b. The Reynolds Number . When viscous forces predominate. 



^P 



from which 



(^i)p (H' ^"^'^'^^ ^"""^^r 



hnXm = h'^p (2-11) 



I'rr, Vr, 



P 



where v = y/p, the kinematic viscosity, and 



-^^ = 1 . (2-12) 



The dimensionless quantity LV/v is called the Reynolds number R^; the 

 required equality of this number, model to prototype, as indicated by 

 equation 2-12, is known as the Reynolds model law. 



c. The Weber and Mach-Cauchy Numbers . When surface-tension effects 

 predominate, the ratio between surface tension and inertia forces gives 



,;, = 1 (2-13) 



and 



V 



(a/pL)^/2 



is known as Weber's number Wj^. If all forces other than those resulting 

 from elastic compression are neglected, the ratio between elastic and 

 inertia forces gives 



V. 



and 



(2-14) 



(E/p)l/2 



is the Mach or Cauchy number M^j. Surface-tension effects are seldom 

 encountered in coastal engineering problems in the prototype, but they 

 are involved with some of the phenomena when reduced in magnitude in 

 scale models. The resulting scale effects can, in most cases, be reduced 

 satisfactorily in model studies by proper selection of the linear scale. 

 The Mach-Cauchy law also has little application in engineering problems 

 involving the flow of water; however, it is useful for those problems 

 concerning the flow of gases at velocities exceeding the speed of sound 

 and the design of structural models where the elastic forces are 

 important. 



27 



