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FLUID MECHANICSChapter 3: FLUID STATICSDr. Randa Hatamleh
Fall 2014
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Pressure Measurements
1. Barometer: measures atmospheric
Pressure = +
Pv = 2.4 x 10-6atm at 20 0C
The Aneroid Barometer
Has some advantages over a mercurybarometer because it is smaller and
allows data recording over time.
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Pressure Measurements
Bourdon-Tube Gage
Low cost, reliable, easy to install,
and available in many different pressure ranges.
Accuracy of the gage can be lower than otherinstruments; and the gage can be damaged by excessive
pressure
Piezometer
Itis a vertical tube in which a liquid risesin response to a positive gage pressure.
simplicity, direct measurement, and accuracy.
Piezometer is limited to low pressures
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Example
What is the maximum gauge pressure of water that can
be measured by a Piezometer of height 1.5m? And if the
liquid had a relative density of 0.85 what would the
maximum measurable gauge pressure?
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Pressure Measurements Pressure
Measurements Manometer: is a device for measuring pressure by
raising or lowering a column of liquid. Manometers
use the relationship between pressure and head to
measure pressure
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Pressure Measurements
The Piezometer tube Manometer
The simplest manometer is a tube, open at the top, which
is attached to the top of a vessel containing liquid at a
pressure (higher than atmospheric) to be measured.
This simple device is known as a Piezometer tube.
As the tube is open to the atmosphere the
pressure measured is relative to
atmosphereic so is gauge pressure
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Example
A manometer connected to a pipe indicates a negative
gauge pressure of 50mm of mercury. What is the absolute
pressure in the pipe in Newtons per square metre is theatmospheric pressure is 1 bar?
[93.3 kN/m2]
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The U Tube Manometer
U-Tube enables the pressure of both liquids and gases
to be measured U is connected as shown and filled with
manometric fluid.
Important points:
1. The manometric fluid density should be greater than of
the fluid measured. man>
2. The two fluids should not be
able to mix they mustbe immiscible.
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Pressure in a continuous static fluid is the same at any
horizontal level.
pressure at B = pressure at CpB= pC
For the left hand arm
pressure at B = pressure at A + pressure of height of liquid
being measured
pB= pA+ gh1
For the right hand arm
pressure at C = pressure at D + pressure of height ofmanometric liquid
pC= patmospheric+ mangh2
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We are measuring gauge pressure we can subtractpatmosphericgiving
pB= pCpA= man gh2- gh1
What if the fluid is a gas?
Nothing changes.
The manometer work exactly the same.
BUT:As the manometric fluid is liquid (usually mercury , oilor water) And Liquid density is much greater than gas,
man>> Ugh1 can be neglected,
and the gauge pressure given by pA= mangh2
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Example
Using a u-tube manometer to measure gauge pressure of
fluid density p = 700 kg/m3 , and the manometric fluid is
mercury, with a relative density of 13.6. What is the gauge
pressure if:
a) h1= 0.4m and h2= 0.9m?
b) h1stayed the same but h2= -0.1m?
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Pressure Measurements
Manometer
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EXAMPLE 3.6
Water at 10C is the fluid in the pipe and mercury is the
manometer fluid. If the deflection h is 60 cm and L is 180
cm, what is the gage pressure at the center of the
pipe?
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EXAMPLE 3.6
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EXAMPLE 3.7
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Pressure difference measurement Using
a U-Tube Manometer. The U-tube manometer can be connected at both ends
to measure pressure difference
between these two points
pressure at C = pressure at D
pC= pD
pC= pA+ g ha
pD= pB+ g (hb+ h) + mang h
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pA + g ha= pB+ g (hb + h) + mang h
Giving the pressure difference
pA- pB= g (hb- ha) + (man- )g h
Again if the fluid is a gas man>> , then the terms involving
can be neglected,
pA- pB= mang h
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Example In the figure below two pipes containing the same fluid of
density = 990 kg/m3 are connected using a u-tubemanometer. What is the pressure between the two pipes if
the manometer contains fluid of relative density 13.6?
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EXAMPLE 3.8
A differential mercury manometer is connected to two pressure taps in
an inclined pipe as shown in Fig. 3.12. Water at 50F is flowingthrough the pipe. The deflection of mercury in the manometer is 1
inch. Find the change in piezometric pressure and piezometric head
between points 1 and 2.
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Example
a tank of oil with one side open to the atmosphere and the
other side sealed with air above the oil. The oil has a
specific gravity of 0.90.
Calculate the gage pressure at
points A, B, C, D, E, and F and
the air pressure in the right side
of the tank.
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Example
Find the location of the surface in the manometer The
distance h is the height of the liquid in the manomoter
above the heavier liquid in the tank.
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Example
Specific weight of fluid