Chapter 5 (Effect of Density On Draft & Displacement) [PDF]

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CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Chapter –5 Effect of Density on Draft & Displacement Exercise -5



Answer 1 Given:1. Displacement = 16000t 2. TPC = 20t/cm 3. DraftSW = 8m FWA



= Displacement 40 * TPC



FWA



= 16000 40 * 20



FWA



= 20cms / 0.2m



Draft in SW + FWA



= Draft in FW



8m + 0.2m



= Draft in FW



8.2m



= Draft in FW



Draft in FW is 8.2m



Answer 2 Given:1. RD of DW 2. FWA RD of SW



= 1.008 = 180mm



= 1.025



DWA = (Difference in Density) * FWA 0.025 DWA = (1.025 – 1.008) * 180 0.025 DWA = 122.4mm/ 12.24cm Change in draft = 12.24cms



Page 1 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT The vessel will rise it will move from lesser density to higher density.



Answer 3 Given:1. RD of water 2. FWA



= 1.01 = 160mm



RD of FW = 1.000 DWA



= Difference in Density * FWA 0.025



DWA



= (1.010 – 1.000) * 160 0.025



DWA = 64mm/ 6.4cms Change in draft is 6.4 cms The vessel will sink as it is moving from greater density to lesser density.



Answer 4 Given:1. FWA = 175mm 2. RD1 = 1.006 3. RD2 = 1.018 DWA = Difference in density * FWA 0.025 DWA = (1.018 – 1.006) * 175 0.025 DWA = 0.012 * 175 0.025 DWA = 84mm/ 8.4cms Change in draft = 8.4cms The vessel will rise as it is moving from lesser density to higher density.



Page 2 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 5 Given:1. Displacement = 18000t 2. TPC = 25t/cm 3. RD1 = 1.018 RD of SW = 1.025 FWA = Displacement 40 * TPC FWA = 18000 40 * 25 FWA = 18cms/ 180mm DWA = Change in Density * FWA 0.025 DWA = (1.025-1.018) * 180 0.025 DWA = 0.007 * 180 0.025 DWA = 50.4mm/ 5.04cms Her loadline can be immersed by 5.04cms



Answer 6 Given:1. Dimensions of vessels = 20m * 4m * 2m 2. Draft in SW = 1.05m 3. RD of DW = 1.012



20m



2m 1.05m 4m RD =1.012 Page 3 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT RD of SW



= Displacement of vessel Underwater Volume



RD of SW



= Displacement of vessel L * B * draft in SW



1.025



= Displacement of vessel 20 * 4 * 1.05



1.025 * 20 * 4 * 1.05



= Displacement of vessel



86.1 t



= Displacement of vessel



DISPLACEMENT OF VESSEL REMAINS CONSTANT RD of DW



= Displacement of vessel Underwater Volume



RD of DW



= Displacement of vessel L * B * Draft in DW



1.012



=



86.1 20 * 4 * Draft in DW



1.012 * 20 * 4 * draft in DW = 86.1 Draft in DW = 86.1 1.012 * 20 * 4 Draft in DW = 1.063m



Answer 7 Given:1. Dimensions of vessel = 18m * 5m * 2m 2. RD of DW = 1.000 3. Draft at RD1.000 = 1.4m 18m



2m 1.4m 5m RD =1.000 Page 4 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT RD of SW



= 1.025



RD of DW



= Displacement of vessel Underwater Volume



RD of DW



= Displacement of vessel L * B * draftDW



1.000



= Displacement of vessel 18 * 5 * 1.4



1.000 * 18 * 5 * 1.4 = Displacement of vessel 126 t



= Displacement of vessel



WE KNOW THAT DISPLACEMENT OF THE VESSEL WILL REMAIN CONSTANT RD of SW



= Displacement of vessel Underwater Volume



RD of SW



= Displacement of vessel L * B * DraftSW



1.025 = 126 18 * 5 * draftSW DraftSW =



126 18 * 5 * 1.025



DraftSW = 1.366m Total height of vessel



= draft + freeboard



2m = 1.366m + freeboard 0.634m = freeboard Total volume of the vessel



=L*B*H



Total volume of the vessel



= 18 * 5 * 2



Total volume of the vessel



= 180m3



Volume of vessel above water line



= L * B * freeboard



Volume of vessel above water line



= 18 * 5 * 0.634



Volume of vessel above water line



= 57.06 m3



%Reserve Buoyancy



= Volume of vessel above water line * 100 Total Volume Page 5 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT % Reserve Buoyancy



= 57.06 * 100 180



%Reserve Buoyancy



= 31.7%



Percentage of reserve buoyancy is 31.7% Answer 8 Given:1. DraftSW = 5m 2. Displacement = 3000t 3. Draft at RD 1.018 = 5m RD of SW = 1.025 RD of SW



= Displacement of vessel Underwater Volume



1.025



= 3000 Underwater Volume



Underwater Volume



= 3000 1.025



Underwater Volume



=2926.829m3



We know that at same draft, the underwater volume remains constant RD of DW



= Displacement of vessel Underwater Volume



1.018



= Displacement of vessel 2926.829



2979.5t



= Displacement of vessel



Displacement of vessel when afloat at 5m draft in water of RD 1.018 is 2979.5t.



Answer 9 Given:1. Displacement of vessel at FW = 4500t 2. RD of DW = 1.020 RD of FW



= Displacement of vessel Underwater Volume Page 6 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT 1.000



= 4500 Underwater Volume



Underwater Volume = 4500m3 We know that at same draft underwater volume remains constant RD of DW



= Displacement of vessel Underwater Volume



1.020



= Displacement of vessel 4500



4590t



= Displacement of vessel



Displacement of the vessel in RD 1.020 at the same draft as in FW is 4590t.



Answer 10 Given:1. 2. 3. 4.



Length of vessel Breath of vessel Block Coefficient (CB) Draft SW



RD of FW



= 100m = 20m = 0.8 = 8.0m



= 1.000



Underwater Volume



= L * B * DraftSW * CB



Underwater Volume



= 100 * 20 * 8 * 0.8



Underwater Volume



= 12800m3



RD of SW



= Displacement of vesselSW Underwater Volume



1.025



= Displacement of vesselSW 12800



13120t



= Displacement of vesselSW



We know that underwater volume at same draft remains constant RD of FW



= Displacement of vesselFW Underwater Volume



1.000



= Displacement of vesselFW 12800



Page 7 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT 1.000 * 12800 = Displacement of vessel FW 12800t



= Displacement of vessel FW



Difference in Displacement = DisplacementSW – Displacement FW Difference in Displacement = 13120t – 12800t Difference in Displacement = 320t Difference in displacement when floating at the same draft in FW is 320t.



Answer 11 Given:1. Displacement = 14500t 2. Till winter load line 3. RD of DW = 1.010 RD of SW



= Displacement of vessel SW Underwater Volume



1.025



= 14500t Underwater Volume



Underwater Volume



= 14500 1.025



Underwater Volume



= 14146.341m3



We know that, at same draft the underwater volume remains constant. RD of DW



= Displacement of vessel DW Underwater Volume



1.01



= Displacement of vessel DW 14146.341



1.01 * 14146.341= Displacement of vessel DW 14287.8 t



= Displacement of vessel DW



Max cargo that can be loaded = Displacement of vessel SW – Displacement of vessel DW Max cargo that can be loaded = 14500t – 14287.8t Max cargo that can be loaded = 212.2 She can load 212.2 t of cargo so that she would float at winter load line in SW. Page 8 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 12 Given:1. Displacement of vesselSW = 12000t 2. Draft SW = 10.0m 3. DW RD = 1.012 RD of SW = 1.025 RD of SW



= Displacement of vessel Underwater Volume



1.025



=



12000 Underwater Volume



Underwater Volume



= 12000 1.025



Underwater volume



= 11707.317m3



We know that at same draft, underwater volume remains constant. RD of DW



= Displacement of vessel DW Underwater Volume



1.012 = Displacement of vessel DW 11707.317 1.012 * 11707.317 = Displacement of vessel DW Displacement of vessel DW = 11847.8t Cargo to discharge = Displacement of vessel SW – Displacement of vessel DW Cargo to discharge = 12000t – 11847.8t Cargo to discharge = 152.2t She should discharge 152.2 t so that her draft in an upriver port of RD 1.012 would be 10.0m



Answer 13 Given:1. 2. 3. 4. 5.



RD of DW = 1.005 Upper edge of summer loadline in water line to stbd Upper edge of summer loadline 50mm above water line to port FWA = 180mm TPC = 24t/cm Page 9 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT PORT SIDE



STBD SIDE



TF



TF F L



R



T



T



S



S



W



W



WNA



F L 50mm



WNA



Arithmetic mean draft = 50mm+ 0mm 2 Arithmetic mean draft = 50mm 2 Arithmetic mean draft = 25 mm above water line Summer load line is 25mm above water line DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.005) * 180 0.025 DWA = 0.02 * 180 0.025 DWA = 144mm/14.4cms Max permissible sinkage = Arithmetic Mean Draft + DWA Max permissible sinkage = 2.5cms + 14.4cms Max permissible sinkage = 16.9cms Cargo to load = Max permissible sinkage * TPC Cargo to load = 16.9 * 24 Cargo to load = 405.6t Cargo that can be loaded in the vessel to bring her to her permissible draft is 405.6t. Page 10 of 21



R



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 14 Given:1. 2. 3. 4. 5.



Draft of vessel = 7.8m RD of DW = 1.010 TPC = 18t/cm FWA = 250mm Max permissible draft SW =8m



DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.010) * 250 0.025 DWA = 0.015 * 250 0.025 DWA = 150mm/15.0cms Change in draft = Max permissible draft – initial draft Change in draft = 8m – 7.8m Change in draft = 0.2m Permissible sinkage = Change in draft + DWA Permissible sinakge = 0.2m + 0.15m Permissible sinakge = 0.35m/35cms TPCDW = TPCSW * RDDW RDSW TPCDW = 18 * 1.01 1.025 TPCDW = 17.737t/cm DWT Available = Permissible sinkage * TPC DW DWT Available = 35 * 17.737 DWT Available = 620.8t DWT Available is 620.8t



Page 11 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 15 Given:1. 2. 3. 4. 5.



Statutory freeboard = 2m RD of DW = 1.015 Freeboard = 2.1m TPCSW = 24t/cm FWA = 200mm



TPCDW = TPCSW * RDDW RDSW TPCDW = 24 * 1.015 1.025 TPCDW = 23.768t/cm DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.015) * 200 0.025 DWA = 0.010 * 200 0.025 DWA = 80mm/8.0cms Change in draft required = Freeboard – Statutory freeboard Change in draft required = 2.1m – 2m Change in draft required = 0.1m/10cms Permissible sinkage = change in draft + DWA Permissible sinkage = 10cms + 8 cms Permissible sinkage = 18cms DWT available = Permissible sinkage * TPCDW DWT available = 18 * 23.768 DWT available = 427.8t DWT available is 427.8t



Page 12 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 16 Given:1. 2. 3. 4. 5.



RD of river birth = 1.01 Summer load line 20mm above water on stbd side Summer load line 50mm above water on port side Summer displacement = 15000t TPC = 25t/cm PORT SIDE



STBD SIDE



TF



TF F L



R



S



F



T



T 20mm



W WNA



S



L 50mm



W WNA



Arithmetic mean draft = 20mm+ 50mm 2 Arithmetic mean draft = 70mm 2 Arithmetic mean draft = 35 mm above water line Summer load line is 35mm above water line FWA = Displacement 40 * TPC FWA = 15000 40 * 25 FWA = 15cms DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.01) * 150 0.025



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CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT DWA = 0.015 * 150 0.025 DWA = 90mm/9cms TPCDW = TPCSW * RDDW RDSW TPCDW = 25 * 1.01 1.025 TPCDW = 24.634t/cm Max permissible sinkage = Arithmetic Mean Draft + DWA Max permissible sinkage = 3.5cms + 9cms Max permissible sinkage = 12.5cms Cargo to load = Max permissible sinkage * TPC Cargo to load = 12.5 * 24.634 Cargo to load = 307.9t Cargo that can be loaded in the vessel to bring her to her permissible draft is 307.9t.



Page 14 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 17 Given:1. 2. 3. 4. 5. 6.



RD of DW = 1.005 Stbd WNA 30mm below water line Port WNA 60 mm below line Summer water draft = 8.4m TPC = 30t/cm FWA = 160mm



PORT SIDE



STBD SIDE



TF



TF F L



R



30mm



T



T



S



S



W



W



F L



60mm



WNA



WNA



Arithmetic mean draft = 30mm+ 60mm 2 Arithmetic mean draft = 90mm 2 Arithmetic mean draft = 45 mm below water line Winter North Atlantic load line is 45mm below water line Distance between WNA and winter load line = 50mm Winter load line = 50mm – 45mm above water line Winter load line = 5mm above water line Distance between summer load line and winter load line = 1 * Summer draft 48 Distance between summer load line and winter load line = 1 * 8.4m 48



Page 15 of 21



R



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Distance between summer load line and winter load line =0.175m/17.5cms DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.005) * 160 0.025 DWA = 0.020 * 160 0.025 DWA = 128mm/12.8cms Max permissible sinkage = DWA + Distance between Summer load line and winter load line + Distance between Winter load line and water line Max permissible sinkage = 12.8cms + 17.5cms + 0.5cms Max permissible sinkage = 30.8cms TPCDW = TPCSW * RDDW RDSW TPCDW = 30 * 1.005 1.025 TPCDW = 29.415t/cm Cargo to load = Max permissible sinkage * TPC Cargo to load = 30.8 * 29.415 Cargo to load = 906t Cargo that can be loaded in the vessel to bring her to her permissible draft is 906 t.



Page 16 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 18 Given:1. 2. 3. 4.



Stbd WNA 60mm above water line Port WNA 20 mm below line Summer water draft = 8.4m TPC = 30t/cm PORT SIDE



STBD SIDE



TF



TF F L



R



T



T



S



S



W



W



F L



20mm 60mm



WNA



WNA



Arithmetic mean draft = 60mm - 20mm 2 Arithmetic mean draft = 40mm 2 Arithmetic mean draft = 20 mm above water line Winter North Atlantic load line is 20mm above water line Distance between summer load line and winter load line = 1 * Summer draft 48 Distance between summer load line and winter load line = 1 * 7.2m 48 Distance between summer load line and winter load line =0.15m/15cms Distance between tropical load line and summer load line = 1 * Summer draft 48 Distance between tropical load line and summer load line = 1 * 7.2m 48



Page 17 of 21



R



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Distance between tropical load line and summer load line =0.15m/15cms



Max permissible sinkage = Distance between Summer load line and winter load line + Distance between tropical load line and summer load line + Distance between Winter load line and water line Max permissible sinkage = 15cms + 15cms + 2cms Max permissible sinkage = 32cms Cargo to load = Max permissible sinkage * TPC Cargo to load = 32 * 20 Cargo to load = 640t Cargo that can be loaded in the vessel to bring her to her permissible draft is 640 t.



Answer 19 Given:1. 2. 3. 4. 5. 6.



Port freeboard = 3cms Stbd freeboard = 2.9cms RD of DW = 1.020 FWA = 200mm TPC = 30t/cm Statutory summer freeboard = 2.8m PORT SIDE



STBD SIDE



2.8m



2.9m



F L



TF



TF



R



T



T



S



S



W



W



WNA



2.8m 3m



F L



WNA



Page 18 of 21



R



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Arithmetic Mean freeboard = Port freeboard + Stbd freeboard 2 Arithmetic Mean freeboard = 3.0 + 2.9 2 Arithmetic Mean freeboard = 2.95m Change in draft required = Arithmetic mean freeboard – Statutory summer freeboard Change in draft required = 2.95m – 2.8m Change in draft required = 0.15m/15cms DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.020) * 200 0.025 DWA = 0.005 * 200 0.025 DWA = 40mm/4cms Max permissible sinkage = change in draft required + DWA Max permissible sinkage = 15cms + 4cms Max permissible sinkage = 19cms TPCDW = TPCSW * RDDW RDSW TPCDW = 30 * 1.020 1.025 TPCDW = 29.854t/cm Deadweight available = TPCDW + Max permissible sinkage Deadweight available = 29.854 * 19 Deadweight available = 567.2t DWT available is 567.2t



Page 19 of 21



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT Answer 20 Given:1. 2. 3. 4. 5. 6. 7.



Port freeboard = 1.68m Stbd freeboard = 1.79m RD of DW = 1.017 Tropical SW freeboard = 1.63m Tropical SW draft = 9.6m FWA = 150mm TPC = 20.4t/cm PORT SIDE



STBD SIDE



TF



1.63m



1.63m



1.79m F L



R



T



T



S



S



W



W



WNA



TF 1.68m



F L



WNA



Arithmetic Mean freeboard = Port freeboard + Stbd freeboard 2 Arithmetic Mean freeboard = 1.68 + 1.79 2 Arithmetic Mean freeboard = 1.735m Change in draft required = Arithmetic mean freeboard – Tropical SW freeboard Change in draft required = 1.735m – 1.63m Change in draft required = 0.105m/10.5cms DWA = (RDSW – RDDW) * FWA 0.025 DWA = (1.025 – 1.017) * 150 0.025 Page 20 of 21



R



CHAPTER – 5 EFFECT OF DENSITY ON DRAFT & DISPLACEMENT DWA = 0.008 * 150 0.025 DWA = 48mm/4.8cms Max permissible sinkage = change in draft required + DWA Max permissible sinkage = 10.5cms + 4.8cms Max permissible sinkage = 15.3cms TPCDW = TPCSW * RDDW RDSW TPCDW = 20.4 * 1.017 1.025 TPCDW = 20.241t/cm Deadweight available = TPCDW + Max permissible sinkage Deadweight available = 20.241 * 15.3 Deadweight available = 309.7t DWT available is 309.7t



Page 21 of 21