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11-21
Buoyancy
11-26C
Solution We are to define and discuss the buoyant force.
11-27C
Solution We are to compare the buoyant force on two spheres.
11-28C
Solution We are to compare the buoyant force on two spheres.
11-29C
Solution We are to compare the buoyant forces on a cube and a sphere.
11-30C
Solution We are to discuss the stability of a submerged and a floating body.
11-31
Solution The density of a liquid is to be determined by a hydrometer by establishing division marks in water and in
the liquid, and measuring the distance between these marks.
In pure water:
cww AghW
In the liquid:
c
AghWliquidliquid
0.3 cm
12 cm
W
11-23
11-32E
Solution A concrete block is lowered into the sea. The tension in the rope is to be determined before and after the
block is immersed in water.
Assumptions 1 The buoyancy force in air is negligible. 2 The weight of the rope is negligible.
11-34
Solution The height of the portion of a cubic ice block that extends above the water surface is measured. The height
of the ice block below the surface is to be determined.
Assumptions 1 The buoyancy force in air is negligible. 2 The top surface of the ice block is parallel to the surface of the
sea.
11-25
11-35
Solution A spherical shell is placed in water. The percentage of the shell’s total volume that would be submerged is
to be determined.
Assumptions The buoyancy force in air is negligible.
3
3
NWS98.5
The buoyancy force:
submergedsubmergedwb
F 9810
06.0
3
4
3
11-26
11-36
Solution An inverted cone is placed in a water tank. The tensile in the cord connecting the cone to the bottom of the
tank is to be determined.
Assumptions The buoyancy force in air is negligible.
2030
rR
and
cm
R
r33.13
3
40
3
2
NFb5.361072.39810 3
20 cm
R=20 cm
11-37
Solution The percentage error associated with the neglecting of air buoyancy in the weight of a body is to be
determined.
NFWW b468.320
6
2.0
81.92.1518.320
3
11-39
Solution An irregularly shaped crown is weighed in air and then in water with a spring scale. It is to be determined if
11-29
11-40
Solution The volume of the hull of a boat is given. The amounts of load the boat can carry in a lake and in the sea are
kg/m3.
Analysis The weight of the unloaded boat is
m/skg 1000
kN 1819
m/skg 1000
kN 1
)m 180)(m/s 81.9)(kg/m 1030( 2
323
seasea,
V
gFB
kN 1
2
Wload
FB
Wboat
PROPRIETARY MATERIAL. © 2017 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
11-41
Solution One section of the duct of an air-conditioning system is laid underwater. The upward force the water
exerts on the duct is to be determined.
Assumptions 1 The diameter given is the outer diameter of the duct (or, the thickness of the duct material is negligible). 2
11-31
11-42
Solution A semi-circular gate is hinged. The required force at the center of gravity to keep the gate closed is to be
NAhF cgRg 1030
2
5.0
3
5.04
981026.1
2
mh 24.2
981091.0
20000
therefore the imaginary oil level would be
mH 50.224.274.4
from glycerin surface. The force applied by oil is then
NAhF cgRo 9508
2
5.0
3
5.04
5.2981091.0
2
Pair=80 kPa (abs)
Glycerin
SG=1.26
4.74 m
11-32
PROPRIETARY MATERIAL. © 2017 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
05.2 ocpRogcpRggcg yFyFyF
05.2784.295082945.010302122.0 F
kN 11.3 NF 11296
