or may be related to the most important force, a particular state of 

 fluid motion can often be simulated in a scale model by considering that 

 either gravity forces or viscous forces predominate. Since inertial re- 

 action is always present in the flow phenomenon, it follows that inertial 

 forces must be considered in any particular flow situation. Equation 2-7 

 is used to express the ratio between the applicable forces for given flow 

 conditions. To express these forces in usable terms their physical equiv- 

 alents in terms of length (L) , mass (M) , gravitational acceleration 

 (g) , density (p) , dynamic viscosity (y) , modulus of elasticity (E) , 

 surface tension (a), and pressure (p) may be used. Thus, 



Fj - mass X acceleration = (pL^XV^/L) = pL^V^ (2-8a) 



Fg = mass X gravitational acceleration = pL g (2-8b) 



Fg^ = unit surface tension X length = aL (2-8d) 



Fg = modulus of elasticity X area = EL^ (2-8e) 



Fpj = unit pressure X area = pL? (2-8f3 



a. The Froude Number . Based on equations 2-7 and 2-8a and when 

 gravitational forces predominate. 



(^Om fg)m (pL2v2)^ (pL^g)^ 



C^i ' (^g)n ' (pL2v2)_ " (pLh\ 



from which 



(2-9) 



8m '-'m 8p "^p 

 and, with subscript r indicating the model-to-prototype ratios, 



= 1 . (2-10) 



(g,L,)l/2 



The dimensionless quantity V/(gL)^^2 is called the Froude number Fj^; 

 the required equality of the Froude number, model-to-prototype, wfiich 

 indicates that the ratio of gravitational to inertial forces in a model 

 should equal the corresponding ratio in the prototype, is known as the 

 Froude model law. 



26 



