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, Piezometer, Single column manometer and also the basic
concept of U-tube manometer in our previous posts.

Today
we will understand here the basic concept of inverted U-tube differential
manometer to measure the difference of low pressures between two points in the
fluid, in the subject of fluid mechanics, with the help of this post.

###
**Let us brief first differential manometer**

Differential
manometer is also one type of pressure measuring device which is basically used
to measure the difference of pressure between two points in a pipe or between
two different pipes.

Let us consider that we have two pipes as displayed here in following figure. A is
one point in first pipe and B is other point in second pipe. There will be one
U-tube contained with heavy liquid and two ends of this U-tube manometer will
be connected with these two points i.e. point A and point B.

Pressure
difference between point A and point B will be measured with the help of
differential manometer. Differential manometers are basically
used to measure the pressure above atmospheric pressure.

###
**Types of differential manometers**

U-tube
differential manometer

Inverted
U-tube differential manometer

We
have already discussed the basic concept of U-tube differential manometer, now it’s
time to go ahead to understand the basic concept of inverted U-tube
differential manometer.

###
**Inverted U-tube differential manometer**

Inverted
U-tube differential manometer will be used for measuring the vacuum pressure. Inverted
U-tube differential manometer will have one inverted U-tube contained with
light liquid.

Let
us consider that inverted U tube differential manometer is connected with two
points in two pipes as displayed here in following figure. These two pipes are
filled with different specific gravity liquid. As displayed here in figure,
point A and point B are at different level.

Let
us consider the following terms as mentioned here.

XX
is the datum line

P

_{A}= Pressure at point A
P

_{B }= Pressure at point B
We need to measure the pressure difference between point A and point B or we need
to find out the expression for difference of pressure i.e. P

_{A}– P_{B}.
h

_{ }= Difference of light liquid level in the U-Tube
h

_{1}= Height of liquid level in left limb of manometer below the datum line
h

_{2}= Height of liquid level in right limb of manometer below the datum line
ρ

_{1}= Density of liquid which is contained in pipe A
ρ

_{2}= Density of liquid which is contained in pipe B
ρ

_{L}= Density of light liquid
We
will now determine the pressure below datum line in left limb of manometer and
also we will secure here the value of pressure below the datum line in right
limb of manometer and we will equate these two pressures to find out the
pressure difference i.e. P

_{A}– P_{B}.
Pressure
in the left limb below the datum line XX = P

_{A}- ρ_{1}g h_{1}
Pressure
in the right limb below the datum line XX = P

_{B}- ρ_{2}g h_{2}- ρ_{L }g h
As
pressure is same for the horizontal surface and therefore we will have
following equation as mentioned here.

P

_{A}- ρ_{1}g h_{1 }= P_{B}- ρ_{2}g h_{2}- ρ_{L }g h###
**P**_{A} - P_{B} = **ρ**_{1}g h_{1 }- ρ_{2}g
h_{2} - ρ_{L }g h

_{A}- P

_{B}=

_{1}g h

_{1 }- ρ

_{2}g h

_{2}- ρ

_{L }g h

We will find out the basic
definition and derivation of total pressure and centre of pressure, in the subject of fluid mechanics, in our next post.

Do you have any suggestions? Please write in comment box.

Do you have any suggestions? Please write in comment box.

###
**
Reference:**

Fluid mechanics, By R. K. Bansal

Image
Courtesy: Google

Very nice explanation

ReplyDeleteThanks a lot

Clearly defined

ReplyDeleteBut why it is used to measure low pressure difference

ReplyDeleteSir, the right hand side is wrong. It should be minus for ρ2g h2. Please correct it

ReplyDeleteThanks for correcting me, i have amended here, please check it once

Delete