Buoyancy and Stability of Floating Bodies

  1. A rectangular pontoon 5.4m wide by 12m long has a draught of 1.5m in fresh water (density 1000 kg/m³). Calculate (a) the mass of the pontoon, (b) its draught in sea water (density 1025kg/m³). (97200kg, 1.47m)
  1. A vessel lying in a fresh – water dock has a displacement of 10000 tones and the area of the water – line plane is 1840m². it is moved to a sea – water dock and after removal of cargo its displacement is reduced to 8500 tones. Assuming that the sides of the vessel are vertical near the water line and taking the density of fresh water as 1000kg/m³ and that of sea water as 1025kg/ m³, calculate the alteration in draught.

(0.924m)

  1. A cubic meter of ice (sp. gr. 0.9) floats freely in a vessel containing water at 0˚ C. (a) How much of the ice is exposed, and (b) what will be the change in the level of the water when the ice melts if the area of the water surface is 4m²? (0.1m³, nil)

  1. The piston of the ball valve shown in figure 3.13 has an effective diameter of 10mm. The valve just closes when I of the volume of the ball is submerged. Calculate the pressure in kN/m² of the mains supply? (552kN/m²)
  1. A ball valve is arranged as in Question 4 but the distance from the center of the ball to the pivot is 300mm and the diameter of the piston is 12.5mm. if the mains pressure is 690kN/m², calculate what fraction of the ball is immersed. What would be the mains pressure if the valve closed when I of the ball was immersed? (0.4, 570kN/m²)
  1. The sides of a ship are vertical near the water line and the area of the water line plane is 2050m². the total mass of the ship is 10000 metrictons when it leaves a fresh – water dock. After a certain time at sea the weight of the ship has been reduced by 1500 metric tons due to consumption of fuel. Find how much the draught has been reduced since leaving dock. Relative density of sea water, 1.025? (0.833m)
  1. A rectangular scow 4.5m by 9.6m having vertical sides weights 36000kg. What is its draught in fresh water?
  1. A ship has a displacement of 2200 metric tons in sea water. Find the volume of the ship below the water line. Density of sea water 1025kg/m³? (2142m³)
  1. A vessel has a displacement of 1500 metric tons of fresh water. A weight of 16 metric tons moved 8.25m across the deck causes a horizontal movement of 175 mm at the lower end of a pendulum 1.5m long. Find the metacetric height (0.754m)
  1. A vessel has a displacement of 1500 metric tons of fresh water. A weight of 16 metric tons moved 8.25m across the deck causes a horizontal movement of 175mm at the lower end of a pendulum 1.5m long. Find the metacentric height. (0.754m)
  1. A rectangular pontoon of mass 90 metric tons floats in sea water. It is 12m long, 7.5m wide and 3m deep. Find the metacentric height. Sea water has a density of 1025kg/m³ and the canter of gravity of the pontoon may be taken at its geometrical canter.
  1. A rectangular pontoon has a mass of 240 metric tons and a length of 18m. The canter of gravity is 0.3m above the canter of cross-section and the metacentric height is to be 1.2m when the angle of heel is 10 deg. The free board must not be less than 0.6m when the pontoon is vertical. Find the breadth and height of the pontoon if floating in fresh water. (6.61m, 2.62m)