1-3.
A piece of metal weighs 350 N in air and when it is submerged completely in water I weighs 240 N.
(1). Find the volume of the metal.
=0.0112𝒎𝟑
(2). Find the specific weight of the metal.
=31.25kN/𝒎𝟑
(3). Find the specific gravity of the metal.
=3.19
4-6.
A prismatic object 200 mm thick by 200 mm wide by 400mm long is weighed in water at a depth of 500
mm and found to be 50 N.
(4). Find its weight in air.
= 206.6 N
(5). Find its specific gravity.
= 1.32
(6). Find its specific weight.
= 12.94 kN/𝒎𝟑
7-9.
A wooden buoy of sp. gr. 0.75 floats in a liquid with sp. gr. 0.85.
(4). What is the percentage of the volume above the liquid surface to the total volume of the buoy?
= 11.8%
(5). If the volume above the liquid surface is 0.0145 𝑚3 , what is the weight of the wooden buoy?
= 0.905 kN
(6). What load that will cause the buoy to be fully submerged?
= 0.121 kN
10-12. (10). What fraction of the volume of a solid object of sp. gr. 7.3 floats above of a container of mercury?
= 0.464
(11). If the volume above the liquid surface 0.014 𝑚3, what is the wt. of the object.
= 1.86 kN
(12). What load applied vertically that would cause the object to be fully submerged?
= 1.61 kN
13-15. An object having a sp. gr. of 0.60 floats in a liquid having a sp. gr. of 0.80.
(13). What is the percentage of the volume above the liquid surface to the total volume of the buoy?
= 75%
(14). If the volume above the liquid surface is 0.024 𝑚3 , what is the weight of the object?
= 0.565 kN
(15). What load that will cause the buoy to be fully submerged?
= 0.188 kN
16-18. A tank with vertical sides is 1.5 m. square, 3.5 m depth is filled to a depth of 2.8 m. of a liquid having a
sp. gr. of 0.80. A cube of wood having a sp. gr. of 0.60 measuring 1 m. on an edge is placed on the
liquid.
(16). Find the weight of the volume liquid displaced.
= 5.885 kN
(17). By what amount will the liquid rise on the tank?
= 0.333 m
(18). What will be the forced increased on one side of the tank?
= 11.629 kN
19-21. A container holds two layers of different liquids, one fluid having a specific gravity of 1.2 is 200 mm deep
and the other fluid having a specific gravity of 1.5 is 250 mm deep. A solid spherical metal having a
diameter of 225 mm and sp. gr. of 7.4 is submerged such a manner that half of the sphere is on the of
the layer and the other half in the bottom layer of fluids.
(19). Compute the weight of the spherical metal.
= 433 N
(20). Compute the buoyant force acting on the object.
= 79 N
(21). Compute the tension in the wire holding the sphere to maintain its position.
= 354 N
22-24. A piece of wood floats in water with 50 mm projecting above the water surface in glycerine of sp. gr.
1.35, the block projects 75 mm above the liquid surface.
(22). Find the height of the piece of wood.
= 0.146 m.
(23). Find the sp. gr. of wood.
= 0.658
(24). Find the weight of the wood if it has a cross sectional area of 200 x 200 mm.
= 38 N
25-27. A prismatic object has a weight of 500 N in air, when the object is completely submerged in a liquid a sp.
gr. of 0.86, it weighs 450 N.
(25). Compute the volume of the object.
= 0.0059 𝒎𝟑
(26). Compute the specific weight of the object.
= 84. kN/𝒎𝟑
(27). Compute the sp. gr. of the object.
= 8.64
28-30. An iceberg in the ocean floats with one seventh of its volume above the surface, unit weight of the
ocean water is 64 pcf.
(28). What is the specific gravity relative to ocean water?
= 0.857
(29). What is the specific gravity relative to pure water?
= 0.879
(30). What portion of its volume would be above surface of ice were floating in pure water?
= 12.1%
31-33. A rectangular barge 18 ft. wide by 46 ft. long by 9 feet deep floats empty with a draft of 4 ft. in a cana
lock 28 ft. wide by 56 ft. long and the water depth 7 ft., When empty barge is present.
(31). What is the weight of the barge?
= 206669 lb.
(32). If 170,000 lb. of steel is loaded onto the barge, what is the new draft of the barge h.
= 7.29 ft.
(33). What is the water depth in the lock (H).
= 8.74 ft.
34-36. An object weights 4 N in water and 5 N in an alcohol having a sp. gr. of 0.80. Assume unit weight of
water is9.79 kN/𝑚3 .
(34). Find the volume of the object.
= 0.0005107 𝒎𝟑
(35). Find the density of the object.
= 1796 kg/𝒎𝟑
(36). Find the mass volume of the object.
= 0.000557𝒎𝟑 /kg
37-39. An iceberg (Ƴ= 9 kN/m3 ) floats in ocean water (Ƴ= 10 kN/m3 ) with 3,000 m3 of the iceberg protruding
above the free surface.
(37). What is the volume of the iceberg below the free surface?
= 27,000 𝐦𝟑
(38). What is the total volume of the iceberg?
= 30,000 𝐦𝟑
(39). What is the weight of the iceberg?
= 270,000 kN
40-42. A rectangular tank of internal width 7 m. partitioned as shown, it contains oil and water. Assume unit
wt. of water is 9.79 kN/m3 .
(40). If the oil has a sp. gr. of 0.84, find its depth h.
= 1.19 m.
(41). If a 900 N block of wood is floated in oil, what is the volume of wood submerged.
= 0.10944 𝐦𝟑
(42). If a 900 N block of wood is floated in oil, what is the rise in free surface of the water in contact with
air?
= 8.54
43-45. A block of wood 0.6 x 0.6 m x “h” meters in dimension was thrown into water, if floats with 0.18 m.
projecting above the water surface. The same block was thrown into a container of a liquid having a sp.
gr. of 0.90 and it floats with 0.14 cm. projecting above liquid surface.
(43). Determine the value of “h”.
= 0.54 m.
(44). Determine the specific gravity of the block.
= 0.667
(45). Determine the weight of the block.
= 1.272 kN
46-48. A board weighing 30 N/m has a cross sectional area of 0.0052 m2 . And a length of 3.4 m. placed in the
tank of oil having a sp. gr. of 0.85. Assuming the hinged to be frictionless.
(46). Compute the specific gravity of the board.
= 0.61
(47). Compute the length of the board which is submerged in oil.
= 1.58 m.
(48). Compute the angle ᶿ for equilibrium conditions.
=34.5°
49-50. A circular log having a diameter of 8 ft. has a length of 15 ft. It has a specific gravity of 0.425.
(49). Determine the weight of the log.
= 19,995.61 lb.
(50). To what depth will the log sink in fresh water.
= 3.53 ft.