546 INMAN AND BAGNOLD [CHAP. 21 



where // is the dynamic transport rate, J is the sediment discliarge in mass 

 transported "[jer unit time, {ps —pYjjps converts to immersed weight, and ii is a 

 factor of proportionahty. In tlie above it should be noted that : 



(1) Both sides of relation (21) have the nature and dimensions of power, or 

 time rate of change of energy. The quantity J , usually measured as mass passing 

 in unit time, can be expressed as transported mass per unit length in the direction 

 of transport midtiplied by a mean velocity of transport, here assumed propor- 

 tional to ui. The dynamic transport rate Ii — {ps—p)gJlps is, therefore, the 

 immersed weight multiplied by the velocity of transport, and Ii tan ^ is the 

 rate of work done in transporting the sediment. 



(2) The quantity ECn is the power transmitted per unit width of wave. The 

 power available to move sediments over unit bed area is the decrement of ECn 

 per unit distance travelled by the wave provided it is assumed that the decre- 

 ment is due entirely to bottom friction [see equation (6)]. If the whole of the 

 power in the breaking wave is dissipated between the plunge line and the shore, 

 then ECn would be the power available to move sediment over the entire width 

 of the surf zone. In fact, however, a high proportion of the power dissipated in 

 the surf zone is dissipated by means other than bottom friction, as discussed in 

 Section 12, and thus the factor K is an index of the proportion of power 

 dissijjated in moving sediment. 



If the position of rip currents is migratory and shows a random distribution 

 with time or distance along the beach, then the most general expression for 

 the mean longshore transport rate of sediment over a long straight beach will 

 be obtained by substituting the value of the mean longshore current velocity, 

 ill, as given in relation (20a) : 



tan ^qh ECn . 



1 1 = K 9 7-7 sm a cos2 a. (22a) 



tan /i -^ Uo 



The relation can be further simplified by assuming that the orbital velocity, 

 Uo, equals \{Hlh)C and that the discharge of water, q, transported forward with 

 the breaking wave, is given by the solitary wave relation leading to equa- 

 tion (20b) : 



^ 8 tan ^ En . „ .^^, > 



y (3y) tan <p T 



The empirical relation from the data of Caldwell and Savage (Section 11-C), 

 in its dimensionally consistent form, can be derived from equation (22b) by 

 substituting Pi for ECn sin a cos a. The relation then becomes 



_. 8 tan ^ „/ h \ „ /.-,.. x 



