SECT. 3] BEACH AND NEARSHORE PROCESSES 515 



stationary boundary. The whole resistance to flow, in the two-dimensional case, 

 is that exerted by the solid phase. 



Unfortunately, no experimental methods have been devised for measuring 

 either the load w?, of grains moving over a grain bed or the mean speed Ui, 

 of their travel. But the product niDUb is the rate jb of mass transport of the 

 load per unit width. This is measurable j)rovided there is no additional load 

 transported in suspension by fluid turbulence. 



Since the tangential thrust stress required to maintain the bed_load in 

 motion is [{ps -p)lps\(jmb cos j8(tan ^ -tan ^), multiplication by Ub gives 

 the work done by the fluid in unit time, i.e. the fluid "power" expended per 

 unit of bed area in transporting the bed load. Whence fluid power expended = 

 [{ps -p)lps]gjb cos ^ (tan ^ -tan ^). 



CaUing the quantity [{ps - p) I ps]gj b cos ^ the "dynamic transport rate" ib, 

 we have : 



Fluid power expended = ib (tan (f> —tan /3). (3) 



This is the fluid energy that is converted directly into heat in unit time by 

 inter-granular friction per unit of bed area in the process of transporting the 

 bed load. 



B. Available Fluid Power 



Now let us regard the fluid as a transporting machine, and apply the principle 

 of energy conservation. The power, ib (tan ^-tan /3), expended in transporting 

 the bed load must be some proportion less than unity of the whole available 

 fluid power. 



The available fluid power per unit boundary area is the whole fluid energy 

 dissipated into heat in unit time per unit of bed area by the effects of boundary 

 resistance. Let this be denoted by oj. We can now write : 



H = CO — ; -z, (4) 



tan (f) —tan p 



where ej, is an efficiency factor which must be less than unity, and both ib and 

 CO are measurable in the same units, i.e. of power. 



In the case of a steadily flowing water stream, and also in that of a train of 

 stable surface waves proj)agated in shallow water, the value of co can be found 

 directly. 



The power, oj, of a stream, per unit area of its bed boundary, is ^pu, where 

 u is the steady mean velocity of flow. Since ^p is the decrement of flow energy 

 per unit distance, x, travelled by the water, we can write : 



CO = ^ fu = pgh -7— u, (5) 



18— s. Ill 



