it follows from the length scale of 1:25 and from equation (69) that 



3/2 



^dm=^^-^ flO'^ ^25^ -'^'' ^''^ 



This is not a value much greater than R^ and it is therefore necessary 

 to incorporate the Reynolds number effect in equation (57) when evalu- 

 ating f. For this purpose it is assumed that a simple test has shown 

 that 



R =170 ; B =2.7 , (74) 



CO -^ 



for the material used in the model. 



Taking R, as given by equation (.73) the expression for f (eq. 57) 

 reads: 



£ n r / 1 16e ,, Cs Z ,-. 



^ ^ FT V 1 " -37 ^1 " rT^ ^i ir - 1^ 



o do 



0.4 [ /l + (1 + ig-)63 -1] = 3.4 , 



(75) 



in which the analogy with the manipulations performed in equation (66) 

 has been utilized. From this result an updated value of A is obtained 

 since X = f/0.8 = 4.25. This value of A is different from the value. 

 A = 3.5, used in determining the particle Reynolds number Rj used in 

 the evaluation of equation (75). With this new value of A, equations 

 (37) and (55) may be used to obtain a new value of Rj. This in turn 

 may be introduced in equation (75) to get a new value of f and the 

 procedure may be continued until convergence is achieved. It may be 

 shown that 



UA 

 ^d,2 = •^d.l ITa; ' f76) 



in which R^ 2 is the new estimate of R^^, whereas Rj •■ is the previous 

 estimate ana A and A^ are the old and new estimates of A, respectively. 



This procedure is generally rapidly converging. Thus, the next 

 iteration outlined above yields f = 3.46 which is reasonably close to 

 the initial estimate obtained in equation (75). 



For the Froude scale model the parameters therefore become 



45 



