10.5 Pressure and Stress —Force Acting Over an Area 271
Another simple, yet important concept for a fluid at rest states that pressure increases with
the depth of fluid. So the hull of a submarine is subjected to more water pressure when cruising
at 300 m than at 100 m. Some of you have directly experienced the variation of pressure with
depth when you have gone scuba diving or swimming in a lake. You recall from your experience
that as you go deeper, you feel higher pressure on your body. Referring to Figure 10.21, the
relationship between the gauge pressure (the pressure that is above atmospheric pressure) and
the height of a fluid column above it is given by(10.15)
where
Pis the fluid pressure at pointB(see Figure 10.21) (in Pa or lb/ft
2
)ris the density of the fluid (in kg /m
3
or slugs /ft
3
)gis the acceleration due to gravity (g9.8 m/s
2
org32.2 ft /s
2
)his the height of fluid column (in m or ft)
Also shown in Figure 10.21 is the force balance between the pressure acting on the bottom
surface of a fluid column and its weight. Equation (10.15) is derived under the assumption of
constant fluid density.
Another concept, which is closely related to fluid pressure distribution is buoyancy. As we
discussed in Chapter 7, buoyancy is the force that a fluid exerts on a submerged object. The net
upward buoyancy force arises from the fact that the fluid exerts a higher pressure at the bottom
surfaces of the object than it does on the top surfaces of the object. Thus, the net effect of fluid
pressure distribution acting over the submerged surface of an object is the buoyancy force. The
magnitude of the buoyancy force is equal to the weight of the volume of the fluid displaced,
which is given here again for convenience.whereFBis the buoyancy force (N), rrepresents the density of the fluid (kg /m
3
),gis accelera-
tion due to gravity (9.8 m/s
2
), and Vis the volume of the object (m
3
).FBrVg
Prgh
■Figure 10.21 The variation of pressure with depth.
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