Page 188 - Introduction to Naval Architecture

174 RESISTANCE

h are the pressure, density, velocity and height above a selected datum
level, then:

Simple hydrodynamic theory deals with fluids without viscosity. In a non-
viscous fluid a deeply submerged body experiences no resistance.
Although the fluid is disturbed by the passage of the body, it returns to its
original state of rest once the body has passed. There will be local forces
acting on the body but these will cancel each other out when integrated
over the whole body. These local forces are due to the pressure changes
occasioned by the changing velocities in the fluid flow.
In studying fluid dynamics it is useful to develop a number of non-
dimensional parameters with which to characterize the flow and the
forces. These are based on the fluid properties. The physical properties
of interest in resistance studies are the density, p, viscosity, /* and the
static pressure in the fluid, p. Taking R as the resistance, V as velocity
and L as a typical length, dimensional analysis leads to an expression
for resistance:

The quantities involved in this expression can all be expressed in terms
of the fundamental dimensions of time, T, mass, M and length L. For
2
instance resistance is a force and therefore has dimensions ML/T , p
3
has dimensions M/L and so on. Substituting these fundamental
dimensions in the relationship above:

Equating the indices of the fundamental dimensions on the two sides of
the equation the number of unknown indices can be reduced to three
and the expression for resistance can be written as:

The expression for resistance can then be written as: