For dynamic similarity the ratio of the inertial force between model 

 and prototype must be the same as the ratio of the individual force com- 

 ponents between the model and prototype. The ratios of the inertial force 

 to the other component forces must also be the same between model and pro- 

 totype. These ratios have developed a reference to specific names, such 

 as the ratio of the inertial force to the pressure force as 



E„ = ^ = -^ (Euler No.) 



^i _ V 

 n - F " (^5172 CFroude No.) 



F„ = 



(7-2) 



F, 



i VL£ 



and 



Rn 



^P. ^ 







Fi 



"Fst' 







Wn 



pV^L 



(Reynolds No.) 



(Weber No.) 



Since only three of these equations are independent, the Euler number will 

 automatically be equal in the model and prototype if the other niombers are 

 equal . 



From the remaining three equations, 



(#), = m, - iM - • • 



It can be demonstrated that no single model fluid will permit all of these 

 equations to be satisfied at once; therefore, true dynamic and kinematic 

 similarity apparently cannot be achieved between a model and the prototype. 



However, one or more of the specific forces is often foimd to be neg- 

 ligible and the number of equations to be satisfied can be reduced accord- 

 ingly. In fact, the phenomena in a particular instance often involve the 

 effect of only one force ratio and the others are negligible. 



The use of water as a model fluid is usually necessary in coastal en- 

 gineering models. Surface tension, the least important term if the depths 

 of the fluid are not excessively small, will have a negligible effect on 

 the flow of water more than 0.25 foot deep, or on waves with lengths ex- 

 ceeding about 1.0 foot in the same water depth. By ensuring that the flow 

 and waves exceed these limiting values, the effect of surface tension can 

 be neglected. 



When both viscous and gravity forces are important, as in open channel 

 flow on mild slopes, the Froude and Reynolds niimbers should both be 



464 



