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COMPRESSORS
INTRODUCTION
• A gas compressor is a device in which work is done on the gas to raise
its pressure, with an appreciable increase in its density.
• The compression of gases is an important process in many power
plants, refrigeration plants, and industrial plants.
• Industrial uses occur in connection with compressed air motors for
tools, air brakes for vehicles, servo-mechanisms, metallurgical and
chemical processes, conveying of materials through ducts,
transporting of natural gas, and production of bottled gases.
•
 Compressed Air Efficiency:
60 to 80% of the power of the prime mover is converted into an
unusable form of energy (HEAT)
And to a lesser extent, into friction, misuse and noise
Approximatel
y 10% gets to
the point of
use!!
Compressors
Dynamic
(Centrifugal)
Positive
displacement
Axial Radial
Single
Stage
Multi
Stage
Reciprocating Rotary
Single
Stage
Roots
Blower
Screw
Compressor
Non-
Lubricated
Single
Cylinder
(air cooled)
Lubricated Single
Stage
Multi
Stage
Multi
cylinder
(water
cooled)
TYPES OF COMPRESSORS
TYPES OF COMPRESSORS
According to working i)Reciprocating & ii) Rotary compressors
According to action i)Single acting & ii)double acting compressors
According to no. of stages i)Single-stage & ii)Multi-stage compressors
(a) positive displacement machines like reciprocating
compressors, Root’s blower and vane-sealed machines and
(b) turbine type like centrifugal and axial flow compressors.
TECHNICAL TERMS RELATED TO COMPRESSORS
1.Inlet Pressure – It is the absolute pressure of air at the inlet of the compressor
2.Discharge pressure- It is the absolute pressure of air at the outlet of the compressor
3.Compression ratio/pressure ratio-The ratio of discharge pressure to the inlet pressure.
As the discharge pressure is always greater than the inlet pressure, the pressure ratio is
always greater than unity.
4.Compressor capacity-The volume of air delivered by the compressor and is expressed
in m3/min or m3/s
TECHNICAL TERMS RELATED TO COMPRESSORS -
Contd…..
• Free air delivery – The actual volume of air delivered by the
compressor at NTP.The capacity of the compressor is generally given
in terms of free air delivery.
• Swept Volume – the volume of air sucked by the compressor during
its suction stroke. The swept volume of a single acting air compressor
is given by
• Vs = (π/4) D2 L
• Where D = dia of the cylinder bore
L = length of piston stroke
Mean effective pressure – The air pressure on the compressor piston
keeps on changing with the movement of the piston in the cylinder.
The mean effective pressure of the compressor is found out by
dividing the work done per cycle to the stroke volume.
A gas compression - adiabatic or involving heat transfer, depending upon the
purpose for which the gas is compressed.
For the use of compressed gas in an engine or in a combustion process,
adiabatic compression is desirable to obtain the maximum energy.
In many applications, the gas is stored in a tank or receiver for use later at
room temperature. The objective of the compression and storage
process is to increase the pressure of the gas without change of temperature.
If the gases is cooled during compression, the work required will be less than
for adiabatic compression. Another advantage of cooling is the reduction in
volume of gas and less pipe friction losses. Since cooling during the
compression process is not very effective, after-coolers are often used to cool
the gas leaving the compressor.
COMPRESSION PROCESSES
FEATURES OF RECIPROCATING COMPRESSOR
A reciprocating compressor is a positive displacement machine
that uses a piston contained within a cylinder to produce
compression.
The piston traverses the cylinder, sucking in atmospheric air at
one end of its stroke, then compressing the air when it reaches the
other end of its stroke.
This type of machine is available as an 'oil-free' compressor or as
a 'lubricated' compressor. The reciprocating compressor probably
accounts for largest number of compressors used worldwide.
RECIPROCATING COMPRESSOR
PRINCIPLE OF WORKING OF RECIPROCATING COMPRESSOR
RECIPROCATING COMPRESSOR
• flow output remains constant over a range of discharge
pressures.
• the compressor capacity is directly proportional to the
speed.
• The output, however, is a pulsating one
• Two stage machines are used for high pressures and
are characterized by lower discharge temperature (140
to 160 0C) compared to single-stage machines (205 to
240 0C)
• Multi staging has other benefits, such as reduced
pressure differential across cylinders, which reduces the
load and stress on compressor components such as
valves and piston rings
SYSTEM COMPONENTS
• Intake Air Filters : Prevent dust and atmospheric impurities from entering
compressor. Dust causes sticking valves, scored cylinders, excessive wear etc.
• Inter-stage Coolers : Reduce the temperature of the air (gas) before it enters
the next stage to reduce the work of compression and increase efficiency. They
can be water-or air-cooled.
• After Coolers : Reduce the temperature of the discharge air, and thereby reduce
the moisture carrying capacity of air.
• Air-dryers : Air dryers are used to remove moisture, as air for instrument and
pneumatic equipment needs to be relatively free of any moisture. The moisture
is removed by suing adsorbents or refrigerant dryers, or state of the art heatless
dryers.
• Moisture Traps : Air traps are used for removal of moisture in the compressed
air distribution lines. They resemble steam traps wherein the air is trapped and
moisture is removed.
• Receivers : Depending on the system requirements, one or more air receivers
are generally provided to reduce output pulsations and pressure variations.
ROTARY COMPRESSORS
• directly coupled to the prime mover and require
lower starting torque as compared to
reciprocating machine.
• require smaller foundations, vibrate less, and
have a lower number of parts - which means less
failure rate.
• Dry types deliver oil-free air and are available in
sizes up to 20,000 cfm and pressure upto 15 bar.
Lubricated types are available in sizes ranging
from 100 to 1000 cfm, with discharge pressure up
to 10 bar.
SCREW COMPRESSOR
DYNAMIC COMPRESSORS -CENTRIFUGAL
• These compressors raise the pressure of air or gas
by imparting velocity energy and converting it to
pressure energy.
• A small change in compression ratio produces a
marked change in compressor output and
efficiency.
• The centrifugal air compressor depends on transfer
of energy from a rotating impeller to the air. The
rotor accomplishes this by changing the
momentum and pressure of the air. This momentum
is converted to useful pressure by slowing the air
down in a stationary diffuser.
• The centrifugal air compressor is an oil free
compressor by design
GENERAL SELECTION CRITERIA FOR
COMPRESSORS
Capacity (m3/h) Pressure (bar)
Type of Compressor
From To From To
Roots power compressor
single stage
100 30000 0.1 1
Reciprocating
- Single / Two stage 100 12000 0.8 12
- Multi stage 100 12000 12.0 700
Screw
- Single stage 100 2400 0.8 13
- Two stage 100 2200 0.8 24
Centrifugal 600 300000 0.1 450
COMPRESSOR PERFORMANCE
WHAT IS FAD- CAPACITY OF A COMPRESSOR?
• Capacity of a compressor is the full rated volume of flow of gas
compressed and delivered at conditions of total temperature, total
pressure, and composition prevailing at the compressor inlet.
• It sometimes means actual flow rate, rather than rated volume of flow. This
is also termed as Free Air Delivery (FAD) i.e. air at atmospheric conditions
at any specific location. Because the altitude, barometer, and temperature
may vary at different localities and at different times, it follows that this
term does not mean air under identical or standard conditions.
PERFORMANCE TERMS AND DEFINITIONS
Compression ratio : Absolute discharge pressure of last stage
Absolute intake pressure
Isothermal Power : It is the least power required to compress the air
assuming isothermal conditions.
Isothermal Efficiency : The ratio of Isothermal power to shaft power
Volumetric efficiency : The ratio of Free air delivered to compressor swept
volume
Specific power requirement: The ratio of power consumption (in kW ) to the
volume delivered at ambient conditions.
COMPRESSOR EFFICIENCY - DEFINITIONS
Isothermal Efficiency
Isothermal Efficiency =
Actual measured input power
IsothermalPower
Isothermal power(kW) = P1 x Q1 x loger/36.7
P1 = Absolute intake pressure kg/ cm2
Q1 = Free air delivered m3
/hr.
r = Pressure ratio P2/P1
COMPRESSOR EFFICIENCY DEFINITIONS
Volumetric Efficiency
3
Free air delivered m /min
Volumetric efficiency =
Compressor displacement
Compressor Displacement =  x D2
x L x S x  x n
4
D = Cylinder bore, metre
L = Cylinder stroke, metre
S = Compressor speed rpm
 = 1 for single acting and
2 for double acting cylinders
n = No. of cylinders
CAPACITY ASSESSMENT IN SHOP-FLOOR
• Isolate the compressor along with its individual receiver being taken for test from main
compressed air system by tightly closing the isolation valve or blanking it, thus closing the
receiver outlet.
• Open water drain valve and drain out water fully and empty the receiver and the pipe line.
Make sure that water trap line is tightly closed once again to start the test.
• Start the compressor and activate the stop watch.
• Note the time taken to attain the normal operational pressure P2 (in the receiver) from initial
pressure P1.
• Calculate the capacity as per the formulae given below :
Actual Free air
discharge
Min.
/
NM
T
V
P
P
P
Q 3
0
1
2



Where
P2 = Final pressure after filling (kg/cm2
a)
P1 = Initial pressure (kg/cm2
a) after bleeding
P0 = Atmospheric Pressure (kg/cm2
a)
V = Storage volume in m3
which includes receiver,
after cooler, and delivery piping
T = Time take to build up pressure to P2 in minutes
Example
• Piston displacement : 16.88 CMM
• Theoretical compressor capacity : 14.75 CMM @ 7
kg/SQCMG
• Compressor rated rpm 750 : Motor rated rpm :
1445
• Receiver Volume : 7.79 CM
• Additional hold up volume,
i.e., pipe / water cooler, etc., is : 0.4974 CM
• Total volume : 8.322 CM
• Initial pressure P1 : 0.5 Kgf / SQCMG
• Final pressure P2 : 7.03 Kgf / SQCMG
• Atmospheric pressure P0 : 1.026
Kgf/cm2A
• Compressor output CMM :
 
time
Pumpup
Pressure
Atm.
Volume
Total
P
P 1
2



 
4.021
.026
1
8.322
5
.
0
03
.
7



= 13.17 CMM
SINGLE – STAGE RECIPROCATING AIR COMPRESSOR
• Fig.18.3 shows the arrangement of a single – stage reciprocating air
compressor, together with a typical indicator diagram. The compressor
operates on a two-stroke cycle as follows:
• Stroke 1 (a-c) The piston withdraws, causing the air in the clearance volume to
expand, and when the pressure in the cylinder falls below
atmospheric pressure (at b) the inlet valve opens & air is drawn
into the cylinder for the remainder of the stroke.
• Stroke 2 (c-a) The piston moves inwards, compressing the air in the cylinder, &
the inlet valve closes when the cylinder pressure reaches
atmospheric pressure. Further compression follows as the
piston moves towards the top of its stroke until, when the
pressure in the cylinder is more than that in the receiver, the
delivery valve opens and air is delivered to the receiver for the
remainder of the stroke.
SINGLE – STAGE
RECIPROCATING
AIR COMPRESSOR –
PRINCIPLE OF
WORKING &
P-V DIAGRAM
WORK DONE ON THE AIR DURING THE CYCLE
• The intercept V on the indicator diagram represents the volume of air taken in
per cycle. It is seen that the effect of clearance air is to reduce the quantity of
air drawn in during the suction stroke, so that in practice the clearance space
is made as small as possible.
• The total area of the indicator diagram represents the actual work of the
compressor on the gas or air. The areas above p2 and below p1 represent work
done because of pressure drop through the valves and port passages; this
work is called the valve loss.
• The idealized machine to which the actual machine is compared has an
indicator like fig.18.4 Both expansion and compression are supposed to follow
the same law pvn = C. The small quantity of high pressure air in the clearance
volume expands to Va and air drawn in during the suction stroke is Vb=Va.
WORK DONE ON THE AIR DURING THE CYCLE
• Work done on the air during the cycle = Enclosed area abcd = Area
dcfh + Area cbef – Area hgad – Area geba.
WORK DONE ON THE AIR DURING THE CYCLE
(p2Vc – p1Vb) ( p2Vd – p1Va)
W = p2 (Vc-Vd) = ------------------- - -------------------- - p1 (Vb – Va)
(n – 1) (n – 1)
n
W = ------- [ (p2Vc – p1vb) – (p2 Vd – p1 Va) ]
(n-1)
• Now, p2 Vc = mc R T2, p1 Vb = mb RT1 and mc – mb = mass of air taken
during compression.
• Also, p2 Vd = md RT2, p1 Va = ma RT1 and ma – md = mass of air present
in the clearance volume after delivery.
WORK DONE ON THE AIR DURING THE CYCLE
n
 Work done/cycle = ------ R [ mb (T2 – T1) - md (T2 – T1)]
(n-1)
n
= ------ (T2 – T1) R (mb – md)
(n-1)
n
= ----- (mb – md ) R T1 [ (p2/ p1)(n-1/n) -1 ]
n-1
• Where mb-md is the difference between the mass of air present at the end of
suction and that present at the end of delivery.
• This the expression is the same as obtained from the steady flow energy
equation where the clearance volume was neglected. Thus the mass of gas in
the clearance volume does not have any effect on the work of compression.
THANK
YOU

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COMPRESSORS-FINAL.ppt

  • 2. INTRODUCTION • A gas compressor is a device in which work is done on the gas to raise its pressure, with an appreciable increase in its density. • The compression of gases is an important process in many power plants, refrigeration plants, and industrial plants. • Industrial uses occur in connection with compressed air motors for tools, air brakes for vehicles, servo-mechanisms, metallurgical and chemical processes, conveying of materials through ducts, transporting of natural gas, and production of bottled gases. •
  • 3.  Compressed Air Efficiency: 60 to 80% of the power of the prime mover is converted into an unusable form of energy (HEAT) And to a lesser extent, into friction, misuse and noise Approximatel y 10% gets to the point of use!!
  • 5. TYPES OF COMPRESSORS According to working i)Reciprocating & ii) Rotary compressors According to action i)Single acting & ii)double acting compressors According to no. of stages i)Single-stage & ii)Multi-stage compressors (a) positive displacement machines like reciprocating compressors, Root’s blower and vane-sealed machines and (b) turbine type like centrifugal and axial flow compressors. TECHNICAL TERMS RELATED TO COMPRESSORS 1.Inlet Pressure – It is the absolute pressure of air at the inlet of the compressor 2.Discharge pressure- It is the absolute pressure of air at the outlet of the compressor 3.Compression ratio/pressure ratio-The ratio of discharge pressure to the inlet pressure. As the discharge pressure is always greater than the inlet pressure, the pressure ratio is always greater than unity. 4.Compressor capacity-The volume of air delivered by the compressor and is expressed in m3/min or m3/s
  • 6. TECHNICAL TERMS RELATED TO COMPRESSORS - Contd….. • Free air delivery – The actual volume of air delivered by the compressor at NTP.The capacity of the compressor is generally given in terms of free air delivery. • Swept Volume – the volume of air sucked by the compressor during its suction stroke. The swept volume of a single acting air compressor is given by • Vs = (π/4) D2 L • Where D = dia of the cylinder bore L = length of piston stroke Mean effective pressure – The air pressure on the compressor piston keeps on changing with the movement of the piston in the cylinder. The mean effective pressure of the compressor is found out by dividing the work done per cycle to the stroke volume.
  • 7. A gas compression - adiabatic or involving heat transfer, depending upon the purpose for which the gas is compressed. For the use of compressed gas in an engine or in a combustion process, adiabatic compression is desirable to obtain the maximum energy. In many applications, the gas is stored in a tank or receiver for use later at room temperature. The objective of the compression and storage process is to increase the pressure of the gas without change of temperature. If the gases is cooled during compression, the work required will be less than for adiabatic compression. Another advantage of cooling is the reduction in volume of gas and less pipe friction losses. Since cooling during the compression process is not very effective, after-coolers are often used to cool the gas leaving the compressor. COMPRESSION PROCESSES
  • 8. FEATURES OF RECIPROCATING COMPRESSOR A reciprocating compressor is a positive displacement machine that uses a piston contained within a cylinder to produce compression. The piston traverses the cylinder, sucking in atmospheric air at one end of its stroke, then compressing the air when it reaches the other end of its stroke. This type of machine is available as an 'oil-free' compressor or as a 'lubricated' compressor. The reciprocating compressor probably accounts for largest number of compressors used worldwide.
  • 10.
  • 11. PRINCIPLE OF WORKING OF RECIPROCATING COMPRESSOR
  • 12. RECIPROCATING COMPRESSOR • flow output remains constant over a range of discharge pressures. • the compressor capacity is directly proportional to the speed. • The output, however, is a pulsating one • Two stage machines are used for high pressures and are characterized by lower discharge temperature (140 to 160 0C) compared to single-stage machines (205 to 240 0C) • Multi staging has other benefits, such as reduced pressure differential across cylinders, which reduces the load and stress on compressor components such as valves and piston rings
  • 13. SYSTEM COMPONENTS • Intake Air Filters : Prevent dust and atmospheric impurities from entering compressor. Dust causes sticking valves, scored cylinders, excessive wear etc. • Inter-stage Coolers : Reduce the temperature of the air (gas) before it enters the next stage to reduce the work of compression and increase efficiency. They can be water-or air-cooled. • After Coolers : Reduce the temperature of the discharge air, and thereby reduce the moisture carrying capacity of air. • Air-dryers : Air dryers are used to remove moisture, as air for instrument and pneumatic equipment needs to be relatively free of any moisture. The moisture is removed by suing adsorbents or refrigerant dryers, or state of the art heatless dryers. • Moisture Traps : Air traps are used for removal of moisture in the compressed air distribution lines. They resemble steam traps wherein the air is trapped and moisture is removed. • Receivers : Depending on the system requirements, one or more air receivers are generally provided to reduce output pulsations and pressure variations.
  • 14. ROTARY COMPRESSORS • directly coupled to the prime mover and require lower starting torque as compared to reciprocating machine. • require smaller foundations, vibrate less, and have a lower number of parts - which means less failure rate. • Dry types deliver oil-free air and are available in sizes up to 20,000 cfm and pressure upto 15 bar. Lubricated types are available in sizes ranging from 100 to 1000 cfm, with discharge pressure up to 10 bar.
  • 16. DYNAMIC COMPRESSORS -CENTRIFUGAL • These compressors raise the pressure of air or gas by imparting velocity energy and converting it to pressure energy. • A small change in compression ratio produces a marked change in compressor output and efficiency. • The centrifugal air compressor depends on transfer of energy from a rotating impeller to the air. The rotor accomplishes this by changing the momentum and pressure of the air. This momentum is converted to useful pressure by slowing the air down in a stationary diffuser. • The centrifugal air compressor is an oil free compressor by design
  • 17. GENERAL SELECTION CRITERIA FOR COMPRESSORS Capacity (m3/h) Pressure (bar) Type of Compressor From To From To Roots power compressor single stage 100 30000 0.1 1 Reciprocating - Single / Two stage 100 12000 0.8 12 - Multi stage 100 12000 12.0 700 Screw - Single stage 100 2400 0.8 13 - Two stage 100 2200 0.8 24 Centrifugal 600 300000 0.1 450
  • 18. COMPRESSOR PERFORMANCE WHAT IS FAD- CAPACITY OF A COMPRESSOR? • Capacity of a compressor is the full rated volume of flow of gas compressed and delivered at conditions of total temperature, total pressure, and composition prevailing at the compressor inlet. • It sometimes means actual flow rate, rather than rated volume of flow. This is also termed as Free Air Delivery (FAD) i.e. air at atmospheric conditions at any specific location. Because the altitude, barometer, and temperature may vary at different localities and at different times, it follows that this term does not mean air under identical or standard conditions.
  • 19. PERFORMANCE TERMS AND DEFINITIONS Compression ratio : Absolute discharge pressure of last stage Absolute intake pressure Isothermal Power : It is the least power required to compress the air assuming isothermal conditions. Isothermal Efficiency : The ratio of Isothermal power to shaft power Volumetric efficiency : The ratio of Free air delivered to compressor swept volume Specific power requirement: The ratio of power consumption (in kW ) to the volume delivered at ambient conditions.
  • 20. COMPRESSOR EFFICIENCY - DEFINITIONS Isothermal Efficiency Isothermal Efficiency = Actual measured input power IsothermalPower Isothermal power(kW) = P1 x Q1 x loger/36.7 P1 = Absolute intake pressure kg/ cm2 Q1 = Free air delivered m3 /hr. r = Pressure ratio P2/P1
  • 21. COMPRESSOR EFFICIENCY DEFINITIONS Volumetric Efficiency 3 Free air delivered m /min Volumetric efficiency = Compressor displacement Compressor Displacement =  x D2 x L x S x  x n 4 D = Cylinder bore, metre L = Cylinder stroke, metre S = Compressor speed rpm  = 1 for single acting and 2 for double acting cylinders n = No. of cylinders
  • 22. CAPACITY ASSESSMENT IN SHOP-FLOOR • Isolate the compressor along with its individual receiver being taken for test from main compressed air system by tightly closing the isolation valve or blanking it, thus closing the receiver outlet. • Open water drain valve and drain out water fully and empty the receiver and the pipe line. Make sure that water trap line is tightly closed once again to start the test. • Start the compressor and activate the stop watch. • Note the time taken to attain the normal operational pressure P2 (in the receiver) from initial pressure P1. • Calculate the capacity as per the formulae given below : Actual Free air discharge Min. / NM T V P P P Q 3 0 1 2    Where P2 = Final pressure after filling (kg/cm2 a) P1 = Initial pressure (kg/cm2 a) after bleeding P0 = Atmospheric Pressure (kg/cm2 a) V = Storage volume in m3 which includes receiver, after cooler, and delivery piping T = Time take to build up pressure to P2 in minutes
  • 23. Example • Piston displacement : 16.88 CMM • Theoretical compressor capacity : 14.75 CMM @ 7 kg/SQCMG • Compressor rated rpm 750 : Motor rated rpm : 1445 • Receiver Volume : 7.79 CM • Additional hold up volume, i.e., pipe / water cooler, etc., is : 0.4974 CM • Total volume : 8.322 CM • Initial pressure P1 : 0.5 Kgf / SQCMG • Final pressure P2 : 7.03 Kgf / SQCMG • Atmospheric pressure P0 : 1.026 Kgf/cm2A • Compressor output CMM :   time Pumpup Pressure Atm. Volume Total P P 1 2      4.021 .026 1 8.322 5 . 0 03 . 7    = 13.17 CMM
  • 24. SINGLE – STAGE RECIPROCATING AIR COMPRESSOR • Fig.18.3 shows the arrangement of a single – stage reciprocating air compressor, together with a typical indicator diagram. The compressor operates on a two-stroke cycle as follows: • Stroke 1 (a-c) The piston withdraws, causing the air in the clearance volume to expand, and when the pressure in the cylinder falls below atmospheric pressure (at b) the inlet valve opens & air is drawn into the cylinder for the remainder of the stroke. • Stroke 2 (c-a) The piston moves inwards, compressing the air in the cylinder, & the inlet valve closes when the cylinder pressure reaches atmospheric pressure. Further compression follows as the piston moves towards the top of its stroke until, when the pressure in the cylinder is more than that in the receiver, the delivery valve opens and air is delivered to the receiver for the remainder of the stroke.
  • 25. SINGLE – STAGE RECIPROCATING AIR COMPRESSOR – PRINCIPLE OF WORKING & P-V DIAGRAM
  • 26. WORK DONE ON THE AIR DURING THE CYCLE • The intercept V on the indicator diagram represents the volume of air taken in per cycle. It is seen that the effect of clearance air is to reduce the quantity of air drawn in during the suction stroke, so that in practice the clearance space is made as small as possible. • The total area of the indicator diagram represents the actual work of the compressor on the gas or air. The areas above p2 and below p1 represent work done because of pressure drop through the valves and port passages; this work is called the valve loss. • The idealized machine to which the actual machine is compared has an indicator like fig.18.4 Both expansion and compression are supposed to follow the same law pvn = C. The small quantity of high pressure air in the clearance volume expands to Va and air drawn in during the suction stroke is Vb=Va.
  • 27. WORK DONE ON THE AIR DURING THE CYCLE • Work done on the air during the cycle = Enclosed area abcd = Area dcfh + Area cbef – Area hgad – Area geba.
  • 28. WORK DONE ON THE AIR DURING THE CYCLE (p2Vc – p1Vb) ( p2Vd – p1Va) W = p2 (Vc-Vd) = ------------------- - -------------------- - p1 (Vb – Va) (n – 1) (n – 1) n W = ------- [ (p2Vc – p1vb) – (p2 Vd – p1 Va) ] (n-1) • Now, p2 Vc = mc R T2, p1 Vb = mb RT1 and mc – mb = mass of air taken during compression. • Also, p2 Vd = md RT2, p1 Va = ma RT1 and ma – md = mass of air present in the clearance volume after delivery.
  • 29. WORK DONE ON THE AIR DURING THE CYCLE n  Work done/cycle = ------ R [ mb (T2 – T1) - md (T2 – T1)] (n-1) n = ------ (T2 – T1) R (mb – md) (n-1) n = ----- (mb – md ) R T1 [ (p2/ p1)(n-1/n) -1 ] n-1 • Where mb-md is the difference between the mass of air present at the end of suction and that present at the end of delivery. • This the expression is the same as obtained from the steady flow energy equation where the clearance volume was neglected. Thus the mass of gas in the clearance volume does not have any effect on the work of compression.