Page 189 - Introduction to Naval Architecture

RESISTANCE .175

Thus the analysis indicates the following non-dimensional combina-
tions as likely to be significant:

The first three ratios are termed, respectively, the resistance coefficient,
Reynolds' number, and Fronde number. The fourth is related to cavitation
and is discussed later. In a wider analysis the speed of sound in water, a
and the surface tension, a, can be introduced. These lead to non-
2
dimensional quantities V/a, and a/gpL which are termed the Mach
number and Weber number. These last two are not important in the
context of this present book and are not considered further. The ratio
IJL/P is called the kinematic viscosity and is denoted by v. At this stage it
is assumed that these non-dimensional quantities are independent of
each other. The expression for the resistance can then be written as:

Consider first / 2 which is concerned with wave-making resistance. Take
two geometrically similar ships or a ship and a geometrically similar
model, denoted by subscripts 1 and 2.

The form of/ 2 is unknown, but, whatever its form, provided gl^/V^ =
fL.2/Vf the values of/ 2 will be the same. It follows that:

5
05
For this relationship to hold ^/(g-L,) = V 2/(gI^)°- assuming p is
constant.