1 3.021 Marine Hydrodynamics
Lecture 1
1
13.021 Marine Hydrodynamics
Lecture 1
Introduction
Marine hydrodynamics is a large and diverse subject and only a few topics can be
covered in an introductory
13.021 Marine Hydrodynamics
Lecture 14
Some Properties of Added-Mass Coefficients
(1) mij= [function of geometry only]
&
F, M = [linear function of mij] * [function of instantaneous U, U, ]
Not of mot
13.021 - Marine Hydrodynamics
Lecture 16
Vortex Shedding and Vortex Induced Vibrations
Uo
Consider a steady flow Uo on a bluff body with diameter D
D
We would expect the average forces to be:
Fx
Fy
F
y
Marine Hydrodynamics
Lecture 17
U, V potential
u, v viscous flow
x
4.6 Laminar Boundary Layers
L
Assume steady 0
t
2D
Uo
0
w,
z
u (x, y ), v (x, y ), p (x, y ), U (x, y ), V ( x, y )
For <L, us
Summary of Boundary Layer over a Flat Plate
Laminar (Blasius)
1
~ Rx 2
x
Turbulent (1/7 power law)
1
~ Rx 5
x
1
4
= 0.047 xRx 5 ~ x 5
8
1
o 0.0227U o2 R 4
1.72 Rx 2 ~ x
1
o 0.332U o2 Rx
1
2
0.029
13.021 - Marine Hydrodynamics
Lecture 19
Turbulent Boundary Layers: Roughness Effects
So far, a smooth surface has been assumed.
In practice, it is rarely so due to fouling, rust, rivets, etc.
Viscous
13.021 Marine Hydrodynamics
Lecture 21
Water Waves
Exact (nonlinear) governing equations for surface gravity waves assuming potential theory
y = (x,z,t) or F(x,y,z,t) = 0
y
x
z
B(x,y,z,t) = 0
Unknown
13.021 Marine Hydrodynamics
Lecture 23
Wave steepness
Diffraction parameter
Wave Forces on a Body
CF =
h
F
A l
= f , , R , , roughness ,.
2
gAl
U = A body velocity, particle velocity
A
Ul Al
=
UT A
13.021 Marine Hydrodynamics
Lecture 12
3.8 Method of Images
1 source: =
m
ln x 2 + y 2
2
m
m
d
=0
dy
Source near wall:
=
y
b
x
m
2
ln x 2 + ( y b )
2
2
+ ln x 2 + ( y + b )
b
Added source for
symme
13.021 Marine Hydrodynamics
Lecture 11
3.9 Forces on a body undergoing steady translation DAlemberts paradox
3.9.1 Fixed bodies & translating bodies Galilean transformation.
y
o
y
o
x
x
U
z
z
Fixed in
13.021 Marine Hydrodynamics
Lecture 2
1
13.021 Marine Hydrodynamics
Lecture 2
Chapter 1 - Basic Equations
1.1 Description of a Flow
Flows are often defined either by a Eulerian description or a Lagran
13.021 Marine Hydrodynamics
Lecture 3
1
13.021 Marine Hydrodynamics
Lecture 3
1.2 Stress Tensor
Stress Tensor ij: The stress (force per unit area) at a point in a fluid needs nine
components so that i
13.021 Marine Hydrodynamics
Lecture 5
Chapter 2 - Similitude
Similitude is a method that allows you to get a conceptual picture of a complicated idea,
occurrence or mechanism.
Similitude: Similarity o
13.021 Marine Hydrodynamics
Lecture 8
Vortex Lines, Tubes, etc.
v
A vortex line is a line everywhere tangent to
A vortex tube (filament) is a bundle of vortex lines.
Some Properties:
Mathematical
v
13.021 Marine Hydrodynamics
Lecture 9
1
13.021 Marine Hydrodynamics
Lecture 9
Vorticity Equation
Return to viscous incompressible flow
v
p
v v v
2v
N-S equation: t + v v = + gy + v
v
v
vv
( )
+ (v v
13.021 - Marine Hydrodynamics
Lecture 10
Boundary Conditions for
(v )
Two types of Boundary Conditions: 1) Kinematic Boundary Conditions V
v
2) Dynamic Boundary Conditions F or P
Kinematic Boundary
Q2 :
The constant (k) for pipes with expansion joints using the relation;
k (1 0.5 )
Here, Poisons ratio as .
k (1 0.5 ) 1 0.5 0.25 0.875
Therefore, the value of the constant k for pipes with expansio