Fluid Mechanics with teacher's notes

the water pressure pushing up on the bottom of the box is P o + rgh 2. The net
pressure on the box is the sum of these two pressures.
P net = P bottom + P top = (P 0 + rgh 2) – (P 0 + rgh 1) = rg(h 2 − h 1) = rgL
From this result, we can find the net vertical force due to the pressure on the
box as follows:
F net = P netA = rgLA = rgV = m fg
Note that this is an expression of Archimedes’ principle. In general, we can say
that buoyant forces arise from the differences in fluid pressure between the
top and the bottom of an immersed object.
Atmospheric pressure is pressure from above
The weight of the air in the upper portion of Earth’s atmosphere exerts pressure
on the layers of air below. This pressure is called atmospheric pressure; the
force it exerts on our bodies (assuming a body area of 2 m 2 ) is extremely large,
on the order of 200 000 N (40 000 lb). How can we exist under such tremendous
forces without our bodies collapsing? The answer is that our body cavities
and tissues are permeated with fluids and gases that are pushing outward
with a pressure equal to that of the atmosphere. Consequently, our bodies are
in equilibrium—the force of the atmosphere pushing in equals the internal
force pushing out.
An instrument that is commonly used to measure atmospheric pressure is
the mercury barometer. Figure 9-9 shows a very simple mercury barometer. A
long tube that is open at one end and closed at the other is filled with mercury
and then inverted into a dish of mercury. Once inverted, the mercury does not
empty into the bowl; rather, the atmosphere exerts a pressure on the mercury in
the bowl and pushes the mercury in the tube to some height above the bowl. In
this way, the force exerted on the bowl of mercury by the atmosphere is equal to
the weight of the column of mercury in the tube. Any change in the height of
the column of mercury means that the atmosphere’s pressure has changed.
Kinetic theory of gases can describe the origin of gas pressure
Many models of a gas have been developed over the years. Almost all of these
models attempt to explain the macroscopic properties of a gas, such as pressure,
in terms of events occurring in the gas on a microscopic scale. The most
successful model by far is the kinetic theory of gases.
In kinetic theory, gas particles are likened to a collection of billiard balls
that constantly collide with one another. This simple model is successful in
explaining many of the macroscopic properties of a gas. For instance, as these
particles strike a wall of a container, they transfer some of their momentum
during the collision. The rate of transfer of momentum to the container wall
is equal to the force exerted by the gas on the container wall (see Chapter 6).
This force per unit area is the gas pressure.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
NSTA
TOPIC: Atmospheric pressure
GO TO: www.scilinks.org
sciLINKS CODE: HF2093
Mercury
Fluid Mechanics
Empty
Figure 9-9
The height of the mercury in the
tube of a barometer indicates the
atmospheric pressure.
329
SECTION 9-2
Demonstration 6
Hydrostatic pressure
Purpose Demonstrate that pressure
increases with depth.
Materials 32 oz plastic soda bottle,
tape, water, bucket; optional:
plastic straw or small pieces of
glass or metal tubing and modeling
clay or silicon
Procedure Drill three holes
about 10 cm apart along the side
of the bottle, with the lowest hole
close to the bottom, and tape
them. The holes should not be
aligned vertically; they should be
displaced horizontally about 1
cm so that the water streams do
not collide. Put small pieces of
tubing into the holes to improve
the flow. Cover the holes with
tape, fill the bottle with water,
and place it at the edge of a table.
Place it high enough above the
bucket so that the effects of depth
on the range of each stream will
be easily observed. Ask students
to predict how the water streams
will compare. Quickly pull the
tape away from all three holes,
and have students observe the
shape of each stream. Water
shooting out from near the bottom
of the bottle exits the bottle
at a higher speed than water
shooting out from near the top
does. The reason is that the pressure
in the bottle increases with
depth.
329