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寒假 報告 老師：曾慶耀 學生：林東駿 學號：19967004
VESSEL INERTIAL DYNAMICS We consider the rigid body dynamics with a coordinate system affixed on the body. A common frame for ships, submarines, and other marine vehicles has the body-referenced x-axis forward, y-axis to port (left), and z-axis up.
Example: Mass on a String Consider a mass on a string, being swung around around in a circle at speed U, with radius r. The centrifugal force can be computed in at least three different ways. The vector equation at the start is
HYDRODYNAMICS: INTRODUCTION The forces and moments on a vessel are complicated functions of many factors, including water density, viscosity, surface tension, pressure, vapor pressure, and motions of the body. The most important factors for large ocean vehicles are density and motion, and we can make simplifications to parameterizethe most prominent relationships. This section pertains to the use of hydrodynamic coefficients for predicting hydrodynamic response.
Letting u = U + u, where U >> u, and eliminating higher-order terms, this set is
The denominator for A's components reduces to Hence the first condition for stability is met:
For the second condition, since the denominators of the Aij are identical, we have only to look at the numerators. For stability, we require When only the largest terms are considered for a vessel, a simpler form is common: C is called the vessels stability parameter.
Stability can also be improved by moving the center of gravity forward. Nonzero xG shows up as follows: Since Nr and Yv are both negative, positive xG increases the (positive) influence of C's first term.
Common Groups in Marine Engineering One frequently encounters the following groups in fluid mechanics and marineengineering: 1.Froude number 2. Cavitation number 3. Reynolds number 4. Weber number
1. Froude number(Fr) U：流體速度 L：物體長度 g：重力加速度 福祿數代表流速與重力的波速之比。 • 當Fr > 1，表示慣性力對流動之影響較重力為大，稱為 超臨界流 （Supercritical flow），為水深小，流速急湍的流況。 • 當Fr < 1為 亞臨界流 （Subcritical flow），為流速緩慢，水深大的流況。 • 當Fr = 1為 臨界流 （Critical flow）。
2. Cavitation number 「空蝕」是一種物理現象，因為流速快的物體壓力低（伯努力定律），有時壓力會低到液體氣化的程度。在一般船艦上，高速旋轉的螺旋槳周圍就常常出現這樣的小氣泡 -- 氣泡中包的不是空氣，而是在低壓下被汽化的水蒸汽。這些氣泡在離開螺旋槳後壓力會突增，導致氣泡內爆，容易損壞螺旋槳。
3. Reynolds number(Re) U：速度 l ：長度 μ：流體動力黏度 ρ：流體密度 雷諾數可視為慣性力和黏滯力之比。雷諾數較小時，黏滯力對流場的影響大於慣性力，流場中流速的擾動會因黏滯力而衰減，流體流動穩定；反之，若雷諾數較大時，慣性力對流場的影響大於黏滯力，流體流動較不穩定，流速的微小變化容易發展、增強。
4. Weber number(W) ρ：流體密度 U：流速 l：長度 σ：流體的表面張力係數 韋伯數代表慣性力和表面張力效應之比，韋伯數愈小代表表面張力愈重要，譬如毛細管現象、肥皂泡、表面張力波等小尺度的問題。一般而言，韋伯數遠大於1.0，表面張力的作用便可以忽略。
To appreciate the origins of these terms from a fluid particle‘s point of view,considera box having side lengths [dx; dy; dz]. Various forces on the box scaleas
