8/13/2019 Tutorial 5 - BMCF 2223 -Buoyancy

1/2

1

UNIVERSITI TEKNIKAL MALAYSIA MELAKAFAKULTI KEJURUTERAANMEKANIKAL

BMCF 2223 MEKANIK BENDALIR I

TUTORIAL 5BUOYANCY

1. A piece of irregularly shaped metal weighs 300 N in air ( air

= 1.293 kg/m3). When the

metal is completely submerged in water, it weighs 232.5 N. Determine the volume of the metal.[0.00689 m3]

2. A balloon weighs 700 N and has a volume of 200 m3. It is filled with helium ( helium = 0.179kgm-3). What load will the balloon support, or what downward force is required to keep it fromrising, if the density of air is 1.293 kgm-3? [1.486 kN]

3. A spherical buoy has a diameter of 1.5 m,weighs 8.50 KN, and is anchored to the sea floorwith a cable as is shown in Figure 1. Although thebuoy normally floats on the surface, at certain timesthe water depth increases so that the buoy iscompletely immersed as illustrated. For this conditionwhat is the tension of the cable? Given, density of

Seawater

Buoy

Cabl

the sea water = 1025 kg/m3. [9.27 kN] Figure 1

4. A concrete cube, 0.3 m on each side, is having the specific gravity of 2.4. Determine themagnitude and direction of the force necessary to hold it in equilibrium and completely

submerged (a) in mercury, and (b) in water. [(a) 2.96 kN Downward, (b) 0.37 kN Upward]

5. A 20 cm diameter solid cylinder 7cm high weighing 1.5 kg is immersed inwater (1000 kg/m3) contained in a tall,upright metal cylinder of 25 cm insidediameter as shown in Figure 2. Beforeimmersion, the liquid was 7 cm deep(x + z = 7 cm). At what level will thesolid cylinder float (z = ?)?

1.5 kg

20 cm

y

x

[0.053 m]

0.666 m

Water

= 1000 kg/m3)

Figure 2

z

25 cm

Figure 3

1.3 m

6. A solid wood cylinder with a diameter of0.666 m, height of 1.3 m and the specific gravityof 0.61 relative to water. Would the cylinder bestable if it is placed vertically in oil (s.g. = 0.85) as

shown in Figure 3? (Given I = d4/64)

[D = 0.933 m, GM = - 0.154 m, unstable]

8/13/2019 Tutorial 5 - BMCF 2223 -Buoyancy

2/2

2

rock. The barge is 7 m wide, 17 mlong, and 2.5 m deep (Figure 4). Ifthe barge and rock weigh 2.0 MN,determine the depth ofsubmergence, d of the barge in

water.

2.5 m

Rock

Barged

17 m

[1.71 m] Figure 4

8. A stone weights 86 N in air (air

= 1.293 kg/m3). When submerged in water it weighs 43 N.

Find its volume and specific gravity. [4.383 x 10-3 m3, 2]

9. Consider the diagram. A 0.15 x 0.15 x 3.6m wooden stick is hinged to the point A in water(Figure 5). The weight of the stick is 700N.

Determine the angle .

Figure 5

[38.41]

10. A rectangular pontoon floatingin seawater (density 1025 kg/m3) is8 m long, 7 m broad and 3 m deep(Figure 6). It weighs 600 kN. Itcarries on its upper deck an employboiler 4 m diameter weighing 400kN. The centre of gravity of thepontoon and boiler are at theirgeometric centres along a verticalline. Is the system stable?

bd3

C2

R2 m

C

C1h B

h/2

A

1.5m

(Take I = )12 7 m

[Final BMCF 2223-Sem2Sesi0203][0.29] Figure 6

11. The density of a liquid is to bedetermined by an old 1-cm-diameter

10 cm

Mark for water

0.5 cm

Unknown

liquidFigure 7

cylindrical hydrometer whose division marksare completely wiped out. The hydrometer isfirst dropped in water, and the water level ismarked. The hydrometer is then dropped intothe other liquid, and it is observed that themark for water has risen 0.5 cm above theliquid-air interface (see Figure 7). If the heightof the water mark is 10 cm, determine the

density of the liquid. [1053 kg/m3]