58: Lesson Pressure in Static Fluid Columns (AP Only)
If you've ever done any deep diving underwater, you'll know about the effects it has on your body.
Most people get the basic idea that as you go deeper underwater, the pressure increases. It's why
it increase that they might not understand perfectly.
At the surface of the water, you'll be experiencing 1 atmosphere (about 1.0e5 Pa) of pressure just from
the normal atmosphere above you.
Now if you go underwater, you need to consider how the weight of the water above you
increases that pressure.
It makes sense, since pressure is just a force acting over an area. In this case, the additional
force of the weight of the water is pushing down across the area of your body.
In Lesson 54, recall how we measured the weight of something if we used measurements of density and
volume.
m
F g= mg =
V
F g = mg m= V
F g = V g
The difference is that now we are going to need to do the measurement as density.
F
P = F g = V g
Remember that V = A h . In this
A
case the height is the height of the
V g
P=
column of fluid above you.
A
Ahg
P=
A
P= g h
So this formula would tell us how much pressure there is due to the fluid above us.
We need to remember that there is still the original pressure from the atmosphere above us
to be added to this additional pressure from the water.
P 2 = P 1 g h
P2 = Final pressure (Pa)
P1 = Initial pressure (Pa)
= density of the fluid (kg/m3)
g = gravity (m/s2)
h = height of fluid (m)
This formula does not just apply to diving underwater (it can be any fluid), and it does not have
to start with an initial pressure at the surface of the water (although it often will).
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Example My wife goes swimming at Kinsman's deep diving pool. She goes down to a depth of
6.7m. Determine the pressure she is experiencing, and compare it to regular atmospheric pressure.
At the surface she would experience 1 atmosphere of regular pressure, and then have the
additional pressure from the water above her.
P 2= P 1 g h
P 2=1.00e5 1.00e3 9.81 6.7
P 2=1.66e5 N / m2
To compare it to regular atmospheric pressure, let's divide it by one atmosphere and see how
many times greater it is...
1.66e5
ratio =
=1.66
1.00e5
We could also just subtract the regular pressure she feels from our total, to say how much the
pressure has increased...
1.66e51.00e5 =6.6e4 N / m 2
Absolute and gauge pressure
From what we've seen here, it looks like we can talk about the additional pressure that was added on, as
well as the actual pressure.
If you want to talk about the amount of pressure we've added on (gh), we call it the gauge
pressure (page 328 Figure 11.13).
This is mostly due to the design of open-tube pressure gauges.
If you want to know how much the total pressure is (P2) we are measuring the absolute
pressure.
Example 2: A tank with some liquid water in it is connected to a open tube manometer as shown here.
The tube has mercury in it. Heat is applied to the water tank, and some of the water vaporizes to steam,
increasing the pressure in the tank. This causes the mercury to be pushed in the tube so that the mercury
rises on the right hand side of the tube (as shown in the diagram). If the height of the mercury is 2.36
cm, determine the change in the pressure. Identify if this is gauge or absolute pressure.
Liquid water
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