Introduction to pressure measurement. Pressure measurement is important because of the following reasons:. Pressure is an important quantity that describes a system. • Pressure is invariably an important process parameter. • Pressure difference is used many a time as a means of measuring the
Pressure is an important quantity that describes a system.
• Pressure is invariably an important process parameter.
• Pressure difference is used many a time as a means of measuring the
flow rate of a fluid.
• Pressure level spans some 18 orders of magnitude from the lowest to
the highest pressures encountered in practice.
The table below (حفظ)
Useful units and conversion factors: are shown in
Pressure Measurement are shown in
Divided into three categories:
1. Absolute pressure – pressure at a point in a fluid relative to a
vacuum (absolute zero of pressure)
2. Gauge Pressure – pressure relative to local atmospheric
3. Differential Pressure – difference between two unknown
pressures, neither of which is atmospheric pressure.
Forms of pressure are shown in
Relationship between absolute and gauge pressures are shown in
Conversion factors for units of pressure are shown in
Manometers are shown in
Column of liquid supported produced pressure P = rh, where is the
density of the liquid and h the height of the column. Thus for case a)
Sensors using elastic properties are shown in
Three types of device:
1. Bourdon Tubes
– basis of many mechanical gauges.
– low cost barometers.
3. Diaphragms or Membranes
– most commonly used structures for pressure
Bourdon Tubes are shown in
Bellows are shown in
a) Single Bellows Gauge
b) Double Bellows Gauge
Diaphragms and Membranes are shown in
Bourdon tube are shown in
Capacitive pressure sensors are shown in
- capacitor – usually differential
-Deformation element = pre-strained metallic membrane – serves as
grounded electrode -Range: Δp = 1 mbar – 10 bar, total p up to 400 bar
U – Tube manometer are shown in
The simplest of the gages that is used for measuring pressure is a U – tube
manometer shown in the figure below. The U tube needs to be vertically oriented
and the acceleration due to gravity is assumed to be known. The height ‘h’ is
the measured quantity.
The pressure to be measured is that of a system that involves a fluid (liquid or a gas) different from the manometer liquid. Let the density of the fluid whose pressure being measured be ρf and that of the manometer liquid be ρf.
Equilibrium of the manometer liquid requires that there be the same force in
the two limbs across the plane AA. We then have
This may be rearranged to read
are also used. A second common liquid is water. When measuring pressures
close to the atmospheric pressure in gases, the fluid density may be quite
negligible in comparison with the manometer liquid density. One may then
use the approximate expression
The manometer liquid is chosen based on its density with respect to the
density of the fluid whose pressure is being measured and also the pressure
difference that needs to be measured. Indeed small pressure differences are
measured using water or organic liquids as the manometer liquid such that
the height h measured is sufficiently large as to be estimated with sufficient
Well type manometer other liquids
Sometimes a well type manometer is used. Schematic of a well type manometer is shown in the figure below.
height is measured. The advantage of the well type design is that relatively large pressure differences may be measured with enough manometer liquid
being available for doing so! We assume that the manometer liquid is
incompressible and hence the following holds:
This expression simply states that there is no change in the volume of the
fluid and hence the mass. Here ‘A’ is the well cross section area given by
while ‘a’ is the tube cross section area given by
Equation the manometer* is recast for this case as
Using Equation * in Equation **, after some rearrangement we get
If the area ratio
is very small compared to unity, we may use the
approximate formula that is identical with Equation
Well type manometer with inclined tube the manometer
In case the measured pressure difference is small one may use an inclined
well type manometer shown in the figure below
The manometer height is now given by the manometer
Can be replaced by
It is clear that the inclination of the tube amplifies the measured quantity and hence improves the precision of the measurement.
Bourdon gage the manometer
Bourdon gages are available to cover a large range of pressures. Bourdon
gages are purely mechanical devices utilising the mechanical deformation
of a flattened but bent tube that winds or unwinds depending on the pressure
difference between the inside and the outside. The motion is against a spring
torque such that a needle attached to the shaft indicates directly the pressure
difference. The working principle of the bourdon gage is explained with
reference to the figure below .
Example of Bourdon tube application : dead weight tester having a bent shape
A Bourdon pressure gage may be calibrated by the use of a dead weight
tester, a schematic of which is shown in Figure
Pressure transducers a piston may be
1. Pressure tube with bonded strain gage
2. Diaphragm/Bellows type transducer
3. Capacitance pressure transducer
The common feature of all these transducers is that the pressure to be
measured introduces a strain or movement in a mechanical element that is
measured by different techniques.
The strain is measured by
a) strain gage
b) linear voltage displacement transducer (LVDT)
c) the change in capacitance.
Pressure tube with bonded strain gage a piston may be
The principle of a pressure tube with bonded strain gage may be understood
by referring to the figure below.
suitable wall thickness one end of which is closed with a thick plate.
- Because the end plate is very thick it undergoes hardly any strain. The tube, however, experiences a hoop strain due to internal pressure (indicated by the blue
A strain gage mounted on the tube wall experiences the hoop strain.
The way the strain gage works is dealt with below.
Diaphragm/Bellows type transducer: of a tube of
Pressure signal is converted to a displacement in the case of
diaphragm/bellows type pressure gage.
The diaphragm or bellows acts as a spring element that undergoes a displacement under the action of the pressure. Schematic of diaphragm and bellows elements are shown respectively in the figures below (a) and (b).
In the above figure a Linear Variable Differential Transformer (LVDT) is used as a displacement transducer. a strain gage for measuring the strain in the diaphragm by fixing it at a
suitable position on the diaphragm .
Capacitance diaphragm gage: Transformer (
- The Figure above shows the schematic of a capacitance type pressure transducer.
-The gap between the stretched diaphragm and the anvil (remains fixed
because of its mass) varies with applied pressure due to the small
displacement of the diaphragm.
This changes the capacitance of the gap.
-The theoretical basis for this is derived below.
Bridge circuit for capacitance pressure gage: pressure transducer.