STABILITY BASIC FORMULAS
SOME BASIC FORMULAS
Area of Waterplane = L x B x CW
…. L = Length of vessel
…. B = Breadth of vessel
...CW = Co-efficient of Waterplane
Volume of Displacement = L x B x d x CB
…. d = depth of vessel
….CB = Block co-efficient
Volume (V) = L x B x d
Displacement (W) = L x B x d x R.D
... R.D = Relative density of water
TRANSVERSE STABILITY
Rectangular Waterplanes
BM = I . where I = LB3
V 12
…. V = Volume of vessel
Depth of centre of buoyancy below water line:
= 1 ( d + V )
3 2 A
LONGITUDINAL STABILITY
a) Rectangular Waterplanes
IL = L3B and BML = IL .
12 V
b) Box Shapes
BML = L2
12d
LIST
GG1(Horizontal) = w x d
W
….d = distance moved horizontal
….w = weight
….W = Final Displacement
GG1(Vertical) = w x d
W
….d = distance moved vertical
….w = weight
….W = Final Displacement
TANq = GG1
GM
….GM = Metacentric height
TANq = Listing Moments
W x GM ….GM = Use Fluid GM
…. W = Final Displacement
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DRY DOCKING
P = trim x MCTC
l
...l = Distance of COF from where vessel touches blocks first
...P = Upward force acts on ship where block first touches
P = COT x MCTC
l …..In case of declivity of Dock
Virtual loss of GM = P x KM
W
Virtual loss of GM = P x KM
(W - P) if P - force is very small
After taking the blocks (F & A):
P = Change in TMD ( cms ) x TPC or
P = Reduction in water level x TPC
….TMD = True mean draft
Change in Draft (rise) (cms) = P …always subtract from draft
TPC
TMD = Draft Aft – ( LCF x Trim )
LBP
….subtract if vessel is by the stern
….add if vessel is by the head
DRY DOCKING
HYDROSTATIC TABLES AND
VESSEL ‘A’ TYPE PROBLEMS
Proceed as follows :
1. Find mean draft from the present given drafts.
2. From this mean draft, look in tables for LCF
3. Using that LCF, calculate TMD
4. From the TMD, look in tables and find
MCTC, LCF and DISPLACEMENT
5. Calculate now P-Force
6. For Displacement (W) at Critical Instant, find W-P
7. From this new (W), look in tables for KMT
8. Now find Virtual loss of GM and use new KMT but old Displacement (W)
9. Find now initial GM, using the new KMT
10. Apply Virtual loss of GM in it and find the
EFFECTIVE GM.
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FREE SURFACE EFFECT / MOMENT
FSE = l.b3.R.D
12W
FSM = l.b3.R.D
12
….R.D = Density of liquid in tank
FSE = FSM
W
Corrected FSM = Tabulated FSM x Actual R.D
Assumed R.D
New FSM = Original FSM x 1
n2
….n = number of tanks which are subdivided
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DYNAMICAL STABILITY
Dynamical Stability = W x Area under the curve
STATICAL STABILITY
Statical Stability = W x GZ
KN CURVES
GZ = KN – KG.SINq
INCLINING EXPERIMENT
GM = w x d x Length of Plumbline
W Deflection
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RIGHTING MOMENT
SMALL ANGLES OF HEEL (UPTO 10O HEEL):
GZ = GM x SINq
LARGE ANGLES OF HEEL (WALL SIDED FORMULA):
GZ = SINq ( GM + 1.BM.TAN2q )
2
WIND HEELING MOMENT:
Total Wind heeling moment = F.A.d
1000
GZ (at angle of heel) = F.A.d
1000W
….d = Distance of centre of buoyancy to centre of windage area
….F = Steady wind force of 48.5 kg/m2
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SIMPSON’S RULES
SIMPSON’S FIRST RULE:
Area = h x ( a + 4b + 2c + 4d + 2e + 4f + g )
3
Remember : 1 4 1
SIMPSON’S SECOND RULE:
1 3 3 1
h h h
Area = 3 x h x sum of products
8
Remember : 1 3 3 1
SIMPSON’S THIRD RULE:
5 8 –1
h h
Area = h x ( 5a + 8b – c )
12
Remember : 5 8 –1
NB:
Divide the value of ‘ h (in degrees) ’ by ‘ 57.3 ’ while calculating the area.
NB:
In the 3rd rule of Simpson, we are only looking for a particular piece between the area i.e., from one co-ordinate to other and this is mainly used by surveyors for calculating sludge in bunker tank etc. Also for knowing the full area, we use Simpson’s first rule.
GM CONDITIONS
GM AT LOLL:
GM = 2(Initial GM)
COSq ….answer will be –ive but write +ive sign
WHEN GM IS NEGATIVE:
WHEN GM IS NIL:
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TURNING CIRCLE
TAN(Heel) = v2BG
gGMr
….v = velocity of ship(m/s)
….r = radius of turning circle
….g = Acceleration due to Gravity
(9.81 m/s)
….T = Period of Rolls (seconds)
….K = Radius of Gyration
….p = 3.142857143 (constant)
….I = Weight Moment of Inertia about
Rolling axis (tonne - metres2)
Hence we get,
Actual New Draft = [ Initial draft + B Tanq ] Cosq
2
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AIR DRAFT
CALCULATING LENGTH OF THE IMMAGINARY MAST
WHICH IS EXACTLY ABOVE THE ‘CF’:
Correction to Aft Mast
= Dist. of center mast from Aft Mast x Diff. of ht between masts
Dist. between the two masts
….subtract this value from the ht of Aft mast
or
Correction to Fwd Mast
= Dist. of center mast from Fwd Mast x Diff. of ht between masts
Dist. between the two masts
….add this value from the ht of Fwd mast
FOR FINDING DRAFT FWD AND AFT
Trim between masts = Trim of vessel
Distance between masts LBP
…..(from this, calculate ‘trim of vessel’ and proceed as follows)
Trim Effect Aft = la x Trim
L
Trim Effect Fwd = lf x Trim
L
GRAIN
Weight of Grain = Volume
S.F
Weight of H.M = Volumetric H.M
S.F
Approx. Angle of heel = Total H.M x 12o
Max.H.M
…. Max.H.M can be found in the Tables of Maximum permissible
Grain heeling moment against ‘W’ and KG
GG1 ( lo) = w x d
W
….w = weight of Grain liable to shift while rolling
….d = horizontal distance of Grain shift
lo = Total volumetric H.M (in m4)
S.F x W
l40 = GG1(lo) x 0.80 ….80% of lo (GG1)
NB:
If value for cargo is given for centroid then follow as normal
but if value given for ‘Kg’ of cargo then,
Multiply H.M value for fully filled compartment by 1.06 and
Multiply H.M value for partially filled compartment by 1.12
TRIM
HYDROSTATIC TABLES AND
VESSEL ‘A’ TYPE PROBLEMS
Proceed as follows :
1. Find mean draft from the present given drafts.
2. From this mean draft, look in tables for LCF
3. Using that LCF, calculate TMD
4. From the TMD, look in tables and find
MCTC, LCB and DISPLACEMENT
5. Calculate now INITIAL LCG
6. Now Calculate FINAL ‘W’ and FINAL LCG by MOMENTS
7. With this FINAL ‘W’, go in tables and look find TMD, LCB, LCF and MCTC
8. Calculate TRIM
9. After this calculate TRIM EFFECTS ( F & A )
10. Now apply this TRIM EFFECT to find FINAL DRAFTS.
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TRIM
Trimming Moment = w x d ( d = distance from COF )
Area of Waterplane = L x B x Cw
Volume of Displacement = L x B x D x CB
TPCsw = 1.025A
100
FWA = W .
40 TPC
DWA = FWA (1.025 – R.D)
0.025
MCTC = WGML
100L
TPCDW = R.D x TPCSW
1.025
MCTCDW = R.D x MCTCSW
1.025
Displacement(DW) = RD x Displacement(sw)
1.025
Sinkage (cms) = w .
TPC
COT = Trimming Moments
MCTC
COD Aft = la x COT
L
COD Fwd = COT – COD Aft
WHEN THE VESSEL IS EVEN KEEL
LCG = LCB
FOR A BOXED SHAPED VESSEL
BM = B2
12d
KB = draft
2
FOR A BOX SHAPED VESSEL WHEN DISPLACEMENT CONSTANT
New Draft = Old Density
Old Draft New Density
FOR A SHIP SHAPED VESSEL WHEN DRAFT CONSTANT
New Displacement = New Density
Old Displacement Old Density
TO KEEP THE AFT DRAFT CONSTANT
d = L x MCTC
la x TPC ….keeping the aft draft constant
d = L x MCTC
lf x TPC ….keeping the fwd draft constant
d = Distance from the CF
la = Distance from the AP
lf = Distance from the FP
TO PRODUCE A REQUIRED TRIM
Change in Draft (cms) = ( l. x w x d ) ± w .
L MCTC TPC
( - ive for Draft Aft)
( + ive for Draft Fwd)
( la for aft and lf for fwd)
Trim (cms) = W (LCB - LCG)
MCTC
(Values for LCB, LCG and MCTC should be final)
COT WITH CHANGE OF DENSITY
COT = W(RD1 – RD2)(LCF – LCB)
RD1 x MCTC2
LCGINITIAL = LCB ± ( Trim (cms) x MCTC )
W
….( - ive for stern trim )
….( + ive for head trim )
TRIM EFFECT AFT = la x Trim
L
TRIM EFFECT FWD = lf x Trim
L
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BILGING
WHEN HEIGHT OF COMPARTMENT IS GIVEN AND ABOVE WATER LEVEL
CALCULATE SINKAGE BY RECOVERABLE BUOYANCY METHOD:
Sinkage = Buoyancy still to be recover
L x B
Buoyancy still to be recover = Lost buoyancy – Recoverable
Buoyancy
Volume of Lost Buoyancy = l x b x draft
Recoverable Buoyancy = ( L – l ) x B x ( Depth – Draft )
To find the Final Draft, add the Sinkage to Tank’s height
WHEN IN QUESTION PERMEABILITY OF THE CARGO IS GIVEN
CALCULATE THE EFFECTIVE LENGTH OF THE TANK:
Permeability ( m ) = Broken Stowage
Stowage Factor
Broken Stowage = Actual Stowage – Solid Stowage
Solid Stowage = 1 .
R.D of liquid in tank
Effective Length = Tank’s length ORIGINAL x Permeability ( m )
NB
After calculating ‘Effective length’ always use this length for tank’s length.
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BILGING
MIDSHIP COMPARTMENT
NON WATER TIGHT WATER TIGHT
Sinkage = v .
A - a …If NON WATER TIGHT
Sinkage = v .
A …If WATER TIGHT
BM = LB3
12V …If WATER TIGHT
BM = (L – l)B3
12V …If NON WATER TIGHT
BILGING
SIDE COMPARTMENT
PLAN VIEW OF A SHIP
Sinkage = v .
A - a …If NON WATER TIGHT
Sinkage = v .
A …If WATER TIGHT
TANq = BB1
GM ….q = List
BB1 = a x d
Final A ….d = Distance from center of tank to
ship’s center line
….Final A = A - a
BM = IOZ
V
IOZ = IAB - Ad2 ….d = B + BB1
2
….A = A - a
IAB = LB3 - lb3
3 3
BILGING
END COMPARTMENT
AFT COMP. BILGED FWD COMP. BILGED
NON WATER TIGHT NON WATER TIGHT
Sinkage = v .
A - a …If NON WATER TIGHT
Sinkage = v .
A …If WATER TIGHT
If ‘KG’ is not given, then GML = BML
BM = L3B
12V …If WATER TIGHT
BM = (L – l)3B
12V …If NON WATER TIGHT
COT = w x d
MCTC ….w = l x b x dft x R.D
….d = L ..(Non water tight case)
2
….d = tank’s center to CF
..(Water tight case)
MCTC = WGML
100L
COD Aft = la x COT
L ….la = ( L - l ) + tank’s length
2
(For measuring the CF from AP) ..(Non water tight case)
…. la = L
2
(CF hasn’t changed and is amidships) ..(Water tight case)
When Fwd compartment is bilged (and non water tight), then just use
….la = ( L - l )
2
(Again for measuring the CF from AP) ..(Non water tight case)
IN CASE OF WATER TIGHT COMPARTMENT BELOW WATER LINE AND BELOW THE TANK THERE IS AN EMPTY COMPARTMENT
a) Deal as normal water tight case
b) Use volume of the tank only which is filled with water but not the portion beneath it.
c) But for KB of tank, use from K to center of tank
NB
IN WATER TIGHT CASE
· BM remains the same before and after
· KB is different before and after bilging
KB1 is half of Original Draft
KB2 is found by moments
IN NON WATER TIGHT CASE
· BM is different before and after bilging
BM1 is LB3 and BM2 is (L - l)B3
12V 12V
· KB is different before and after bilging
KB1 is half of Initial Draft
KB2 is half of New Draft
PLEASE NOTE THE FOLLOWING CONDITIONS
WATER TIGHT CASE NON WATER TIGHT CASE
Calculate:
a) Sinkage by non w/t method
b) KB2 by Moments
NB:
In all cases of WATER TIGHT COMPARTMENT, calculate KB by the MOMENTS METHOD& use ‘New Draft’ in calculating this KB when calculating volume.
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TANKER CALCULATIONS
TOTAL OBSERVED VOLUME (T.O.V.):
The Total Observed Volume of all Petroleum Liquids and Free Water at observed temperature.
GROSS OBSERVED VOLUME (G.O.V.):
The Total Volume of all Petroleum Liquids, excluding Free Water at observed temperature.
G.O.V. = T.O.V. - Vfw (at observed temperature)
GROSS STANDARD VOLUME (G.S.V.):
The Total Volume of all Petroleum Liquids, excluding Free Water, corrected by appropriate Volume Correction Factor for the observed temperature and API Gravity 60º F, Relative Density 60º F / 60º F or Density 15º C.
G.S.V. = G.O.V. X V.C.F.
FREE WATER (Vfw):
The volume of water present in a tank which is not in suspension in the contained liquid at observed temperature.
ONBOARD QUANTITY (O.B.Q):
Quantity of water, oil, slops, residue, sludge or sediment, remaining in the tanks prior to loading.
TOTAL CALCULATED VOLUME (T.C.V.):
It is the Gross Standard Volume plus Free Water.
T.C.V. = G.S.V. + Vfw
TOTAL RECEIVED VOLUME (T.R.V.):
Is equal to the Total calculated Volume minus O.B.Q.
Weight Correction Factor (W.C.F.) is applied to this Volume to obtain Weight in Metric Tons or Long Tons.
Shore Gross B/L figure is to be compared with this figure.
Whenever Free Water is found in Cargo:
T.R.V. = T.C.V. - O.B.Q.
LOADED OIL WEIGHT:
Is equal to the Gross Standard Volume minus O.B.Q.
Weight Correction Factor is applied to this Volume to obtain weight in Metric Tons or Long Tons.
Shore Gross B/L figure is to be compared with this figure when no Free Water is found in Cargo.
LOADED OIL WEIGHT = (G.S.V. - O.B.Q.) W.C.F.
VESSEL’S EXPERIENCE FACTOR (V.E.F.):
Is equal to the Total of Gross B/L figures divided by the Total of Ship’s figures over the last 10 voyages.
For the purpose of calculating V.E.F., 10 TO 20 Voyages may be taken. However all voyages must ‘qualify’. A minimum of 5 ‘qualified’ voyages is needed for some level of V.E.F.
The defination of a “qualified voyage is one that meets the following criteria:
· Any voyage that is within +/- 0.0030 of then average ratio of all voyages listed. (eg. If the average listed is 1.00105, then all voyages within the range 0.99805 through 1.00405 would qualify)
· Excludes all voyage prior to any structural modification which affected the vessel’s cargo capacity.
· Excludes load or discharge data where shore measurements were not available.
This Factor is not to be applied to ship’s figure for assessing Ship / Shore difference.
The Factor may be applied to Ship’s figure to obtain an approximate B/L figure, only as a counter check where:
SHIP’S FIGURE X V.E.F = APPROXIMATE B/L FIGURE.
TABLES, VOLUME AND DENSITY:
API = AMERICAN PETROLEUM INDEX
ASTM = AMERICAN STANDARD OF TESTING MATERIALS
Previously there were 3 versions of ASTM Tables:
· USA Version - Giving API at 60º F
· UK Version - Giving Specific Gravity at 60º / 60º F (Ratio of density of Oil at 60º F to density of Water at 60º F = Specific Gravity)
· Metric Version - Giving Density at 15º C (eg. 0.865 kg/m3)
IN PRACTICE:
Volume at observed temperature is calculated by taking ullages.
Density at 15º C is given by Shore authorities.
Now Volume at 15º C = Volume at observed temperature X V.C.F.
And Volume at 15º C X Density at 15º C = Weight at 15º C (IN VACUUM)
But we want Weight IN AIR, therefore we apply the W.C.F.
W.C.F. = DENSITY AT 15º C - 0.0011
NOTES:
Now all 3 Versions are combined together and made into total 14 Volumes which contain all calculations regarding CRUDE, LUBE OIL, DIESEL OIL and all kinds of fluids / liquids.
A particular ship may have selected Volumes only, for the trade on which she is being run.
HYDROMETER - TO MEASEURE DENSITY OF WATER
PICNOMETER - TO MEASURE DENSITY OF ANY LIQUID OTHER THAN WATER
SOLVED NUMERICALS:
1. Volume at observed temperature = 10000 m3
Density at 15º C. Use observed temperature = VCF
Volume at 15º C = 9000 m3 (Volume at observed temperature X VCF)
Therefore Weight in Vacuum = 9000 X 0.8 = 7200
Density at 15º C - 0.0011 = WCF
0.8 - 0.0011 = 0.7989
Therefore W = Volume at 15º C X 0.7989
OBQ = ON Board Quantity
ROB = Remaining On Board
TOV = Vo + Vfw at observed temperature
GOV = TOV - Vfw
GSV = GOV x VCF
TCV = GSV + Vfw
TRV = TCV - obq
TRU x WCF is the figure used to compare B/L figure.
(GSV – OBQ) x WCF = Weight of Oil Loaded
API at 60º F = 141.5 - 131.5
SG 60º / 60º F
API 10 is for fresh water.
Higher the API, the lighter the product
1m3 = 6.28981 barrels
6A A - stands for Crude Oil
6B B - stands for Product Oil
2. On commencement of discharge of No. 3 © tank at 1324, EK draft of 9.00 m, ullage of 0.20 m with waterdip 15 cm.
On completion of bulk discharge at 1800, sounding of 3 © was 20 cm.
The tank is box shaped with dimensions L = 14, B = 12, D = 10, density at 15º C = 0.8937
Average Cargo temperature = 26.0º C. Find the rate of discharge.
TOV = 14 x 12 x 9.8 = 1646.4 m3
Vfw = 14 x 12 x 0.15 = 25.2 m3
GOV = 1646.4 – 25.2 = 1621.2 m3
GSV = GOV x VCF = 1608.026 m3
By Interpolation:
0.8937
0.890 0.895
26º C 0.9918 0.9919
therefore VCF = 0.991874
WCF = 0.8937 - 0.0011 = 0.8926
Therefore Weight of oil on arrival = 1608.026 x 0.8926 = 1435.324 Tons
Volume ROB (0.2 x 14 x 12) x VCF x WCF = 29.747 Tons
Therefore Rate of Discharge in MT = (1435.324 - 29.747)
TIME
WEDGE FORMULA:
It is applicable to Center Tanks only and when the ship is upright and trimmed.
Refer to Figure 1.
Let Breadth of the tank = ‘b’, trim = 0º, dist. of ullage port from aft b/head = ‘d’, height of the tank = ‘h’.
In triangle DGB, angle DGB = 90º
DB = DG Cosec 0 [ DG = Sounding = Pm = Pmiddle ]
= Pm Cosec 0
EC = Dist of ullage port from aft b/head = d
Now, BE = EC + BD – CD
Therefore BE = (d + Pm Cosec 0 – h Tan 0) ………………………. (A)
BE is < / = AE [Wedge is formed]
EF = BE Tan 0
= (d + Pm Cosec 0 - h Tan 0) x Tan 0
Therefore Volume of Wedge = [1/2 x BE x EF] x b
Vwedge = [1/2 x BE x P] x b (B)
Now, Trim = 0
Therefore Tan 0 = Trim = T ………….(1)
Length L
Also from Figure 1
Tan 0 = EF (2)
BE
Comparing (1) and (2)
T = EF
L BE
Therefore BE = EF x L = P x L ………(3)
T T
Putting value of BE (3) in (B),
Vwedge = ½ x (P x L) x P x b
T
Vwedge = L x b x P2 Where P = EF = Ht. Of liquid at aft b/head
2T T = Trim
See Figure 2. below
IN CASE WHEN TRAPEZIUM IS FORMED INSTEAD OF WEDGE
Refer to Figure 3 as above.
Corrected Sounding (P) = {Obs. Sounding (P’) + [d – (h – T/L)] x T/L}
Area of Trapezium = [ (Pmax + z) + z] x l = [ 2P – Pmax] x l
1 2
Where P = Corrected sounding at aft b/head
P’ = Sounding observed from ullage port
d = Dist of ullage port from aft b/head
h = Height of the tank
T = Trim, L = Length of the ship, l = Length of the tank, b = Breadth of the tank
Pmax Max EF due to wedge
Pmax = T/L x l ………………………………….(1)
Pcorr. sdg = P’ + [ d – (h x T/L) ] x T/L ……….(2)
If (1) < (2) ie. Pmax < Pcorr. sdg
The instead of wedge, a trapezium is formed of volume…
Volume = [ Pmax + 2z ] x l x b
2
MORE NUMERICALS:
1. Given tank ullage = 37 cm
Observed temperature of Cargo = 19.3º C
Density of Cargo in Vacuum at 15º C = 0.857 t/m3
Water Content = 165 m3
Calculate amount of Cargo in the tank in MT.
TOV = 3014.9 m3 at 19.3º C
GOV = TOV - Vfw
GOV = 3041.9 – 165 = 2876.9 m3
GSV = 2876.9 x VCF
= 2876.9 x 0.9966
= 2867.1185 m3
WCF = 0.8570 – 0.0011 = 0.8559
Therefore amount of Cargo in MT = 2867.1185 x 0.8559
= 2453.967 MT
2. LBP = 150 M, Trim = 1.30 m
P’ = 58 cm = 0.58 m
d = 1.500 m, l = 12, b = 15, h = 19
R.D. = 0.89
Pmax = T/L x l = 1.3/150 x 12 = 0.104 m
Pcorr.sdg = P’ + [ d – (h x T/L) ] x T/L
= 0.58 + [ 1.5 – (19 x 1.3/150) ] x 1.3/150 = 0.592 m
Since Pmax < Pcorr.sgd, therefore a trapezoid if formed.
Area of Trapezium ABCF,
= ( 0.592 + 0.488 ) x 12 = 6.48 m2
2
Volume of the trapezoid = 6.48 x 15
Therefore amount of Oil in the tank = 6.48 x 15 x 0.89 = 86.508 MT
2. The vessel is on even keel
(A) Ullage = 0.43 m, Water dip = 0.12 m
Density at 15º C = 0.8572
Observed temperature = 33.5º C
For ullage 0.43 m,
Tov = 1955.0 m3
Vfw = 14.8 m3
Therefore GOV = TOV – Vfw = 1940.2 m3
VCF = 0.985388
GSV = GOV x VCF = 1940.2 x 0.985388 = 1911.8498
WCF = 0.8572 – 0.0011 = 0.8561
Therefore the amount of Cargo = 1911.8498 x 0.8561
(B) At the end of discharge,
Ullage = 10.3 m, Sdg = 0.20 m = P’
Trim = 2 m, l x b x h = 20 x 8 x 10.5
d = 1.000 m, LBP = 150
Pmax = T/L x l = 2/150 x 20 = 0.266
Pcorr.sdg = P’ + [ d – (h x T/L) ] x T/L
= 0.20 + [ 1.0 – (10.5 x 2/150) ] x 2/150 = 0.21466
Since Pmax > Pcorr. sdg, therefore a wed ge is formed
P = BE Tan 0 = [ d + Pm Cosec 0 – h Tan 0 ] x Tan 0.
(Tan 0 = 2/150. Therefore 0 = 0.1458. Cosec 0 = 81.404 )
P = [ 1.0 + 0.2Cosec 0 – 10.5 x 2/150] x 2/150
= [ 1.0 + 0.2 x 81.404 – 10.5 x 2/ 150 ] x 2/150 = 0.22854
Volume of wedge = L x b x P2 = 150 x 8 x (0.228544 x 0.228544)
2T 2 x 2
Therefore Volume of wedge = 15.6697 m3
3. l x b x h = 40 x 20 x 20 m3
Ullage of oil = 1.24 m Trim = 3 m
Height of ullage point = 1.10 m LBP = 200 m
Depth of free space above oil = 0.14 m d = 1.6 m
Depth of oil = P’ = 19.86 m
Water dip = 21.1 – 20.94 = 0.61 m
Pmax = T/L x l = 3/20 x 40 = 0.60 m
Pcorr.sdg = { [P’] + [ (d – h x T/L) ] x T/L }
= [ 19.86 + ( 1.6 – 20 x 3 / 200) x 3 / 200 ] = 19.8795
Since Pmax < Pcorr.sdg, a trapezium is formed.
Volume of trapezium = ( 19.2795 – 19.8795) x 40 x 20 = 15663.8 m3
2
Now considering the water dip,
Pmax = EF /AE = T/L
Pmax = 3/200 x 40 = 0.60 m
Present P’ = ( d + Pm Cosec 0 – h Tan 0) x Tan 0
= ( 1.6 + 0.16 x 66.901 – 20 x 0.015 ) x 0.015 = 0.180 m
Since Pmax > P a wedge is formed
Volume of wedge EBF = L x b x P2/ 2T = 200 x 20 x 0.18 x 0.18/ 2 x 3 = 21.6 m3
TOV = 15663.8 m3
Vfw = 21.6 m3
GOV = 15642.2 m3
VCF = x 0.980784
GSV = 15341.619 m3
WCF = x 0.8135
Therefore amount of oil in Tonnes = 12480.407 MT