SIMPLE MANOMETER: U-TUBE MANOMETER, ADVANTAGES AND DISADVANTAGES

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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Paddle wheel work, flow work

Shaft work

Stirling cycle

Ericsson cycle

Thin cylindrical and spherical shells, 

Stresses in thin cylindrical shells

Circumferential stress or Hoop stress

Longitudinal stress