# Ship Stability

## 전체 글

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Planning Procedure of Naval Architecture and Ocean Engineering, Fall 2013, Myung-Il Roh 1

## Ship Stability

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### Stability, SDS)

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Planning Procedure of Naval Architecture and Ocean Engineering, Fall 2013, Myung-Il Roh 3

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### Introduction to Hydromechanics

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### Concept of Hydrostatics

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Vacuum

F

D -DF DA

### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.361, 2004

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### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.360, 2004

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### D F

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### change the situation very significantly.

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### (Incompressible fluid)

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### ∴ Conservation of Energy is satisfied.

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### pressure as a function of depth or altitude.

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1

2

z dz+

z

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### å F =

= Density of the fluid element

= Mass of the fluid element

= Horizontal base(or face) area

= Force that acts at the bottom surface(due to the water below the rectangular solid)

= Force that acts at the top surface(due to the water above the rectangular solid)

= Pressure at

= Pressure at

z

z dz+

2

1

( )z r dm A F1

F2

Pz dz+

Pz

z+dz z

z dz+

z

2

1

nd

1

2

1

2

### minus delta mg must be zero.

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### Newton’s 2ndLaw :

= Density of the fluid element

= Mass of the fluid element

= horizontal base(or face) area

= Force that acts at the bottom surface(due to the water below the rectangular solid)

= Force that acts at the top surface(due to the water above the rectangular solid)

= Pressure at

= Pressure at

z

z dz+

2

1

( )z r dm A F1

F2

Pz dz+

Pz

z+dz z

### Fluid Element

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### Newton’s 2ndLaw :

= Density of the fluid element

= Mass of the fluid element

= horizontal base(or face) area

= Force that acts at the bottom surface(due to the water below the rectangular solid)

= Force that acts at the top surface(due to the water above the rectangular solid)

= Pressure at

= Pressure at

z

z dz+

2

1

( )z r dm A F1

F2

Pz dz+

Pz

z+dz z

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1

2

1

2

1

2

### .

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2 2

1 1

z

2 1

2 Integrate by z

1

2

1

z

2

1

2

1

2 2

1 1

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z

2 1

2 Integrate by z

1

2

1

z

2

1

### In the fluid

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### Force

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2

1

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sw

obj

2

1

2

1

2

1

1

2

nd

1

2

1

2

1

2

### , is so called the ‘Buoyant force’.

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sw

obj

2

1

2

1

2

1

1

2

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sw

obj

2

1

2

1

2

1

1

2

### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.368, 2004

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3 3

air

sw

sw

air

air

sw

2 3

1 1

2

1

2 1

P

P

3 2 3

1 1 2

z z z

sw air

z z z

2 3

1 2

z z

sw air

z z

2 1 3 2

sw

air

sw

obj

2

1

2

1

2

1

1

2

3

1

2

2

3

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W1

crown

immersed

W rw

1

immersed

T

mg

mg FB T

### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.369, 2004

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1

1

Loss

1

immersed

w

B

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sw

obj

2

1

2

1

1

2

### m × g

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### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.377, 2004

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### V

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1

2

,1

Boat

,2

Boat

Anchor

Water

Baot

Anchor

Water

Anchor

Total

,1

Baot Anchor Boat

Water

Boat,2 Boat

Water

Anchor Anchor

Anchor

Anchor Water

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Total

Luggage Water

,1

Boat Anchor

Total Water

Water

,2

Boat Anchor

Total Water

Water Anchor

Anchor Water

Anchor Water

### V

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### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.377, 2004

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### * Serway, R. A., College Physics, 8th Ed., Brooks/Cole, pp.273, 2009.

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### Freeboard = Depth D - Draft T + t

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TF

WNA TF

WNA

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### and Bernoulli Equation

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1

2

1

2

1

1

2

2

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1

2

1

2

1

1

2

2

### * Halliday, D., Fundamentals of Physics, 7th Ed., Wiley, pp.371, 2004

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1

2

1

2

1

1

2

2

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### v > v

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