Intact Stability GM Quick Check: Metacentric Height, Free Surface Correction and a Worked Example

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Every loading condition on a ship or workboat starts with one question: is the vessel stable enough to sail? The fastest first answer is the transverse metacentric height, GM. This post sets out the hydrostatic fundamentals behind it, shows how free surface in slack tanks erodes it, explains how the inclining experiment fixes the lightship KG, and works through a loading condition for a small cargo vessel. It ends with the first checks against the IMO 2008 Intact Stability Code. It is a screening method, not a substitute for a full stability booklet. It also sits alongside our wider overview of marine engineering and naval architecture . Fundamentals: KB, BM, KM, KG and GM A floating vessel is in equilibrium when weight equals buoyancy and both act along the same vertical line. Buoyancy is the resultant of hydrostatic pressure on the hull, a topic we cover in pressure and fluid statics . When the vessel heels through a small angle, the underwater shape changes, and the centre of buo...

Liquid

Liquid

These states of matter have the basic difference in their Kinetic energies. 

Surface Tension:

Surface Tension is defined as:
The elastic tendency of a fluid surface to acquire minimum surface area. 
  • Surface Tension is inversely proportional to temperature. 
  • Surface Tension of a liquif is measured by Stalagmometer (Drop Pipette). 
  • It is a force acting perpendicular in the opposite direction of weight. 

Methods to Study Surface Tension:

There are two methods to study surface tension, namely:
1. Capillary Rise method
2. Drop Formation method

1. Capillary Rise Method:

The formula for the surface tension by capillary rise method is given by:

This formula is derived and explained in the video given below:


2. Drop Formation Method:

  • This study is based on the formation of drop. 
  • Surface Tension exist at outer circumference. 
  • Surface Tension is inversely proportional to the weight (volume) of liquid. 

(a) Drop Weight Method:

The formula for the surface tension by drop weight method is given by:


Y1/Y2 = m1/m2

(b) Drop Number Method:


The formula for the surface tension by drop number method is given by:
Y1/Y2 = d1n2/d2n1

Reason: Why the drop of liquid is spherical in shape? 

Buffers:

Buffer is defined as:
The solution which resist the drastic change in pH after the addition of small amount of acid or base. 

Acidic Buffer:

It is the solution of weak acid with its conjugate base. 


 Basic Buffer:

It is the solution of weak base with its conjugate acid. 

Equation for Buffer Capacity (Handerson-Hasselbach Equation):


Water is a medium, so we take its concentration constant. Therefore, 
The equation of buffer capacity for base is given by:
Handerson-Hasselbach Equation is used to determine:
  • Dissociation Constant for acid and base. 
  • pH of Buffer solution. 
  • Ratio of concentration of salt/acid or salt/base.
  • For 1/2 equivalence point (concentration of acid=salt), then  pKa = pH and pKb = pOH. 

Osmosis:

Osmosis is defined as:
The movement of solute particles from its higher concentration to lower concentration. 
  • It is the bilateral movement of solute and solvent particles. 

Osmotic Pressure:


The pressure applied to stop the movement of solvent molecules is called Osmotic Pressure.
The concept of osmotic pressure, osmosis, hyoertonic solution, hypotonic solution, isotonic solution, hydrostatic pressure can be cleared by video given below:

Reverse Osmosis:

It can be defined as:
The movement of solute particles from its low concentration to high concentration by the application of external force.

  •  Filtration of water in filter plants is based on reverse osmosis. 

Van't Hoff Theory of Dilute Solution (About Osmotic Pressure) :

According to the Van't Hoff theory of dilute solution, osmotic pressure is directly proportional to the concentration and the temperature of solvent molecules. 


Now, by combining the above relation, we get:
ฯ€ ∝ nT/V
ฯ€ = nRT/V
ฯ€V = nRT

Viscosity:

Viscosity is defined as, 
Internal resistance to the flow of liquid. 

  • It is the sharing force (to change shape) which help liquid to flow in the form of layer. 
  • The force of viscosity is directly proportional to the area and velocity gradient and inversely proportional to the distance between layers. 
F ∝ Adv/dx
F = nA dv/dx
Where, 
  • A is the area. 
  • dv = V1 - V2, is the difference in velocity. 
  • dx is the distance between layers of liquid. 
  • n is the coefficient of viscosity. 

Ostwald's Viscometer (Poisell's Equation) :


Absolute viscosity if liquid can be found by using following formula:
Where, 
  • V is the volume of vessel
  • n is the coefficient of viscosity 
  • ๐™p is the change in pressure
  • L is the length of vessel
  • t is the time
  • r is the radius 
And, also the viscosity of liquid is given by:
Where, 

Spectrophotometry:

It is defined as, 
The quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. 

Chromophore:

Light absorbing species are called chromophore.

Laws of Spectrophotometry:

Spectrophotometry is based on 2 laws:

1. Beer's and Lambort's Law:


Absorption of wavelength of light is directly proportional to the concentration and the path of the liquid. 
A ∝ C
A ∝ b
By combining the above relations and by introducing the constant, we get:
A = ๐œ–bC
Where, ๐œ– is the Molar Absoptivity or Molar Extinction coefficient. It defines how well a chemical specie absorbs the given wavelength of light.

Types of Spectrophotometer:

There are two types of spectrophotometer, namely:

  1. Single Beam Spectrophotometer 
  2. Double Beam Spectrophotometer 

Single Beam spectrophotometer is explained in the video given below:
And, double beam spectrophotometer is explained in the video given below:
  • Transducer is a component which read potential and convert it into absorbance. 
  • Absorbance is inversely proportional to the tramitted light. 
  • A = - log T
  • T = 10^-A

Note: If anyone want numericals on the related topic discribed above can contact me by comment.


Comments

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