What are effects of Free Surface of liquids in tanks on the ships ?

Effect of free surfaces of liquids in tanks are :
  1. For all loading conditions, the initial metacentric height and the righting lever curve should be corrected  for the  effect of free surfaces of liquids in tanks.
  2. Free surface effects should be considered whenever  the  filling level in a tank  is less than   98% of full      Free surface effects  need  not be considered  where  a tank  is nominally  full, i.e.  filling level is 98% or above.  Free surface effects for small tanks  may be ignored .
  3. Tanks which are taken  into consideration when determining the  free surface correction  may be in one of two categories:
    • Tanks with filling levels fixed (e.g.  liquid cargo, water  ballast). The free surface correction  should be defined for the actual  filling level to be used in each tank.
    • Tanks with  filling levels variable  (e.g.   consumable  liquids  such  as fuel oil, diesel oil and  fresh water,  and  also liquid  cargo and  water ballast  during  liquid  transfer  operations).   Except  as  permitted in  paragraph 5 and 6, the  free surface  correction  should  be the  maximum value  attainable between  the filling limits  envisaged  for each  tank, consistent with any operating instructions.
  4. In calculating the free surface effects in tanks containing consumable  liquids, it should be assumed  that for each type of liquid at least one trans- verse pair  or a single centre line tank  has  a free surface  and  the  tank  or combination of tanks  taken  into account should be those where the effect of free surfaces is the greatest.
  5. Where water  ballast tanks,  including  anti-rolling tanks  and  anti heeling tanks,  are to be filled or discharged  during the course of a voyage, the free surface  effects should  be calculated to take  account of the  most  onerous transitory stage relating  to such operations.
  6. For ships  engaged  in liquid  transfer  operations, the  free surface  corrections at  any stage of the liquid transfer operations may be determined in accordance  with the filling level in each tank  at that stage of the transfer operation.
  7. The corrections to the initial  metacentric height and to the righting  lever curve should be addressed  separately as follows.
    • In determining the correction  to  initial  metacentric height, the transverse moments  of inertia  of the tanks  should be calculated at 0 degree  angle of heel according  to the categories .
  8. The righting lever curve may be corrected  by any of the following methods  subject to the agreement of the Administration:
    • Correction based on the actual  moment of fluid transfer  for each angle of heel calculated.
    • Correction based on the moment of inertia, calculated  at 0 degree   angle of heel, modified at  each angle of heel calculated.
    • Correction based on  the  summation of M fsvalues  for all tanks taken  into consideration
  The values of Mfs for each tank  may be derived  from the formula:

M f  =vbρk(d)1/2

Mfs     is the free surface moment at any inclination, in m.tonnes
v      is the tank  total  capacity, in m3
b      is the tank  maximum  breadth, in m
ρ      is the mass density  of liquid in the tank,  in tonnes/m3
d      is equal to v/blh  (the  tank  block coefficient)
h      is the tank  maximum  height, in m
1      is the tank  maximum  length,  in m
k      is the dimensionless coefficient to be determined from table.

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