9.4 Similitude and Dimensional Analysis
325
Table 9.1: Similitude criteria
Name
Form
Application area
Froude Number (Fr)
u/ViL
free surface flow
Reynolds Number (Re)
U L/ll
viscous dominated flow
Euler Number (Eu)
p/pU~
flow under pressure
Mach Number (Ma)
U /Gs
compressible flow
Weber Number (We)
pU'.l L/(J
flow when influence of surface
tension is important
Richardson Number (Ri)
8p/8z
(g/ p) (8u/8z)2
flow in stratified fluid
Peclet Number (Pe)
UL/D
flow with diffusion effect
Most flows with a free surface are under the influence of gravity forces, and
consequently the Froude Number, Fr, is the most important criterion to be
considered when modelling such flows. The Froude criterion requires that:
(9.32)
or:
(9.33)
in which variables with subscript p are related to the prototype and variables
with subscript m correspond to the model. The relationship (9.33) can be
expressed in terms of scale ratios as follows:
(9.34)
Assuming now that the model is built on the Earth, gravity accelerations, gp
and gm" are the same; thus Ng = 1 and:
(9.35)
Therefore, if our model dimensions are one hundredth of the prototype dimensions (N L), Froude criterion implies that velocities on the model are one tenth
of velocities in the prototype (Nu = 10). In other words, velocities measured