Statical Stability. The scow shown in Fig. A above is 15 m long, 6 m wide, and 4 m deep. It has a draft of 3 m when floating in an upright position. The center of gravity of the scow is on the axis of symmetry, 0.5 m above the water surface. Compute (a) the initial metacentric height, and (b) the righting moment in sea water when the angle of heel is 10 degrees. Specific weight of sea water is 10,045 N/m . Initial Metacentric Height, MG, - MB, - CB, - - ca,. LWd OM •Vessel in Heeled Position (at an angle 0) Metacentric Height,MC, = M3,-CB, =: WLdcose 12dcose OB, Fig. A d/2 Righting Moment, R. M.=y.V.MC,siné

Statical Stability. The scow shown in Fig. A above is 15 m long, 6 m wide, and 4 m deep. It has a draft of 3 m when floating in an upright position. The center of gravity of the scow is on the axis of symmetry, 0.5 m above the water surface. Compute (a) the initial metacentric height, and (b) the righting moment in sea water when the angle of heel is 10 degrees. Specific weight of sea water is 10,045 N/m . Initial Metacentric Height, MG, - MB, - CB, - - ca,. LWd OM •Vessel in Heeled Position (at an angle 0) Metacentric Height,MC, = M3,-CB, =: WLdcose 12dcose OB, Fig. A d/2 Righting Moment, R. M.=y.V.MC,siné

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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3. Statical Stability. The scow shown in Fig. A above is 15 m long, 6 m wide, and 4 m deep. It has a draft of 3 m when floating in an upright position. The center of gravity of the scow is on the axis of symmetry, 0.5 m above the water surface. Compute (a) the initial metacentric height, and (b) the righting moment in sea water when the angle of heel is 10 degrees. Specific weight of sea water is 10,045 N/m³. Initial Metacentric Height, 12 M73 LWd (+) MC, = MB.- CB, = CB, = 12d OM •Vessel in Heeled Position (at an angle 0) d. Metacentric Height,MC, = MB,-CB,= WLdcose %3D %3D 12dcose OB. Fig. A d/2 Righting Moment, R. M.=7.V.MC,sin6 W
A loaded scow has a draft of 1.8m in freshwater when erect. The scow is 6m wide, 12m long, and 2.4m high. Its center of gravity is 0.6m below the top of the scow along the vertical axis of symmetry. What maximum single weight W can be moved transversely over the edge of the side without sinking the scow? Assume the center of gravity is at the same point.
A loaded scow has draft of 1.6 m in sea water (sg = 1.03) when in upright position. The scow is 6 m wide and 12 m long and 2.4 m high. The center of gravity of the scow is 1.8 m above the bottom along the vertical axis of symmetry. Assume that the center of buoyancy is located half of the height of draft. What is the maximum single weight in kN that can be moved transversely from the center of the unloaded scow over the top edge without sinking the scow? (Considering rolling position)
A rectangular barge is 15 ft wide and 40 ft long and floats with a draft (submerged height) of 4 ft. It is piled so high with gravel that its center of gravity is 3 ft above the waterline. Is it stable with respect to its roll stability? The roll axis is parallel to the 40-ft side.
The object shown below is stable and floating in the water. (1) Please match center distance MB and MG with correct distance options for Figure (a).
A pontoon measuring 10 m (length) × 7.5 m (width) × 2.5 m (depth) weighing 800 kN floats in sea water. On its upper deck it carries a boiler 5 m in diameter and weighing 500 kN. The centre of gravity of each unit coincides with geometrical centre of the arrangement and lies in the same vertical line. Calculate the metacentric height. Take the specific weight of sea water = 10 kN/ 3 m' [Ans. 0.875 m]
Compare the initial metacentric heights of two barges, each 50 m long, 10m beam at the waterline, 6 m deep, floating upright on an even keel at 4 m draft and having KG 3 m. One barge is in the form of a rectangular prism and the other is in the form of a triangular prism, floating apex downwards. (be sure to look at the examples from the book "ship stability for masters and mates" chapter 12.).
In Fig. , curved section AB is 5 m wide into the paperand is a 60 ° circular arc of radius 2 m. Neglecting atmosphericpressure, calculate the vertical and horizontalhydrostatic forces on arc AB .
A rectangular pontoon has a mass of 240 metric tons and a total length of 18 m. The centre of gravity is 0.3 m above the centre of cross-section and metacentric height is to be 1.2 m when the angle of heel 10 degree. The freeboard must not be less than 0.6 m when the pontoon is vertical. Find the breadth and the height of the pontoon if floating in fresh water.
A loaded scow has draft of 1.6 m in sea water (sg = 1.03) when in upright position. The scow is 6 m wide and 12 m long and 2.4 m high. The center of gravity of the scow is 1.8 m above the bottom along the vertical axis of symmetry. Assume that the center of buoyancy is located half of the height of draft. Determine the metacentric height due to pitching if the scow is tilted until one end is just submerged in seawater.
Our ancestors found that by tying two or more circular logs together to form a raft instead of digging a hollow in each log, it would have a more stable platform to carry more weight and enabled them to migrate further across the oceans. The reasons for this added stability are: (i) It increases the metacentric height GM by increasing the height of metacenter M. (ii) It increases the metacentric radius BM. It enables a large shift of the centre of buoyancy B laterally to produce a strong restoring moment when it is tilted. (A) (i) and (ii) (B) (ii) and (iii) (C) (i) and (iii) (D) All of the above In flow of air past an aerofoil with velocity U, a viscous boundary layer is formed arising from the viscous effect on the surface of the aerofoil. Due to no-slip condition at the wall, the velocity at the wall is zero. Across the boundary layer, the relationship between the static pressure at the wall and that at the edge of boundary layer is given by: P> P P₁ = Pe P₂ P
SOLVE THE FF, SHOW YOUR COMPLETE SOLUTION (ANSWERS MUST BE IN 3 DECIMAL PLACES). The vessel is 20m long, 10m wide and 5 m deep. It has a draft of 4, when floating in an upright position. The center of gravity of the scow is on the axis of the symmetry, Find: (a) The initial metacentric height (at initial position) (b) The metacentric height in tilted position when the vessel is at the point of submergence. (c) The distance between weight and the buoyancy in tilted position. (d) The moment created. (e) Classify the kind of moment. (f) The shifted distance of buoyancy.