Density of a substance is its mass per unit
volume.
Density = Mass/Volume
Where mass is in tonnes (t), Volume is in cubic metres (m^3), Density is in tonnes per cubic metre (tm^3)
Density of water is 1 tm^3
Relative density is the number of times a substance is heavier than water. Being a ratio, RD has no Unit.
Thrust is the total pressure exerted on a given surface.
Thrust = pressure * area
unit => ton or kN
1 ton = 9.81 kN
Density = Mass/Volume
Where mass is in tonnes (t), Volume is in cubic metres (m^3), Density is in tonnes per cubic metre (tm^3)
Density of water is 1 tm^3
Relative density is the number of times a substance is heavier than water. Being a ratio, RD has no Unit.
•Vol.
of tank = vol. of oil + vol. of free space
•Free
Vol. = l*b*h
=> h = free vol. / ( l*b ) where, h is ullage.
Pressure is the load per unit area.
Pressure = density * depth
unit = t/m2
1 bar = 10.2 t/m2
1 ton/m2 = 9.81 kN/m2
Pressure = density * depth
unit = t/m2
1 bar = 10.2 t/m2
1 ton/m2 = 9.81 kN/m2
Thrust is the total pressure exerted on a given surface.
Thrust = pressure * area
unit => ton or kN
1 ton = 9.81 kN
Archimedes Principle
states that when a body is totally or partially submerged in a fluid, it
suffers an apparent loss of weight which is equal to the weight of fluid
displaced.
Since the word fluid includes both, liquids and gases, and the
fact that merchant ships are only expected to be partially immersed in water, a
modified version of Archimedes' Principle may be called the Principle of flotation
Principle of flotation: When a body is floating in a liquid, the weight of liquid displaced equals to the
weight of the body.
Displacement is commonly used to denote the mass of a ship in tonnes. Technically, it is the mass of water displaced by a ship and, when floating freely, the mass of water displaced equals to the mass of the ship.
Displacement is commonly used to denote the mass of a ship in tonnes. Technically, it is the mass of water displaced by a ship and, when floating freely, the mass of water displaced equals to the mass of the ship.
Light displacement is the mass of the empty ship - without any cargo, fuel, lubricating oil, ballast water, fresh and feed
water in tanks, consumable stores, and passengers and crew and their
effects
Load displacement is the total mass of the ship when she is floating in salt water with her summer loadline at the water surface.
Present displacement is the mass of the shjp at present. It is the sum of the light displacement of the ship and everything on board at present.
Load displacement is the total mass of the ship when she is floating in salt water with her summer loadline at the water surface.
Present displacement is the mass of the shjp at present. It is the sum of the light displacement of the ship and everything on board at present.
Deadweight (DWT) of a ship is the total mass
of cargo, fuel, freshwater, etc., that a ship can carry, when she is floating
in salt water with her summer loadline at the water surface.
DWT = Load displacement – Light displacement
Deadweight aboard is the total mass of cargo, fuel, ballast, fresh water, etc., on beard at present.
DWT aboard = present displ - light displ
DWT = Load displacement – Light displacement
Deadweight aboard is the total mass of cargo, fuel, ballast, fresh water, etc., on beard at present.
DWT aboard = present displ - light displ
Deadweight available is the total mass of cargo, fuel,
fresh water, etc., that can be put on the ship at present to bring her summer loadline to the water surface in salt
water.
DWT available = load displ - present displ
Waterplane coefficient (Cw), or coefficient of fineness of the water-plane area, is the ratio of the area of the water-plane to the area of a rectangle having the same length and maximum breadth.
Cw = Area of water-plane
L x B
DWT available = load displ - present displ
Waterplane coefficient (Cw), or coefficient of fineness of the water-plane area, is the ratio of the area of the water-plane to the area of a rectangle having the same length and maximum breadth.
Cw = Area of water-plane
L x B
Area of water-plane = L x B x Cw
Block coefficient (Cb), or Coefficient of fineness of displacement, at any draft is the ratio of the underwater volume of the ship at that draft to a rectangular box having the same extreme dimensions.
Cb = Underwater volume
LxBxd
Block coefficient (Cb), or Coefficient of fineness of displacement, at any draft is the ratio of the underwater volume of the ship at that draft to a rectangular box having the same extreme dimensions.
Cb = Underwater volume
LxBxd
The term block coefficient may also be used with respect to a
tank in which case it would be the ratio of the volume of the tank to the
volume of a rectangular box having the same extreme dimensions as the tank
Cb = Volume of tank
LxBxD
Volume of tank = L x B x D x Cb
Cb = Volume of tank
LxBxD
Volume of tank = L x B x D x Cb
Reserve buoyancy (RB) is the volume of the enclosed spaces above the waterline. It maybe expressed as a volume in
m3 or as a percentage of the total volume of the ship.
RB = Total volume - underwater volume
RB % = Above water volume x 100
Total volume
RB = Total volume - underwater volume
RB % = Above water volume x 100
Total volume
Reserve buoyancy is so called because, though it is not
displacing any water at that time, it is available for displacement if weights
are added or if bilging takes place. Bilging is the accidental entry of water
into a compartment, due to underwater damage
Tonnes per centimetre (TPC) is the number of tonnes required to cause the ship to
sink or rise by one centimetre
Considering 1 cm sinkage
Increase in underwater volume = A x 1/100 m^3
Increase in W = A/100 x density of water displaced.
Or TPC = A/100 x density of water displaced
TPC in SW = A/100 x 1.025 = 1.025A/100
TPC in FW = A/100
TPC in DW of density RD = (RD x A)/ 100
Increase in underwater volume = A x 1/100 m^3
Increase in W = A/100 x density of water displaced.
Or TPC = A/100 x density of water displaced
TPC in SW = A/100 x 1.025 = 1.025A/100
TPC in FW = A/100
TPC in DW of density RD = (RD x A)/ 100
In the foregoing formulae, the area of the water-plane of a
ship-shape has been considered constant since the sinkage or rise being considered is only
1 cm. However, the area of the water-plane of a ship-shape usually increases as
draft increases. Hence, its TPC also increases as draft increases.
In view of this, calculations involving TPC should generally be
confined to small values of sinkage or rise, say less than about 20 cm, in the case of
ship-shapes. Otherwise, the accuracy of the calculation will tend to
suffer.
In the case of a box-shaped vessel, the area of the water-plane is the same at all drafts and hence its TPC does not change with draft.
In the case of a box-shaped vessel, the area of the water-plane is the same at all drafts and hence its TPC does not change with draft.
Page 24, Problem 3 of Stability book 1 by Capt. Subramaniam please refer there also.
Rectangular Log B=3m, H=2M floats with breadth horizontal. Density of log is 0.7t/m3
Find its draft in water of R.density 1.01
Vol of log = l x 3 x 2
Weight of log = l x 3 x 2 x 0.7
Being a homogenous uniform log, ratio of weight/volume will be the ratio of immersion to the height in fresh water.
Therefore, draft in FW will be
Wt x h
Vol
6l x 0.7 x 2 = 4.2 x 2 = 1.40
6l 6
Draft in water of density 1.010 = 1.40 x 1/1.010
= 1.386
Rectangular Log B=3m, H=2M floats with breadth horizontal. Density of log is 0.7t/m3
Find its draft in water of R.density 1.01
Vol of log = l x 3 x 2
Weight of log = l x 3 x 2 x 0.7
Being a homogenous uniform log, ratio of weight/volume will be the ratio of immersion to the height in fresh water.
Therefore, draft in FW will be
Wt x h
Vol
6l x 0.7 x 2 = 4.2 x 2 = 1.40
6l 6
Draft in water of density 1.010 = 1.40 x 1/1.010
= 1.386
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