SINGLE COLUMN MANOMETER

 SINGLE COLUMN MANOMETER .

           Single column manometer is a modified form of a U -tube manometer in which a reservoir, having a large cross -sectional area (about 100 times) as compared to the area of the tube is connected to one of the limbs (say left limb) of the manometer as shown in figure. Due to large cross -sectional area of the reservoir, for any variation in pressure, the change in liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of the liquid in the other limb. The other limb may be vertical or inclined. Thus there are two types of single column manometer as :

    1. Vertical Single Column Manometer. 

    2. Inclined Single Column Manometer. 

VERTICAL SINGLE COLUMN MANOMETER

VERTICAL SINGLE COLUMN MANOMETER

  Above figure shows the vertical single column manometer. Let X-X be the datum line in the reservoir and in the right limb of manometer, when it is not connected to the pipe. When the manometer is connected to the pipe, due to high pressure at A, the heavy liquid in the reservoir will be pushed downward and will rise in the right limb. 

Vertical Single Column Manometer

2.  Inclined Single Column Manometer. 

     

Inclined Single Column Manometer

  

  Figure shows the inclined single column manometer. This manometer is more sensitive. Due to inclination the distance moved by the heavy liquid in the right limb will be more. 

Inclined Single Column Manometer

MEASUREMENT OF PRESSURE

MEASUREMENT OF PRESSURE. 

          The pressure of a fluid is measured by the following devices :

1. Manometers 

2. Mechanical Gauges 

1. MANOMETERS. 

              Manometers are defined as the devices used for measuring the pressure at a point in a fluid by balancing the fluid column by the spring or dead weight. The commonly used mechanical pressure gauges are : 

 (a) Diaphragm pressure gauge, 

 (b) Bourdon tube pressure gauge, 

 (c) Dead -weight pressure gauge, and 

 (d) Bellows pressure gauge. 

SIMPLE MANOMETERS. 

            A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and other end remains open to atmosphere. Common types of simple manometers are : 

(1) Piezometer, 

(2) U -tube Manometer, and

(3) Single Column Manometer. 

(1) PIEZOMETER. 

              It is the simplest form of manometer used for measuring gauge pressures. One end of this manometer is connected to the point where pressure is to be measured and other end is open to the atmosphere as shown in figure. The rise of of liquid gives the pressure head at that point. If at a point A, the height of liquid say water is h in piezometer tube, then pressure at A

                           =  ⍴ × g × h  N/m²

Piezometer

(2)  U -tube Manometer. 

                        It consists of glass tube bent in U-shape, one end of which is connected to a point at which pressure is to be measured and other end remains open to the atmosphere as shown in figure. The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured. 

(a) For Gauge Pressure. 

(a) For gauge pressure

For gauge pressure

(b) For Vacuum Pressure. 

(b) For vacuum pressure

For vacuum pressure

ABSOLUTE, GAUGE, ATMOSPHERIC AND VACUUM PRESSURES

ABSOLUTE, GAUGE, ATMOSPHERIC AND VACUUM PRESSURES. 

            The pressure on a fluid is measured in two different systems. In one system, it is measured above the absolute zero or complete vacuum and it is called the absolute pressure and in other system, pressure is measured above the atmospheric pressure and it is called gauge pressure. Thus :

1. Absolute pressure is defined as the pressure which is measured with reference to absolute vacuum pressure. 

2. Gauge pressure is defined as the pressure which is measured with the help of a pressure measuring instrument, in which the atmospheric pressure is taken as datum. The atmospheric pressure on the scale is marked as zero. 

3. Vacuum pressure is defined as the pressure below the atmospheric pressure. 

    The relationship between the absolute, gauge pressure and vacuum pressure are shown in figure:

Relationship between pressures

Note. (1) The atmospheric pressure at sea level at 15°C is 101.3 kN/m² or 10.13 N/cm² in SI unit. In case of MKS units, it is equal to 1.033 kgf/cm².

(2) The atmospheric pressure head is 760 mm of mercury or 10.33 m of water. 

PRESSURE VARIATION IN A FLUID AT REST

Pressure Variation In A Fluid At Rest. 

                      The pressure at any point in a fluid at rest is obtained by the Hydrostatic Law which states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point. This is proved as : 

    Consider a small fluid element as shown in figure :

Forces on a fluid element.

Let    ∆A = Cross -sectional area of element

          ∆Z = Height of fluid element

            p = Pressure on face AB

            Z = Distance of fluid element from free surface. 

Derivation of Hydrostatic Law. 

FLUID PRESSURE AT A POINT & PASCAL'S LAW

FLUID PRESSURE AT A POINT. 

                       Consider a small area dA in large mass of fluid. If the fluid is stationary, then the force exerted by the surrounding fluid on the area dA will always be perpendicular to the surface dA. Let dF is the force acting on the area dA in the normal direction. Then the ratio of (dF/dA) is known as the intensity of pressure or simply pressure and this ratio is represented by p. Hence mathematically the pressure at a point in a fluid at rest is 

                                      p = dF /dA.

 If the force (F)  is uniformly distributed over the area (A)  , then the pressure is given by

                            p = F /A = Force /Area  . 

So,      Force or pressure force, 

                                     F =  p ×A  . 

The units of pressure are : (1) kgf /m² and kgf /cm² in MKS units, (2)  Newton /m² and N /mm² in SI units. N /m² is known as Pascal and is represented by Pa. Other commonly used units of pressure are MPa ( Mega pascal) , kPa ( kilo pascal) and bar . 

PASCAL'S LAW. 

                          It states that the pressure or intensity of pressure at a point in a static fluid is equal in all directions. This is proved as :

       The fluid element is of very small dimensions i.e. , dx, dy and ds. 

Page -1 ( PASCAL'S law) 

and the rest part is : 

 

Page -2 (PASCAL'S law)

VAPOUR PRESSURE AND CAVITATION

VAPOUR PRESSURE AND CAVITATION.

                                 A change from the liquid state to the gaseous state is known as vaporization. The vaporization (which depends upon the prevailing pressure and temperature condition) occurs because of continuous escaping of the molecules through the free liquid surface.
Consider a liquid (say water) which is confined in a closed vessel. Let the temperature of liquid is 20°C and pressure is atmospheric. This liquid will vaporise at 100°C . When vaporization takes place, the molecules escape from the free surface of the liquid. These vapour molecules gets accumulated in the space between the free liquid surface and top of the vessel. These accumulated vapour exert a pressure on the liquid surface. This pressure is known as vapour pressure of the liquid or this is the pressure at which the liquid is converted into vapours.
          Again consider the same liquid at 20°C at atmospheric pressure in the closed vessel. If the pressure above the liquid surface is reduced by some means, the boiling temperature will also reduce. If the pressure is reduced to such an extent that it becomes equal to or less than the vapour pressure, the boiling of the liquid will start, though the temperature of liquid is 20°C. Thus a liquid may boil even at ordinary temperature, if the pressure above the liquid surface is reduced so as to be equal or less than the vapour pressure of the liquid at that temperature.
               Now consider a flowing liquid in a system. If the pressure at any point in this flowing liquid becomes equal to or less than the vapour pressure, the vaporization of the liquid starts. The bubbles of these vapours are carried by the flowing liquid into the region of high pressure where they collapse, giving rise to high impact pressure. The pressure developed by the collapsing bubbles is so high that the material from the adjoining boundaries gets eroded and cavities are formed on them. This phenomenon is known as cavitation.
                       Hence the cavitation is the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and sudden collapsing of these vapour bubbles in a region of higher pressure. When the vapour bubbles collapse, a very high pressure is created. The metallic surfaces, above which the liquid is flowing, is subjected to these high pressures which cause pitting action on the surface. Thus cavities are formed on the metallic surface and hence the name is cavitation.

CAPILLARITY

CAPILLARITY 

                      Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small tube relative to the adjecent general level of liquid when the tube is held vertically in the liquid. The rise of liquid surface is known as capillary rise while the fall of liquid surface is known as capillary depression. It is expressed in terms of cm or mm of liquid. Its value depends upon the specific weight of the liquid, diameter of the tube and surface tension of the liquid.

CAPILLARITY RISE 

EXPRESSION FOR CAPILLARY RISE. 

                     Consider a glass tube of small diameter ‘d’ opened at both ends and is inserted in a liquid, say water. The liquid will rise in the tube above the level of the liquid. 

      Let, h  = height of the liquid in the tube

                        Under a state of equilibrium, the weight of liquid of height ‘h’ is balanced by the force at the surface of the liquid in the tube is due to surface tension. 

      Let  𝛔 = Surface tension of liquid

              θ = Angle of contact between liquid and glass tube.

EXPRESSION FOR CAPILLARITY RISE

   

                                   The End. 

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