pressure and its types

                     Pressure                           

Definition:-

Pressure is an expression of force exerted on a surface per unit area, i.e., the force applied is perpendicular to the surface of object per unit area.

As the amount of gas increases assuming the volume of chamber and the temperature remain constant the pressure increases.

Unit:-
            Standard unit and also the S.I. unit of pressure is Pascal (Pa) and Metric unit of pressure is Bar.

1 Pascal is defined as a force of one newton per square metre

i.e.,          1 Pascal = 1 N/m2

                1 Bar = 10^5 N/m2

FPS   =  lb/in^2

CGS   =  g/cm^2

MKS  =  kg/m^2

SI unit = N/m^2

Types of Pressure:-

1 Absolute pressure
2 Atmosphere pressure
3 Gauge pressure

Measuring Instruments:-

I) Manometers

a)  Simple manometer

i Piezometer

ii 'U' tube manometer

iii single column manometer

b)  Differential manometer

i 'U' tube differantial manometer

ii Inverted 'U' tube manometer

II) Mechanical Gauges

a)  Diaphragm pressure gauge

b)  Bourdon's tube pressure gauge

c)  Dead weight pressure gauge

d)  Bellows pressure gauge

Properties of Pressure:-

1. The pressure in a liquid increases with increase in depth.

2. The pressure at a point increases with the density of the liquid.

3. The pressure is same in all directions about a point in liquid at rest.

4. Upward pressure at a point in a liquid is equal to downward pressure.

Pascal's Law:-

A French scientist, Pascal stated that the pressure applied at any point in liquid, at rest is transmitted equally in all directions. This is known as Pascal' law.

Applications of Pascal's law:-

Pascal's law is applied in many devices like the siphon, hydraulic press, hydraulic lift, air compressor, rotary pump and hydraulic brake. These hydraulic machines are based on the principle of transmission of pressure in liquids.

Principle of Hydraulic press:-

Two cylinders having different cross sectional area are connected to each other by a horizontal connecting tube.

The apparatus is filled with a liquid. The two cylinders are fitted with air tight piston .

By giving a small input force on a plunger of a small crosss sectional area cylinder a large output force are produced on the ram of large cross sectional area cylinder. 

  According to Pascal's law, small input pressure exerted on plunger

is transmitted by the liquid to the ram without any loss.

Therefore a small force can be used to lift a much large force or weight. 

 Force on plunger (F) ÷  Plunger area(a)
Weight on the ram(W) ÷ Ram area(A)

          F/a  = W/A

Weight on the ram (W) = FxA / a

Properties of Air:-

• Actually speaking, air is a mixture of gases. Air is invisible, colourless,odourless and tasteless.

• Composition: The main constituents of air by volume are 78% nitrogen, 21% oxygen, and 1% other gases. such as argon and carbon dioxide.

• The gaseous layer of air around the earth is known as atmosphere.

Pressure Relationship :- 
  Atmospheric pressure:-  
                                            The air surrounding the earth exerts a pressure on the earth's surface. The pressure prevailing directly on the earth's surface is known as atmospheric pressure.

• The atmospheric pressure is also referred to as reference pressure. Normally it considers the sea level as its reference point.

• The atmospheric pressure may be calculated from the fundamental principle of barometer which states that the barometer reads the pressure due to the height of mercury (Hg) in the tube and its weight.

∵ Atmospheric pressure = ⍴ g h

Where (rho) ⍴ = Density of Hg = 13600 kg/m^3

g = Acceleration due to gravity = 9.81 m/s^2

h = height of Hg column = 760 mm of Hg at normal sea level.

Substituting the above values in equation, we get

Atmospheric pressure = 13600 x 9.81 x 0.76 = 1,01,396 N/m^2

                    = 1.013 bar

But for easy and simple calculation, we take the atmospheric pressure as 1 bar.

1. Absolute pressure:-  
                                 absolute pressure is defined as the pressure which is measured with reference in absolute vacuum pressure.

2 Gauge pressure:- 
                                It 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 a zero.

3 Vacuum pressure:-
                                   It is defined as the pressure below the atmospheric pressure.

Mathematically:

i) Absolute pressure = Atmospheric pressure + Gauge pressure

              Pab = Patm + Pg

ii) Absolute pressure = Atmospheric pressure - Vacuum pressure

             Pab = Patm - Pvacc

iii) Vacuum pressure = Atmospheric pressure – Absolute pressure

1 Atmospheric pressure = 76 cm of mercury = 33.91 ft of water

= 76 x 13.6 gm/cm^2

= 76 x 13.6 x 10-3 kg/cm^2

= 76 x 13.6 x 10-3 x 9.8 N/cm^2

= 10.13 N/cm^2

= 1.013 bar

1 Pascal = 1 N/m^2

1 bar = 10^5 Pascal = 10^5 N/m^2 = 10 N/cm^2

1 bar = 0.986923 atmosphere

1 millibar = 0.01 N/cm^2 = 10^-2 N/cm^2

1 atmospheric Pressure (FPS) = 14.7 Pound/inch^2 (psi)

1 atmospheric Pressure (Metric) = 1.0336 Kg/cm^2

1 atmospheric Pressure (Metric) = 1.014 x 10^6  dyne /cm^2

Pressure gauges:-

They are instruments or devices used to measure the pressure of liquid steam or gas contained in a vessel. There are also known as mark meters.

Types of manometers:-

• Open tube

• Closed tube

• Differential type

• Inverted type

Mechanical pressure gauges:-

• Bourden's pressure gauges

• Diaphragm pressure gauges:-

Diaphragm pressure gauges are used to measure gases and liquids. They cover measuring spans from 10 mbar to 40 bar. The measuring element consists of one circular diaphragm clamped between a pair of flanges. The positive or negative pressure acting on these diaphragms causes deformation of the measuring element.

 

• Dead weight pressure gauges:-

A dead weight tester apparatus uses known traceable weights to apply pressure to a fluid for checking the accuracy of readings from a pressure gauge.

• Bellows pressure gauge:-

Bellow gauge of the two A bellows gauge contains an elastic element that is a convoluted unit that expands and contracts axially with changes inpressure. The pressure to be measured can be applied to the outside or inside of the bellows.

Open tube manometer:-

It is more suitable to measure pressure in vessels which is having little variation to atmospheric pressure. It is a 'u' shaped tube containing mercury having its one end connected to the vessel container in which the liquid is there whose pressure is to be determined. The other end is open. The manometer will show a difference in both the limbs of the tube when the pressure inside the vessel is more or less than the air pressure outside.

For a barometer reading with reference to an atmospheric pressure of 1 bar we have

Pa = 1 + Po

Pa = 1 - Pu

 Bourdon tube pressure gauges :-

In I.C. Engines, Bourdon tube pressure gauges are widely employed for measurement of pressure, temperature and vacuum. In these gauges, a Bourdon tube which is a tempered, one is used and it attempts to straighten out under pressure and temperature and contact under vacuum.

phosphor bronze tube or elliptical cross section is used and bent to an arc of a circle. The free end of the tube is sealed under internal pressure (or temperature), it attempts to straighten out. During this process, it operates sector, pinion and needle which indicates pressure or temperature over a calibrated dial. The entire unit is mounted on a casing and covered with glass and frame and around it.

Vacuum gauges:-

These are also of Bourdon tube type gauges where the tube attempts to contract under vacuum thus recording vacuum of the engine in mm Hg (millimeters of mercury)

A reading of 760 mm Hg is prefect vacuum (zero absolute pressure)

A zero of say 300 mm Hg means to say that 300 mm of vacuum is equivalent to (760-300) 460 milli Hg absolute pressure.

• Vacuum gauges are often used by service mechanics to find out the mechanical condition of the engine and whether valves, ignition timing and carburettor setting are correct and carry out fine adjustments to obtain the best performance of the engine.

• Vacuum in Diesel Engine governors:- This is measured by water column methods in fuel injection test bench

• Vacuum in manifolds of an engine:- This can be measured by using vacuum gauge

• Over-pressure:- The gas pressure of the tyre is bigger than the pressure of the atmosphere. In the tyre we have over pressure.

• Under-pressure:- The gas pressure in the cylinder during the suction process is smaller. There is under pressure in the cylinder.

• Absolute pressure:- The absolute pressure = air pressure + over-pressure. The pressure in vacuum is 0 bar.

The unit for gas pressure is bar.

Pa = absolute pressure

Po = over pressure

Pu = under pressure

Air pressure in technical calculations is assumed to be 1 bar.

Rules and examples

Absolute pressure = over-pressure + air pressure

Pa = Po + 1 bar

Over-pressure = absolute pressure - air pressure

Po= Pa - 1 bar

Under-pressure = air pressure - absolute pressure

Pu = 1 bar - Pa

Absolute pressure = air pressure - under-pressure

Pa = 1 bar - Pu

Properties of gases:-

1 Charle’s law

First law or law of volume

At constant pressure the volume (V) of a given mass of gas is directly proportional to its absolute temperature(T)

V ∝T ; V/T = K (K - Constant)

Second law or law of pressure

At constant volume the pressure (P) of a given mass of gas is directly proportional to its absolute temperature(T).
P∝T;   P /T = K (K - Constant)

2 Boyle’s law or Gas law

At constant temperature the volume (V) of a given mass of gas is inversely proportional to its pressure. (P)

V∝ 1/P ; PV = K (K - Constant)

3 Perfect gas equation

Since boyle’s law and charle’s law can not be applied independently due to changes in pressure, volume and temperature a combined law called “gas equation” has been formulated.

                    Gas equation is relating to pressure, volume and temperature of perfect gas which obeys both the boyle’s law and charle’s law. A gas which obeys boyle’s and charle’s law is called ideal gas.

As per boyle’s law

V∝ 1/P ;  PV = K (Constant)
P1 V1= P2 V2=K

As per charle’s law
V∝T     V/T=K(constant)  V1 / T1 = V2 / T2 = K

Combining the above two laws,

P1 V1 = P2 V2   = R

   T1        T2
                                                                    [R = gas constant]

P V / T = R

P V = RT

If mass of the gas is m, then

PV = mRT

Gas constant R = 29.27 kgf.m / kg/ k

                         = 287 joule/Kg/k

True gas and its properties

1 It has mass and volume. So, it has weight.

2 It can be compressed or expanded into a container.

3 It is invisible.

4 General Gas Law

Boyle's, Charles', and Gay-Lussac's laws can be combined to obtain the general gas law is given by,

PV/T = Constant (or)
P1V1/ T1    =         P2V2 / T2             =      P3V3 / T3

In the perfect gas law, the P and T represents

absolute pressure and absolute temperature

(in °K) respectively.