### Pressure Measurement

```What is Fluid Pressure?

Fluid contained in a vessel exerts force on
all its sides. The force per unit area is
called Fluid Pressure.

Mathematically-
p= P/A
where P= the force and
A= area on which the force acts
p= intensity of pressure
S.I. unit is N/m2 or Pascal
Pressure HeadRepresents the internal energy of a fluid
due to the pressure exerted on its
container. It may also be called static
 Mathematically,
h=p/γ
p=intensity of pressure
γ=specific wt. of the liquid
Hence, pressure intensity may be expressed
in two ways1. As force per unit area &
2. As an equivalent static head.

Pascal’s Principle:
Any change in the pressure of a fluid is transmitted
uniformly in all directions throughout the fluid.
A small force F1 applied to a piston with a small
area produces a much larger force F2 on the larger
piston. This allows a hydraulic jack to lift heavy
objects.
Atmospheric,absolute and gauge pressure
Devices used for measuring pressureFluid pressure may be measured by following
devices1. Manometers(a) Simple manometers-

PIEZOMETER, U-TUBE MANOMETER &
COLUMN MANOMETER.
SINGLE-
(b) Differential manometersU-TUBE DIFFERENTIAL MANOMETER & INVERTED
U-TUBE DIFFERENTIAL MANOMETER.
2. Mechanical gaugesBOURDON TUBE PRESSURE GAUGE, DIAPHRAGM
PRESSURE GAUGE & VACUUM GAUGE.
MANOMETER- measures pressure at a point in
a fluid by balancing the column of fluid by the
same or another column of fluid.
U-TUBE MANOMETER
PIEZOMETER
SINGLE-COLUMN
MANOMETERS
INCLINED
VERTICAL
Differential manometers-
U-TUBE
DIFFERENTIAL
MANOMETER
INVERTED U-TUBE
DIFFERENTIAL
MANOMETER
Simple manometersConsists of a glass-tube whose one end is
connected to a point where pressure is to
be measured and the other end is exposed
to the atmosphere
IncludesPiezometers
U-tube manometers &
Single-column manometers
PIEZOMETER-It is the simplest form of
Manometer,used for measuring
moderate pressure.It consist of a
Tube,open at one end to the
Atmosphere,in which,Liquid can
rise freely without overflow,the
Height,to which the Liquid rises up
in the Tube,gives the Pressure
p= γ h
Measures gauge pressure only.
-not suitable for measuring
Negative Pressure because Air will
enter in the pipe through the Tube
Cannot be used for
measuring large pressures in
case of lighter liquids.
&
Cannot be used for
measuring gas pressures
U-tube manometer"U"-Tube manometer
S2
enables the pressure of
both liquids and gases to
be measured with the
same instrument.
 The fluid whose pressure
is being measured should
have a mass density less
S1
than that of the
manometric fluid and the
two fluids must be
immiscible.
The pressures in the right limb and the left limb
above the datum line B-C are equal
FOR POSITIVE
Pressure head above B-C in the right limb= h2S2
GAUGE
Pressure head above B-C in the left limb = h+h1S1
PRESSURE
Equating,

h+h1S1= h2S2 OR, h= h2S2 _ h1S1
.
U-TUBE MANOMETER
The pressures in the right limb and the left limb above
the datum line X-X are equal
Pressure head above X-X in the right limb= 0
Pressure head above X-X in the left limb = h+h1S1+h2S2
Equating,
h+h1S1+h2S2 = 0 OR ,h = _( h1S1+h2S2)
S2
FOR
NEGATIVE
GAUGE
PRESSURE
S1
SINGLECOLUMN
MANOMETER
(VERTICAL)
A>>a
Light liquid
A= area of
crossection
a= area of
crossection
Datum line
A x Z1 = a x h 2
Or, Z1= (a x h2)/A ............(1)
Equating the pressure heads above the datum line Z-Z,
Heavy liquid
S2
h +(h1+ Z1)S1 = (h2+ Z1)S2
or, h = (h2+ Z1)S2 _ (h1+ Z1)S1 or, h = Z1 (S2 _ S1) + h2S2 _ h1S1
= { (a x h2)/A } (S2 _ S1) + h2S2 _ h1S1
As A>>a, so ratio A/a is very very small and can be neglected and above equation becomes,
h = h2S2 _ h1S1…………………………………………………… (2)
#useful for the
measurement of
small pressures
and is more
sensitive than the
vertical tube.
-# Due to
inclination the
distance moved by
the heavy liquid in
the right limb is
more.
Let,
l = length of the heavy liquid moved in the right limb,
θ = inclination of right limb horizontal and
Z2 = vertical rise of liquid in the right limb from X-X= l sin θ
Putting the value of Z2 in equation (2) we get,
h = l sinθ x S2 _ h1S1
SINGLECOLUMN
MANOMETER
(INCLINED)
Differential U-tube manometer
a differential manometer is used to
measure the difference in pressures
between two points in a pipe, or in two
different pipes.
-most commonly used types1.U-tube differential manometer.
2.Inverted U-tube differential
manometer
Case 1.Figure (a) below shows a differential
manometer whose two ends are connected
with two different points A and B at the same
level and containing same liquid.
We know that the pressures in the left limb and the
right limb , above the datum line X-X, are equal
Pressure head in the left limb = hA + (h +h1)S1
Pressure head in the right limb = hB + h1S1 + hS
Equating,
hA + (h +h1)S1 = hB + h1S1 + hS
or, hA - hB = h ( S – S1)
h A - h B = h ( S – S1 )
case 2- Figure (b) below shows a
differential manometer whose two ends
are connected with two different points A
and B at different levels and containing
different liquids.
We know that the pressures in the left limb and
the right limb , above the datum line X-X, are
equal
Pressure head in the left limb = hA + (h +h1)S1
Pressure head in the right limb = hB + h2S2 + hS
Equating,
hA + (h +h1)S1= hB + h2S2 + hS
or,
h A - h B = h ( S – S1 ) + h 2 S 2 - h 1 S1
Thus, difference of pressure at A and B,
h A - h B = h ( S – S1 ) + h 2 S2 - h 1 S1
Mechanical gaugesUsed for measuring medium and high
pressures.
 Employs elastic systems such as tubes,
diaphragms, bellows,etc.
 TypesBourdon tube pressure gauge.
Diaphragm gauge &
Vacuum gauge.

Bourdon tube pressure gauge
The bourdon tube pressure instrument is
one of the oldest pressure sensing
instruments in use today. The bourdon tube
consists of a thin-walled tube that is
flattened diametrically on opposite sides to
produce a cross-sectional area elliptical in
shape, having two long flat sides and two
short round sides. The tube is bent
lengthwise into an arc of a circle of 270 to
300 degrees. Pressure applied to the inside
of the tube causes distension of the flat
sections and tends to restore its original
round cross-section. This change in crosssection causes the tube to straighten
BOURDON TUBE PRESSURE GAUGE
slightly.
Since the tube is permanently fastened at
one end, the tip of the tube traces a curve
that is the result of the change in angular position with respect to the centre. Within
limits, the movement of the tip of the tube can then be used to position a pointer to
indicate the applied internal pressure.
Diaphragm gauge
This type of gauge employs a
metallic disc or diaphragm
instead of a bent tube. This
tube or diaphragm is used
for actuating the indicating
device.
Referring to the figure below,
when pressure is applied on
the lower side of the
diaphragm it is deflected
upward. This movement of
the diaphragm is transmitted
to a rack and pinion. The
latter is attached to the
spindle of needle moving on
a graduated dial. The dial can
suitable scale.
Vacuum GaugeBourdon gauges discussed earlier
can be used to measure vacuum
instead of pressure. Slight changes in
the design are required for this
purpose. Thus, in this case, the tub is
bent inwards instead of outwards as in
pressure gauges. Vacuum gauges are