CIVIL ENGINEERING FORMULAS

298 CHAPTER TWELVE

Similar equations may be written for the YandZdirections. The impulse–
momentum equation often is used in conjunction with the Bernoulli equation but
may be used separately.

SIMILITUDE FOR PHYSICAL MODELS

A physical model is a system whose operation can be used to predict the
characteristics of a similar system, or prototype, usually more complex or
built to a much larger scale.
Ratios of the forces of gravity, viscosity, and surface tension to the force of
inertia are designated, Froude number,Reynolds number, and Weber number,
respectively. Equating the Froude number of the model and the Froude number
of the prototype ensures that the gravitational and inertial forces are in the same
proportion. Similarly, equating the Reynolds numbers of the model and proto-
type ensures that the viscous and inertial forces are in the same proportion.
Equating the Weber numbers ensures proportionality of surface tension and
inertial forces.
TheFroude number is

F (12.9)

V

Lg

P 1 x

P 1

V 1 x

V 1 y

P 1 y

V 1

Fx

Fy R

θ

Y

X

P 2 V 2

FIGURE 12.4 Force diagram for momentum.