ft' Coefficient of dynamic viscosity of the fluid inside the fluid body 



a Interfacial tension 



The complete set of dimensionless products will therefore contain five such products. In 

 principle, it is immaterial which complete set is chosen for the representation of the phenom- 

 enon. For example, we may use 



fAC D , Re, We, £_, £,) = 

 n' p 



or 



f 2 {C D , Re, M, Re',±.) = 



and so on, where C n is the drag coefficient, 



Re is the Reynolds number f = £.1 , 



We is the Weber number (= 2lU P) , 



Re' is the Reynolds number inside the fluid body J = ££il£_\ and 



M is a dimensionless parameter I = .££_ | 



V na 3 l 



If the density and viscosity of the gas inside a bubble are considered negligible, the physical 

 variables are reduced to six. The dimensionless products then take the form of 



f 3 {C D , Re, We) = 

 or 



f 4 (C D , Re, M) =0 

 or 



f 5 {C D , We, M) =0 



etc. 



When experimental data on gas bubbles are plotted in terms of dimensionless products, 

 complete correlation will be obtained provided the variables chosen are all the variables upon 

 which the phenomenon depends. 



In the case of bubbles, it is most convenient to use a length parameter which is based 

 on its volume rather than a physical dimension as is customary for rigid bodies. The length 

 parameter chosen is the equivalent radius r where 



. _ 3/~voi 



volume 



*The coefficient of surface viscosity is not included since there is no experimental evidence that dynamic 

 surface tension, as postulated by Boussinesq, exists. 



