Fluid Dynamics, Leon Liebenberg, 2019
Lecture Notes 4
Fluid Statics
(Chapter 2)
1. We previously saw that, for an incompressible fluid, p h , or
p
h ; h is therefore the pressure expressed as the height of the
column of liquid;
h is often called the pressure _____________________ [head; loss]
For instance, a head of 1 m of water is equivalent to
_________________ kPa.
Note: In a vessel filled with a fluid, the internal pressure is NOT due to the volume but due
to the hydrostatic depth only! This presents a curiosity if one were to consider the
downward force due to the weight of the liquid. This is known as “Pascal’s Paradox”.
The pressure is the same at all points on a horizontal plane in a given fluid regardless of geometry,
provided that the points are interconnected by the same fluid.
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2. p h can be used to measure static pressure. Like with a barometer that measures
atmospheric pressure. Barometers use a fluid with a high
density and a low vapor pressure, such as mercury. Then,
pB p A Hg h
with pB ________________________ and p A ____
So, ________________________ with Hg 133.35kN / m3
3. p h is also applied in manometry to measure the gage pressure in fluids. A popular
type is the U-tube manometer.
One end of the tube is filled with a fluid of specific weight and the other end is
open to the atmosphere.
To measure high pressures, use is made of a fluid with a high specific weight '
(such as mercury) in the U-tube. Then we can say the following:
p A ___________________ and pC ________ _________
pC pD and pD patm ' hDE
Combining all the above:
p A patm ' hDE hBC
If the fluid in the vessel is a gas, 0 , then the above
equation reduces to ___________________________
Manometer Rule:
Start at a point where the pressure is to be
determined,
and proceed to add to it the pressure ( h ) if
moving to a greater depth,
and subtract h from it if moving to a lesser
depth,
until you reach the liquid surface at the
other end of the manometer.
pbelow pabove g z pabove s z
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4. Example: Pressure gage B is used to measure the
pressure at point A in a water flow. If the pressure at
B is 87 kPa, estimate the pressure at A. Assume all
fluids are at 20°C. [Answ.: 96.4 kPa]
oil 8720 N/m3
water _____________________
mercury _____________________
Manometer Rule = ________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
5. Manometers have limitations, of course. Their tubes should have large enough diameters to
avoid capillary effects. For very accurate measures, attention must be paid to the fluid
temperature (that changes the fluid density). Also, manometers require the use of liquids
and gases that form a well-defined meniscus, to ensure accurate visual readings.
Manometers also respond slowly; they are of little use for fluctuating pressures.
(Nowadays we use piezoelectric pressure transducers to overcome the above problems.)
6. A differential U-tube manometer is sometimes used to measure the difference in pressure
between two points in a closed conduit through which the fluid is flowing.
For the example alongside, you will use the
following equation:
p ' hBC
See if you can derive this equation by applying
the “Manometer Rule”.
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7. To measure very
small pressure
changes (also called
“pressure drops”), an
inclined-tube
manometer may be
used.
From the “Manometer Rule”, we find the following:
p A pB 2 2 sin
p A pB
2
2 sin
You will note that any slight pressure change will cause the distance 2 to be significantly
altered, since the elevation-change depends on the factor sin . If 20 , the
“magnification factor” will be about 3.
