1. An iceberg (SG=0.91) floats in water. If 4.5m3 is above the water surface, what is the total volume of the iceberg?

2. A solid object of specific gravity 7.3 floats in mercury.a. What fraction of its volume is above the liquid surface?b. What is its weight if 0.014m3 is below the liquid surface?c. What vertical force will fully submerge the object?

3. A stone weighing 471N weighs 304N in water?a. What is its volume?b. What is its specific weight?c. What vertical force will fully submerge the object?

4. A hollow cylinder 1.0 m and2.8 m high weighs 3.84 kN.

a. How many kN of lead weighing 110 kN/m3 must be fastened to the outside bottom to make the cylinder float vertically with 2.3 m submerged in fresh water?

b. How many kN of lead weighing 110 kN/m3 must be placed inside thecylinder to make it float vertically with 2.3 m submerged in fresh water?

c. What additional load must be placed inside the cylinder to make its top flush with the water surface?

D

BF

W

G

Bo

B

L

Axis of tilting

W

G

Bo

BF

B’o

M

W

G

BF

B’o

M

B- width of the bodyD- draft or depth of floatationV- total volume submergeG- center of gravity of the body Bo- center of buoyancy of the body in the upright positionB’o- center of buoyancy of the body in the tilted position

M- metacenter; point of intersection between the buoyant force and the tilted axis of the body which determines its stabilityGM- metacentric height; distance between the metacenter and the center of gravity of the body which measures its stability.

Bo

Stability of Floating Bodies

Example Problem #1

A rectangular scow 9 m wide, 15 m long, and 3.6 m high has a draft in sea water (s=1.03) of 2.4 m. Its center of gravity is 2.70 m above the bottom of the scow. Determine the following:

a. the initial metacentric height.

b. the metacentric height when the scow tilts until one side is just on the point of submergence.

c. the righting or overturning moment for the case of part b above.

1. A 48in diameter steel pipe, ¼ in thick, carries oil (0.822) under a head of 400ft oil.

a. What is the pressure inside the tank?b. What is the stress in the steel?c. What thickness of the pipe is required to carry a

pressure of 250psi with an allowable stress of 18000psi?

2. A 3-m diameter spherical tank contains a gas under pressure of 1500kPa. For an allowable stress of 60000kPa, determine the minimum wall thickness?