Chapter 13: Liquids
The atoms or molecules in liquids have a strong attraction for each other, but the
forces holding them together do not hold them in fixed positions relative to each other,
but rather they can "slide past" each other and easily change the shape of the
An important concept in both liquids and gasses is pressure. Pressure is
defined as the force per unit area. A force of 100N spread over 0.5m2 produces
a pressure of 200N/m2 or 200Pa. (1Pa = 1 Pascal = 1N/m2.) Similarly
a pressure of 1,000Pa acting on an area of 3m2 will produce a force of 3,000N.
- Gravity acting on a liquid will tend to cause the liquid to deform so that the liquid is
as close to the center of the earth as possible. If the liquid is confined by the walls of
a container, i.e. jar, the liquid will deform to make the surface of the liquid as close
to the center of the earth as possible. (Note that other forces can alter this shape
slightly e.g. adhesion of the liquid atoms or molecules to the surfaces of the
container or the cohesive forces holding the liquid atoms or molecules together will
change the shape of the liquid surface.)
- Gravity acting on a static liquid will produce a pressure in the liquid. This
pressure will increase as you move down in the liquid. In the container at the right, the
pressure is greater at B than at A. However, the pressure at C is the same as the pressure
at B, i.e. the pressure will not change as you move horizontally, only vertically. (Note
that this is only strictly true in a static liquid.) If the vertical distance between A
and B is h, and the density of the fluid is D, the difference in pressure between points A
and B is
PB PA = Dgh
Where g = 10m/s2 on the earth. If the liquid is water, D = 1,000kg/m3,
and the height difference is 2m, the pressure at B is 20,000N/m2, or 20,000Pa,
greater than the pressure at A.
One way of understanding this is to note that the fluid at B must support the weight of
the material above it, and there is more material above B than above A.
- If an object is completely submerged in a liquid, it displaces, or pushes aside, a volume of liquid
equal to its own volume. If it is only partially submerged, the volume of liquid is less
than it own volume.
- If I weigh an object in air with a scale and weigh it when it is immersed in liquid,
e.g. water, the "weights" will not be the same. It will appear to weigh less in
water. Actually its weight will not change, but the water exerts a force on the material
so that the springs in the scale will not have to support the entire weight of the object.
(It is like weighing yourself while leaning on a counter. The scale will not read your
true weight because the counter is supporting part of your weight.) This force the liquid
exerts on the object is called a buoyant force.
- The buoyant force on an object is equal to the weight of the liquid displaced. One way
of looking at it is to note that the pressure at the top of the object pushing it down is
less than the pressure at the bottom pushing it up, resulting in an upward force, the
- If an object is submerged in a liquid and weighs more than the buoyant force on it, it
will sink, if only gravity and the buoyant force act on it. If it weighs less than the
buoyant force it will rise and float. If an object floats, it weighs the same as the
liquid it displaces.
- Note that if a solid object sinks, it
displaces a volume of liquid equal to its own volume.
Pascal's principle says that if I increase the pressure by Pinc
on one part of a liquid in an enclosed container, the pressure everywhere in the
by the same amount, Pinc. In the figure at the right, the
pressure under the piston, i.e. the plunger, was simply the air pressure, 105Pa..
At the bottom of the container it was 1.5x105 Pa because of the
variation of pressure with depth. When I push on the piston, of area 0.01m2,
with a force of 200N, I increase the pressure under the piston by Pinc
= Force/Area = 2x104Pa. Then the pressure just under the piston
becomes P = 105Pa + Pinc = 1.2x105Pa. The
pressure at the bottom will also increase by 2x104Pa and become
This effect is used in hydraulic systems (power steering, brakes
etc.) It allows us to amplify force, but not
work! The typical arrangement is to have two pistons of different areas as
shown at the right. The left piston has an area of 0.01m2 and
the right one and area of 0.05m2. If I place a 5kg mass (weight
= 50N) on the left piston, the pressure will increase by 5x103Pa.
It will also increase by 5x103Pa under the right one. This
produces an extra force on the right piston of 5x103Pa x 0.05m2
= 250N. Note that for the two forces to "balance", Fleft/Aleft
= Fright/Aright , i.e. the two
pressure changes must be equal.
Cohesion and Adhesion
- Cohesion or Cohesive Forces: The attractive forces between the same type of atom or
molecule. These forces hold the liquid together. In the absence of gravity or other
forces, these will pull the liquid into a spherical shape. If you put a small
drop of water on a piece of plastic it will form a bead. Gravity does not completely
flatten it because the cohesive forces try to keep the molecules close together.
- Adhesion or Adhesive Forces: The attractive forces between different types of atoms or
molecules. If you put some water in a glass you will notice that the water is not
perfectly flat, but rises at the edges. This is due to the adhesive force between the
water molecules and the glass.