ABSTRACT
This chapter proposes that equations must be dimensionally homogeneous. It defines several dimensionless ratios that are commonly encountered in fluid mechanics. The Chapter explores dimensionless ratios as scaling parameters in modeling problems. It derives various dimensionless ratios such as Reynolds, Froude, and Weber numbers and examines the requirements of geometric and dynamic similarity. The chapter discusses Similitude and modeling, as were dimensionless ratios that are important in various flow situations. Flow in an open channel such as a river or spillway is maintained by gravity forces analogous to pressure forces in pipe flow. Flows at gas—liquid or liquid—liquid interfaces where no solid surfaces are in contact are called unbounded flows. The force exerted in the direction of flow is called the drag forceDf. The force in the numerator is an inertia force; the denominator is a viscous force. Thus, the Reynolds number is a ratio of inertia to viscous forces in the flow.
