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Free Surface Effect

The free surface effect occurs when liquid in a partially filled tank on a ship's centerline moves across the tank as the ship heels, shifting the ship's center of gravity away from the centerline. This reduces stability by decreasing the righting lever and metacentric height, further increasing the heel angle. The size of the shift in the center of gravity and reduction in metacentric height due to the free surface effect depends on factors like the tank's moment of inertia, the ship's displacement, and the densities of the liquid and ship. Dividing tanks into compartments or fully pressing up tanks can help reduce the free surface effect.

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811 views8 pages

Free Surface Effect

The free surface effect occurs when liquid in a partially filled tank on a ship's centerline moves across the tank as the ship heels, shifting the ship's center of gravity away from the centerline. This reduces stability by decreasing the righting lever and metacentric height, further increasing the heel angle. The size of the shift in the center of gravity and reduction in metacentric height due to the free surface effect depends on factors like the tank's moment of inertia, the ship's displacement, and the densities of the liquid and ship. Dividing tanks into compartments or fully pressing up tanks can help reduce the free surface effect.

Uploaded by

Rachit
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPT, PDF, TXT or read online on Scribd
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FREE SURFACE EFFECT

WHEN A TANK ON THE SHIPS CENTRELINE IS


NOT COPLETELY FULL OF LIQUID, AND THE
SHIP HEELS, THE LIQUID IN THE TANK MOVES
ACROSS THE TANK IN THE SAME DIRECTION AS
THE DIRECTION OF HEEL.
BECAUSE OF THIS EFFECT, THE CENTRE OF
GRAVITY OF THE SHIP MOVES AWAY FROM THE
CENTRELINE,WHICH REDUCES THE RIGHTING
LEVER GZ & THE HEIGHT OF THE
METACENTRE, WHICH FURTHER INCREASES
THE ANGLE OF HEEL.
THIS EFFECT IS KNOWN AS THE FREE
SURFACE EFFECT.
LET US CONSIDER A TANK PARTLY FULL OF WATER IN A
SHIP OF DISPLACEMENT , AND INCLINED TO SOME
ANGLE .
THE SHIPS CENTRE OF GRAVITY WILL MOVE
FROM G TO G1, AS THE WEDGE OF LIQUID MOVES
ACROSS THE TANK.
WE KNOW THAT,
MOMENT OF SHIFT OF SHIPS BUOYANCY
= MOMENT DUE TO SHIFT OF BUOYANCY WEDGE.
x GG1 = m x gg1
m x gg1
GG1 = ----------

v x x gg1
GG1 = ---------------= SHIFT OF C.G. ---------------------(1)
x 1
Where
v = Volume of wedge, = Density of wedge, 1 = Density of S.W
= Volume of displacement. m = Mass of wedge
NOW AS THE WEDGE OF LIOQUID IS TRIANGULAR AND
IT IS ASSUMED TO BE DEVIDED IN TO THIN STRIPS OF
LENGTH x
VOLUME OF STRIP OF WEDGE = x y x ytan x x
= y2 tan x x
MASS OF STRIP OF WEDGE = x y2 tan x x
MOMENT OF TRANSFER OF STRIP OF WEDGE
= (4/3y) x x y2 tan x x
= tan x 2/3 y3 x
MOMENT OF TRANSFER OF TOTAL WEDGE
= tan x (2/3 y3 x) ---(2)
ALSO, MOMENT OF TRANSFER OF TOTAL WEDGE
= v x x gg1 ------------------(3)
THEREFORE FROM (2) AND (3)
v x x gg1 = tan x (2/3 y3 x) ------------------------------------(4)
BUT,
(2/3 y3 x) = II MOMENT OF AREA OF FREE SURFACE
ABOUT THE CENTRELINE OF THE TANK
= Ixx = (1/12 x l x b) -----------------------------(5)
THEREFOE FROM (3) AND (5),
v x x gg1 = tan x Ixx -----------------------------------------(6)
NOW FROM (1) AND (6)
tan x Ixx
GG1 = ----------------- = SHIFT OF C.G. -----------------------(7)
x 1
AS A RESULT OF THIS MOVEMENT (SHIFT) OF THE
SHIPS CENTRE OF GRAVITY FROM G TO G1 , THE
RIGHTING LEVER GZ IS REDUCED TO G1Z
REDUCTION IN RIGHTING LEVER
DUE TO FREE SURFACE EFFECT = G1Z = G2Z
= G2M sin
NOW FROM TRIANGLE GG1G2
GG1
------ = tan
GG2
GG2 = REDUCTION IN METACENTRIC HEIGHT
GG1
= -------- ----------------------------------------------(8)
tan

THEREFORE FROM (7) AND (8)


tan x Ixx 1
GG2 = ----------------- x -------
x 1 tan

REDUCTION IN METACENTRIC HEIGHT DUE TO FREE


SURFACE EFFECT
x Ixx
= GG2 = --------- -------------------(9)
x 1
THE EFFECT OF FREE SURFACE OF LIQUID MAY BE
MOST DANGEROUS IN A VESSEL WITH SMALL
METACENTRIC HEIGHT AND MAY EVEN CAUSE
THE VESSEL TO BECOME UNSTABLE.
IN SUCH SHIPS, THE TANKS WHICH ARE
REQUIRED TO CARRY LIQUID SHOULD BE PRESSED
UP TIGHT.
IF THE SHIP IS INITIALLY UNSTABLE AND
HEELING TO PORT, THEN ANY ATTEMPT TO
INTRODUCE WATER BALLAST WILL REDUCE THE
STABILITY FURTHER.
THEREFORE BEFORE BALLASTING, AN ATTEPT
SHOULD BE MADE TO LOWER THE CENTRE OF
GRAVITY OF THE SHIP BY PRESSING UP THE
EXISTING TANKS AND LOWERING THE MASSES OF
THE SHIP.
How to reduce free surface
effect?
By swashbulkheads
By sluice valve
By pressing up the tanks fully
Subdivision of tanks
Instead of big tanks tanks to be in
compartments

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