Hydromechan
127
Part A | 7.1
7. Hydromechanics
Karl Dietrich von Ellenrieder, Manhar R. Dhanak
Ocean engineering is a systems engineering field
and requires a relatively broad background in
several aspects of engineering. The role of hydrodynamics is central to all ocean engineering
activities and despite an ocean engineer’s specialist designation, sooner or later some aspects
of hydrodynamics will encroach upon the problem he or she is trying to solve. The intent of
this chapter is not to provide an exhaustive treatment of marine hydrodynamics, but instead to act
as a reference source to provide enough working
knowledge to solve practical problems, or at least
a good idea of where to start looking. A range of
topics is covered including dimensional analysis,
static and dynamic flows, potential and viscous
flows, laminar and turbulent flows, boundary layers, wakes, jets and shear layers, and drag and lift
forces.
7.1 Dimensional Analysis, Basic Estimation,
and Model Testing ................................ 127
7.1.1 Drag Force on a Sphere ................. 127
7.1.2 Physical Significance
of the Dimensionless ˘ Groups..... 129
7.1.3 Similitude ................................... 134
7.1.4 Skin-Friction Drag ........................ 135
7.1.5 Estimating the Drag on a Ship
from Model Testing ...................... 136
7.1.6 Hydrofoil Lift and Drag ................. 138
7.1.7 Screw Propellers........................... 143
7.1.8 Air and Wind Resistance ............... 146
7.1.9 Hydrodynamic Characterization
of Marine Surface Vessels .............. 146
7.2 Fluid Statics . ......................................... 153
7.2.1 Pressure Forces on Surfaces ........... 153
7.2.2 Static Stability.............................. 154
7.3 Hydrodynamics ..................................... 155
7.3.1 Flow Kinematics .......................... 155
7.3.2 The Navier–Stokes Equations ........ 156
7.3.3 Flow of an Ideal Fluid .................. 159
7.3.4 Flow of a Viscous Fluid ................. 169
References................................................... 174
7.1 Dimensional Analysis, Basic Estimation, and Model Testing
At a fundamental level, dimensional analysis and similitude allow the development of physical laws and
equations, from-scratch or based on observation and
measurement.
Dimensional analysis is the starting point for understanding many physical phenomena. It is most often
used for:
Estimating the effects of different parameters
Interpreting experimental data
Defining scaling laws that can be used to predict
the performance of full-sized prototypes using the
data from measurements conducted on engineering
models.
In hydromechanics, the use of dimensional analysis and similitude is especially important as there are
a small number of exact solutions to the equations governing fluid flow and numerical solutions are limited
to flows with fairly simple geometries or to restricted
ranges of conditions.
The use of dimensional analysis might be best explained through use of a simple example.
7.1.1 Drag Force on a Sphere
Here we wish to find an estimate for the drag force
D acting on a spherical body completely immersed in
a flowing fluid and far from any boundaries. We might
start by asking ourselves what physical properties of the
flow and spherical body the drag might depend upon.
One could argue that the size of the sphere is likely
important and pick the diameter A of the sphere as being a characteristic or representative length scale of the
body. The speed of the flow will also likely play a role
and so the freestream speed U of the flow can be used as
a characteristic value. One could argue that part of the
127
Part A | 7.1
7. Hydromechanics
Karl Dietrich von Ellenrieder, Manhar R. Dhanak
Ocean engineering is a systems engineering field
and requires a relatively broad background in
several aspects of engineering. The role of hydrodynamics is central to all ocean engineering
activities and despite an ocean engineer’s specialist designation, sooner or later some aspects
of hydrodynamics will encroach upon the problem he or she is trying to solve. The intent of
this chapter is not to provide an exhaustive treatment of marine hydrodynamics, but instead to act
as a reference source to provide enough working
knowledge to solve practical problems, or at least
a good idea of where to start looking. A range of
topics is covered including dimensional analysis,
static and dynamic flows, potential and viscous
flows, laminar and turbulent flows, boundary layers, wakes, jets and shear layers, and drag and lift
forces.
7.1 Dimensional Analysis, Basic Estimation,
and Model Testing ................................ 127
7.1.1 Drag Force on a Sphere ................. 127
7.1.2 Physical Significance
of the Dimensionless ˘ Groups..... 129
7.1.3 Similitude ................................... 134
7.1.4 Skin-Friction Drag ........................ 135
7.1.5 Estimating the Drag on a Ship
from Model Testing ...................... 136
7.1.6 Hydrofoil Lift and Drag ................. 138
7.1.7 Screw Propellers........................... 143
7.1.8 Air and Wind Resistance ............... 146
7.1.9 Hydrodynamic Characterization
of Marine Surface Vessels .............. 146
7.2 Fluid Statics . ......................................... 153
7.2.1 Pressure Forces on Surfaces ........... 153
7.2.2 Static Stability.............................. 154
7.3 Hydrodynamics ..................................... 155
7.3.1 Flow Kinematics .......................... 155
7.3.2 The Navier–Stokes Equations ........ 156
7.3.3 Flow of an Ideal Fluid .................. 159
7.3.4 Flow of a Viscous Fluid ................. 169
References................................................... 174
7.1 Dimensional Analysis, Basic Estimation, and Model Testing
At a fundamental level, dimensional analysis and similitude allow the development of physical laws and
equations, from-scratch or based on observation and
measurement.
Dimensional analysis is the starting point for understanding many physical phenomena. It is most often
used for:
Estimating the effects of different parameters
Interpreting experimental data
Defining scaling laws that can be used to predict
the performance of full-sized prototypes using the
data from measurements conducted on engineering
models.
In hydromechanics, the use of dimensional analysis and similitude is especially important as there are
a small number of exact solutions to the equations governing fluid flow and numerical solutions are limited
to flows with fairly simple geometries or to restricted
ranges of conditions.
The use of dimensional analysis might be best explained through use of a simple example.
7.1.1 Drag Force on a Sphere
Here we wish to find an estimate for the drag force
D acting on a spherical body completely immersed in
a flowing fluid and far from any boundaries. We might
start by asking ourselves what physical properties of the
flow and spherical body the drag might depend upon.
One could argue that the size of the sphere is likely
important and pick the diameter A of the sphere as being a characteristic or representative length scale of the
body. The speed of the flow will also likely play a role
and so the freestream speed U of the flow can be used as
a characteristic value. One could argue that part of the