where 



2 

 AA = change in cross-sectional beach area (m ) 



Ay = change in shoreline position (m) 

 D = maximum depth for sand motion (depth of closure) (m) 



6. The principle of mass conservation must apply to the system at all 

 times. By considering a control volume of sand and formulating a mass balance 

 during an infinitesimal interval of time, the following differential equation 

 is obtained (see Figure 1) : 



9Q + ^ = 



9x 3t 



(2) 



where 



Q = longshore sand transport rate (m /sec) 



2 

 A = cross-sectional area of the beach (m ) 



x = space coordinate along the axis parallel to the trend of the 

 shoreline (m) 



t = time (sec) 



Shoreline 



Figure 1. Schematic illustration of a hypothetical equilibrium 



beach profile 



7. Equation 2 states that the longshore variation in the sand transport 

 rate is balanced by changes in the shoreline position. If, in addition to 

 longshore transport, a line source or sink of sand at the shoreline is con- 

 sidered, Equation 2 takes the following form: 



