CE 332(HYDRAULICS)
BSCE-3
BUOYANCY AND ARCHIMEDES PRINCIPLE
LEARNING OUTCOMES:
• Define Buoyant Force
• State Archimedes principle
• Understand the relationship between density and Archimedes' principle
DISCUSSION
Why do some things float and others sink? The first thing that comes to mind for many people is that it
depends on how heavy an object is. While an object's weight, or more properly its mass does play a role,
it is not the only factor. If it were, we could not explain how a giant ocean liner floats while a small
pebble sink. Mass matters, but there is more to it.
The ability of an object to float is described as its buoyancy. The buoyancy of an object is its tendency to
float on or rise in a liquid. An object that floats in water is said to be positively buoyant. An object that
sinks is negatively buoyant. To determine an object's buoyancy, both its mass and volume must be taken
into consideration. The relationship between object's volume and mass is called its density.
The pressure increases with depth in a fluid. This means that the upward force on the bottom of an
object in a fluid is greater than the downward force on top of the object. There is an upward force, or
buoyant force, on any object in any fluid. If the buoyant force is greater than the object’s weight, the
object rises to the surface and floats. If the buoyant force is less than the object’s weight, the object
sinks. If the buoyant force equals the object’s weight, the object can remain suspended at its present
depth. The buoyant force is always present, whether the object floats, sinks, or is suspended in a fluid.
In order to explain how an object's density influences its buoyancy, the behavior of an object placed in
water must be understood. When an object is placed in water, even a floating object displaces some of
that water. The amount of water displaced is a function of the object's mass. The object sinks into the
water until it displaces an amount of water equal to its own mass. A 1g object will sink until it displaces 1
g of water. This is independent of its size or shape. Since water has a density of 1 g/cm3, a 1 g object will
displace 1 cm3 of water.
The following experiment is illustrated in Figure 1. The overflow
can is filled to the spout with water. The heavy metal cube
is first weighed in still air and weighs 10 lb. It is then weighed
while completely submerged in the water and it weighs 3 lb.
The difference between the two weights is the buoyant force
of the water. As the cube is lowered into the overflow can, the
water is caught in the catch bucket. The volume of water which
overflows equals the volume of the cube. (The volume of irregular
shaped objects can be measured by this method.) If this experiment
is performed carefully, the weight of the water displaced by the
metal cube exactly equals the buoyant force of the water, which
the scale shows to be 7 lb.
FIGURE 1
Archimedes (287–212 B.C.) performed similar experiments. As a result, he discovered that the buoyant
force which a fluid exerts upon a submerged body is equal to the weight of the fluid the body displaces.
This statement is referred to as Archimedes’ principle.
Archimedes Principle
This principle applies to all fluids, gases as well as liquids. Just as water exerts a buoyant force on
submerged objects, air exerts a buoyant force on objects submerged in it.
Just how large a force is buoyant force? To answer this question, think about what happens when a
submerged object is removed from a fluid, as in (Figure 2). If the object were not in the fluid, the space
the object occupied would be filled by fluid having a weight Wfluid
FIGURE 2
This weight is supported by the surrounding fluid, so the buoyant force must equal the weight of the
fluid displaced by the object.
The buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes’
principle is Fb= Wfluid, where Fb is the buoyant force and Wfluid is the weight of the fluid displaced by the
object.
If the buoyant force is more than the object weighs, the object will float. If the buoyant force is less than
the object weighs, the object will sink. For the object that sinks, its measurable weight will be less by the
weight of the displaced fluid.
Archimedes’ principle refers to the force of buoyancy that results when a body is submerged in a fluid,
whether partially or wholly. The force that provides the pressure of a fluid acts on a body perpendicular
to the surface of the body. In other words, the force due to the pressure at the bottom is pointed up,
while at the top, the force due to the pressure is pointed down; the forces due to the pressures at the
sides are pointing into the body.
Since the bottom of the body is at a greater depth than
the top of the body, the pressure at the lower part of the
body is higher than the pressure at the upper part, as shown
in (Figure 3). Therefore, a net upward force acts on the body.
This upward force is the force of buoyancy, or simply buoyancy.
Density and Archimedes Principle
If you drop a lump of clay in water, it will sink. But if you mold the same lump of clay into the shape of a
boat, it will float. Because of its shape, the clay boat displaces more water than the lump and
experiences a greater buoyant force, even though its mass is the same. The same is true of steel ships.
The average density of an object is what ultimately determines whether it floats. If an object’s average
density is less than that of the surrounding fluid, it will float. The reason is that the fluid, having a higher
density, contains more mass and hence more weight in the same volume. The buoyant force, which
equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object
denser than the fluid will sink.
We can derive a quantitative expression for the fraction submerged by considering density. The fraction
submerged is the ratio of the volume submerged to the volume of the object, or
Now we can obtain the relationship between the densities by substituting
Substituting into the first equation, we can derive
We can use this relationship to measure densities.
Links for Additional learning:
https://byjus.com/physics/buoyant-force/
https://www.britannica.com/science/Archimedes-principle
https://www.youtube.com/watch?v=khc2wUBsFU4&t=70s
https://www.youtube.com/watch?v=Qgl_l0H7Qgc
