We were discussing the basic definition
and significance of Pascal’s
Law along with its derivation , Vapour
pressure and cavitation, Absolute
pressure, Gauge pressure, Atmospheric pressure and Vacuum pressure, pressure
measurement and also the basic concept of Piezometer in our previous
posts.
Today we will understand here the basic
concept of U- Tube manometer to measure the pressure at a point in fluid, in
the subject of fluid mechanics, with the help of this post.
We will discuss here the pressure
measuring instrument i.e. U- Tube manometer in detail with the help of this
post. We will also see here the advantages and drawbacks of U- Tube manometer.
Further, we will discuss another simple
manometer i.e. Single column manometer in our next post. So let us brief here
simple manometer and U-Tube manometer.
Simple Manometer
Simple manometer is basically, a
pressure measuring device, used to measure the pressure at a point in fluid by
balancing the column of fluid by the same or another column of fluid.
Simple manometer will have one glass
tube made of pyralex glass. One end of glass tube will be connected with a
point where we need to measure the pressure and another end will be open to
atmosphere.
U-Tube manometer
U-Tube manometer will have one glass
tube in U shape. One end of this glass tube will be connected with the point
where we need to measure the pressure and another end will be open to
atmosphere.
Glass tube will be filled with mercury
or any other liquid having more specific gravity as compared with the specific
gravity of the liquid whose pressure needs to be measured.
Let us consider we have one container
filled with a liquid and we need to measure the pressure of liquid at point B
in the container. Let us consider that we are using the pressure measuring
device “U-Tube manometer” here to measure the pressure of liquid at point B as
displayed here in following figure.
We will discuss here the following two
cases.
Case 1:
For gauge pressure
Gauge pressure is basically
defined as the pressure which will be measured above or below the atmospheric
pressure i.e. atmospheric pressure here will be taken as datum line. Gauge
pressure will be measured with the help of pressure measuring instrument.
Atmospheric pressure will be marked as zero on the scale of pressure measuring
instrument.
Let us consider the following terms from
above figure.
P = Pressure at point B and we need to
measure this pressure or we need to find the expression for pressure at this
point.
A-A = Datum Line
h1 = Height of lower specific
gravity liquid above the datum line
h2 = Height of higher
specific gravity liquid above the datum line
S1 = Specific gravity of the
light liquid
S2 = Specific gravity of the
heavy liquid
ρ1 = Density of the light
liquid = 1000 x S1
ρ2 = Density of the heavy
liquid = 1000 x S2
Pressure in the left column above the
datum line = P + ρ1g h1
Pressure in the right column above the
datum line = ρ2g h2
As pressure is same for the horizontal
surface and therefore we will have following equation as mentioned here
P + ρ1g h1 = ρ2g
h2
P = ρ2g h2 - ρ1g
h1
P = (ρ2h2 - ρ1h1) x g
Case 2:
For vacuum pressure
Vacuum pressure is basically
defined as the pressure which will be measured below than the atmospheric
pressure and therefore that measured pressure will be with negative sign and we
will say it vacuum pressure or negative gauge pressure.
Vacuum pressure will be
measured by analyzing the manometer which is displayed above. Heavy liquid here
is going down below the datum line as displayed above and we will have
following equation.
Pressure in the left column above the
datum line = P + ρ1g h1 + ρ2g h2
Pressure in the right column above the
datum line = 0
P + ρ1g h1 + ρ2g
h2 = 0
P = - [ρ1g h1 + ρ2g
h2]
Advantages of U–Tube manometer
There are following advantages of using U
– Tube manometer for measuring the pressure at a point of fluid in a container
and these are as mentioned here.
Technique of using U – Tube manometer is
very simple
Pressure measurement with U – Tube
manometer is quite economical
U – Tube manometer will provide the
accurate pressure reading
U – Tube manometer is quite simple in
construction
Disadvantages of U–Tube manometer
There are following disadvantages of
using U – Tube manometer for measuring the pressure at a point of fluid in a
container and these are as mentioned here.
Liquid will be exposed to atmosphere in U
– Tube manometer and therefore liquid must be clean and non-toxic.
Insensitive when head will be small as
it will be very difficult to measure the pressure if h will be small.
We will discuss another type of simple
manometer i.e. Single column manometer in detail in our next post. We will
see there the advantages and disadvantages of Single column manometer too.
Do you have any suggestions? Please
write in comment box.
Reference:
Fluid mechanics, By R. K. Bansal
Image Courtesy: Google
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