Page 197 - Introduction to Naval Architecture

RESISTANCE 185

Frictkmal resistance

Water is viscous and the conditions for dynamic similarity are geometric
similarity and constancy of Reynolds' number. Due to the viscosity the
particles immediately adjacent to the hull adhere to it and move at the
speed of the ship. At a distance from the hull the water is at rest. There
is a velocity gradient which is greatest close to the hull. The volume of
water which moves with the body is known as the boundary layer. Its
thickness is usually defined as the distance from the hull at which the
water velocity is 1 per cent of the ship speed.
Fractional resistance is associated with Reynolds because of the study
he made of flow through pipes. He showed that there are two distinct
types of flow. In the first, laminar flow, each fluid particle follows its own
streamlined path with no mass transfer between adjacent layers. This
flow only occurs at relatively low Reynolds' numbers. At higher
numbers the steady flow pattern breaks down and is replaced by a more
confused flow pattern called turbulent flow.
Reynolds showed that different laws of resistance applied to the two
flow types. Further, if care was taken to ensure that the fluid entered the
mouth of the pipe smoothly the flow started off as laminar but at some
distance along the tube changed to turbulent. This occurred at a
critical velocity dependent upon the pipe diameter and the fluid
viscosity. For different pipe diameters, d, the critical velocity, V c, was
such that V cd/v was constant. Below the critical velocity, resistance to
flow was proportional to the velocity of flow. As velocity increased above
the critical value there was an unstable region where the resistance
appeared to obey no simple law. At higher velocity again the flow was
fully turbulent and resistance became proportional to V raised to the
power 1.723.
Reynolds' work related to pipes but qualitatively the conclusions are
relevant to ships. There are two flow regimes, laminar and turbulent.
The change from one to the other depends on the critical Reynolds'
number and different resistance laws apply.
Calculations have been made for laminar flow past a flat surface,
length L and wetted surface area S, and these lead to a formula
developed by Blassius, as:

Plotting the values of Q against Reynolds' number together with results
for turbulent flow past flat surfaces gives Figure 8.6.
In line with Reynolds' conclusions the resistance at higher numbers
is turbulent and resistance is higher. The critical Reynolds' number at