/wd = 

 0) will give the dimensionless force when the trough is at the wall: 

 F^/wd^ . For the example problem, with H^/gT^ = 0.0043 and H^/d = 0.50 , 



F F 



a t 



= 0.63; = -0.31 (T = 6 s) 



2 2 



wd wd 



3 3 



Therefore, assuming a weight per unit volume of 10 kN/m (64.0 lb/ft ) for 



sea water. 



F^ = 0.63 (10) (3)2 = 56.7 kN/m (3,890 lb/ft) (T = 6 s) 



F^ = -0.31 (10) (3)2 = -27.9 kN/m (-1,900 lb/ft) (T = 6 s) 



The values found for F and F, do not include the force due to the 

 hydrostatic pressure distribution below the still-water level. For 

 instance, if there is also a water depth of 3 meters (10 feet) on the 

 leeward side of the structure in this example and there is no wave action on 

 the leeward side, then the hydrostatic force on the leeward side exactly 

 balances the hydrostatic force on the side exposed to wave action. Thus, in 

 this case, the values found for F and F. are actually the net forces 

 acting on the structure. 



7-171 



