(c) After-inlet nourishment needed to maintain the historic erosion rate on 

 the beach to the left of the inlet. 



(d) After-inlet nourishment needed to eliminate erosion left of the inlet. 



SOLUTION ; Divide the beach under study into four sand budget compartments 

 (control volumes called reaches) as shown in Figure 4-50. Shore- 

 perpendicular boundaries are established where important changes in the 

 littoral system occur. To identify and quantify the hefore-irilet system, 

 the continuity of the net transport rate along the entire spit must be 

 established. The terminology of Figure 4-43 and Table 4-15 is used for the 

 sand budget calculation. The average annual volume of material contributed 

 to the littoral system per meter of eroding beach Reaches 2 and 3 is 



q_,-. = qo/'oN = h^x = (4.6 + 9.1) 0.9 = 12.33 cubic meters per year per 



meter (4.91 cubic yards per year per foot) 



Then, from equation (4-58) the total annual contribution of the eroding 

 beaches to the system can be determined as 



* + *+ 

 ^3C2') "*" ^3f3") " ^^'^ *™ '*' ^'^ ^^ (1000 meters per kilometer) 

 (12.33 cubic meters per year per meter) 

 = 87,500 cubic meters per year (114,400 cubic yards per year) 



Since there is no evidence of sand accumulation to the right of the eroding 

 area, the eroding beach material effectively moves to the left, becoming a 

 component of the net transport volume C^ toward the end of the spit. 

 Continuity requires that erosion volume and Reach 1 (^ combine to equal 

 the accretion at the end of the spit (305,000 cubic meters per year). 

 Thus, (^ at the root of the spit is 



(L(,, „s = 305,000 cubic meters per year - 87,500 cubic meters per year 



^, «v = 217,500 cubic meters per year (284,500 cubic yards per year) 



C^ across the boundary between Reaches 2 and 3 ((^o 3)^ ^^ 



*+ 

 ^(2,3) " ^(1,2) "^ ^3(2) • 



^(2,3) " ^(1,2) ^ ^(2) ^^3(2)^ 



^(2 3) " 217,500 + (2.1 kilometers) (100 meters per kilometer) (12.33 

 ' cubic meters per year per meter) 



C^,2 ■\\ ^ 243,400 cubic meters per year (318,000 cubic yards per year) 



4-130 



