from which, by dimensional analysis, 



f(Hj, Hj, X, d, g, Q3^, p^, p^, p^j, IX, a) = 



and 



Si = ff?,^. 



Pair Pwgd pl/3ri Q,ir 



ad 



X'X'P^' Pat ' q2/3 ' 



P Q • 



(6-14a3 



(6-14b) 



If a model study could be conducted in which (for individual test condi- 

 tions) all the u terms within f were held constant, then 



(6-15) 



However, only the first five tt terms in f can be held constant, 

 simultaneously; therefore, before accurate transference equations can 

 be determined for use in a model study, special scale-effect tests must 

 be conducted over a wide range of values of the last two tt terms to 

 determine 



(6-16) 



where the subscripts refer to model-to-prototype ratios. The reduction 

 ratio should be determined as a function of the two tt terms in f" for 

 a range of values of Hi/X and d/X that occur in the prototype. 



Each value of d used in the scale-effect tests would correspond to 

 another model; therefore, the linear scales of the models, one to another, 

 would be 



(6-17) 



in both the vertical and horizontal directions. Thus, the tests would 

 correspond to model studies using undistorted linear scales. This ensures 

 that Hi/A and d/X would be constant, model-to-prototype, for the same 

 selected prototype test conditions. The third tt term, Pair/Pw> would 

 be held constant during scale-effect tests by using air and water as the 

 two fluids for all tests. For the fourth tt term to be constant 



Pwg^\ lP^^Sd 

 Pat 



(6-18a) 



since (p^,)^ = (p„) and g^ = gp. 



W 

 (H 



d„ L_ 



(6-18b) 



331 



