**1.**

**A box-shaped vessel 120m long and 15m wide has a light draft of 4m and a load draft of 9.8m in SW. find her light displacement, load-displacement. and DWT.**

*Solution ***:**

**:**

*Area of box shape vessel = (L x B)**= 120m x 15m**Light draft = 4m*

*Light displacement = (u/w volume) x ( density)**= (L x b x d )x (1.025)**= (120 x 15 x 4) x (1.025)**= 7380 t*

*Load draft = 9.8m*

*So load displacement = (u/w volume) x (1.025)**= ( L x b x d) x (1.025)**= (120 x 15 x 9.8) x (1.025)**= 18081t*

*Hence, DWT = (Load displacement – Light displacement)**= ( 18081 – 7380 )**= 10, 701t*

**2. **

**A box-shaped vessel 100m long and 14m wide is floating in SW at a draft of 7.6m. Her light draft is 3.6 m and load draft 8.5m. Find her present displacement, DWT aboard and DWT available.**

**Solution:**

**Solution:**

*A rea of box shape vessel = (L x B)*

*= (100m x 14m)*

*Present draft = 7.6m**Present displacement = (Lx b x d) x (density)**= (100 x 14 x 7.6) x (1.025)**=10906 t**Light draft = 3.6m*

*Light displacement = (L x B x D) x(1.025)**= (100 x 14 x 3.6 ) x (1.025)**= 5166t*

*When Load draft is = 8.5m*

*Load displacement = ( L x b x d )x (1.025)**= (100 x 14 x 8.5) x (1.025)**= 12,197.5t*

*We know that*

*DWT aboard = (present displacement – Light displacement)**= (10906 t – 5166 t )**= 5740 t*

*DWT available = (Load displacement – present displacement)**= ( 12,197.5 t – 10,906 t )**= 1291.5t.*

**3.**

**A ship is 200m long 20m wide at the waterline. If the coefficient of fineness of the water-plane is 0.8, find her TPC in SW, FW, and DW of RD 1.015.**

**Solution :**

**Solution :**

*Given : (L x B) = (200m x20) , Cw = 0.8*

*As we know that :**Cw = Area of water plane / ( L x B )**0.8 = Area of water plane / (200 x 20)**(0.8 x 200 x 20) = Water plane area*

*A = 3200m ^{2}*

*We can calculate :*

*TPC in SW = (A/ 100 x 1.025)**= (3200 / 100 x 1.025)**= 32.8 t/cm*

*TPC in FW = (A / 100x 1 )**= (3200/100)**= 32 t/cm*

*TPC in RD of 1.015 =( A /100 x 1.015)**= (3200 /100 x 1.015)**= 32.48 t/cm.*

*Note : here “A” refers to waterplane area.*

**4. **

**A double bottom tank 20m x 10.5m x 1.0m has a block a coefficient of 0.82. Calculate how much fuel oil of RD 0.9, it can hold.**

**Solution :**

**Solution :**

*Given : – (L x B x H) of double bottom tank =( 20 x 10 .5 x 1)**Cb = 0.82 , RD = 0.95*

*We know that:*

*Cb = (volume of tank) /( L x B x depth)**0.82 = (volume of tank) /(20 x 10.5×1)**volume of tank = 0.82 x ( 20 x 10.5x 1)**= 172.2 m ^{3}*

*Weight of oil can be calculated as :- (volume of tank) x(density)**= (172.2 x 0.95)**= 163.59 t*

**5.**

*A ship floating in SW at a draft of 8m is 110m long and 14m wide at the water line . If her block coefficient is 0,72, find her displacement. If her load displacement is 12000 t, find the DWT available .*

*Solution:*

*Solution:*

*Given: – (L x B) = 110m x 14m,**Present draft = 8m**Cb = 0.72*

*Load displacement = 12000 t ,*

*We know that :-*

*Cb = (u/w volume ) / (Lx B x D)**0.72 = (u/w volume) / (110 x 14 x8)*

*u/w volume = 0.72 x ( 110 x 14 x 8 )**= 8870.4 t*

*DWT available = (Load displacement – present displacement)**= (12000 – 8870.4)**= 3129.6t.*

**6. **

*A vessel of 14000t displacement is 160m long and 20m wide at the water line . If she is floating in SW at a draft of 6.1m, find her block coefficient.*

*Solution:*

*Solution:*

*Given : – W = 14000 t ,**(L x B) of waterline = (160m x 20m),**Present draft = 6.1m*

*We know that :*

*Weight = (u/w volume )x (density of displaced water)**14000 = (u/w volume) x 1.025**u/w volume = 14000/ 1.025**= 13658.536 t*

*We also know that:-*

*Cb = (u/w volume )/( Lx B x D)**Cb = 13658.536 /(160 x 20 x6.1)**= 0.699m**= 0.7m*

**7.**

**A box-shaped vessel 18m x 5m x2m floats in SW at a draft of 1.4m. Calculate her RB %.**

**Solution :**

**Solution :**

*Given :- (L x B x H) of box shape vessel =(18m x 5m x 2m), Present draft = 6.1m*

*We know that :-*

*RB % = (Above water volume )/(total volume ) x 100**Total volume can be calculated as = (L x B x D)**= 18 x 5x 2m**= 180m ^{3} *

*U/w volume = (L x B x present draft)**= 18 x 5 x 1.4**= 126m ^{3} *

*Hence, Above water volume = (180 – 126)**= 54m3*

*RB % = (Above water volume) / (total volume ) x 100**Hence, RB % = (543/180 x 100)**= 30%*

**9.**

**9.**

** A box –shaped of 2000t displacement is 50m x 10m x 7m. Calculate her RB% in FW**

**Solution :**

**Solution :**

*Given :- W = 2000t,*

* (L x B x H) of box shaped vessel = (50m x 10m x 7m)** Total volume = 3500m ^{3} *

*W = ( u/w volume) x (density)*

*2000 = (u/w volume) x (1.00)*

*u/w volume = 2000 m*

^{3}*Above water volume = (Total volume) – (u/w volume )** = (3500 – 2000)** = 1500 m ^{3} *

*RB % = (Above water volume) / (total volume ) x 100**RB % = (1500 /3500)x 100** = 42.857%*

**10. A ship is a floating a draft of 8.2m in DW of RD 1.010. If her TPC in SW is 40, find how much cargo she can load to bring her draft in DW to 8.4m.**

**10. A ship is a floating a draft of 8.2m in DW of RD 1.010. If her TPC in SW is 40, find how much cargo she can load to bring her draft in DW to 8.4m.**

**Solution :**

**Solution :**

*Given:-**RD of DW = 1.010,**Present Draft = 8.2m**Cargo can be load up to draft = 8.4m,**So, Sinkage = 0.2m = 20cm*

*TPC in SW = (A / 100) x (1.025)**40 = (40/100) x (1.025)**A = (40 x100)/ (1.025)**= 3902.44m ^{2}*

*Now, TPC in DW = (A/100) x (1.010)**= (3902.44 / 100) x(1.010)**=39.41 t/cm.*

*Cargo can be load = (39.41 x 20)**= 788.2 t*