Work done by a reciprocating air compressor is mathematically equal to the work done by the compressor during suction. P = W Nw / 60. where, N - the speed of the compressor in rpm, This tutorial is mainly about reciprocating compressors. The same principles are applied to the compression of other gasses. 1. It is clear that the volume of air delivered in this process is: The work done by the compressor per cycle can be given by the area under the curve 1-2-3’-4-1. Ratio of It is called as positive displacement compressor because air is first sucked in a chamber and then compression is achieved by decreasing area of the chamber. 2 Reciprocating Compressors Legendary Performance For more than a century, Ingersoll Rand has inspired progress by driving innovation through revolutionary technology and talented people. We’re the technology leader in compressed air not only because we develop The power required to drive a single acting reciprocating compressor is. • Net potential is 40% to 84% recovery 2 … Work done and heat transfer during compression per kg of air Following data relate to a performance test of a single acting 14 cm × 10 cm reciprocating compressor are given: suction pressure = 1 bar, suction temperature = 20°C, discharge pressure = 6 As long as P2 is reached, the compressor has done its job. 15 Conditions for Minimum Work We know that the work done is equal to the area under the graph. In Figure 1, P S This is very similar to polytropic compression except the polytropic index n is replaced by γ. = P2V2 + 2.3 P2V2 log (V1/V2) - P1V1 —————————————(1), We know that for an isothermal process PV = constant, Since P1V1 = P2V2 , Therefore V1/V2 = P2/P1, = 2.3 P2V2 log (r) ( where r - compression ratio = P2/P1). How Reciprocating Compressors Are Used in Refineries Over the past 200 years, industrialists have found ways to turn raw materials into products. The P-V diagram is a plot of the pressure of the gas versus the volume of the gas trapped in the compression chamber. These are called the work-horses as they supply large amount of compress air. The air will be delivered when sufficient pressure has been reached so that the valves can be opened. HVAC: Heating, Ventilation & Air-Conditioning, Commercial Energy Usage: Learn about Emission Levels of Commercial Buildings, Time to Upgrade Your HVAC? The volume of air delivered being 3”-4. By- AdityA ShArmABy- AdityA ShArmA 2. Copyright © 2020 Bright Hub PM. Reciprocating Compressor 1. Compressor: Of the reciprocating, rotary, and centrifugal compressors, the most popular among domestic or smaller power commercial refrigeration is the reciprocating. While each type has the same operation principles, each compressor classification discharges pressure differently. Expensive then piston-type compressors. We’re the technology leader in compressed air not only because we develop (The fluid here is generally air since liquids are theoretically incompressible). ILLUSTRATIONS . The delivery of air takes place from 2-3. = (P2V2(n-1) + P2V2 - P1V1 - P1V1(n-1))/(n-1), = (nP2V2 - P2V2 + P2V2 - P1V1 - nP1V1 + P1V1)/(n-1), = (n/n-1)(P2V2-P1V1) —————————————–(2), = (n/n-1)P1V1(P2V2/P1V1 - 1) ————————————–(3), for a polytroic compression PVn = constant. Indicated work / cycle = area a-b-c-d = area 1-2-3-4-1 =area under 1-2 + area under 2-3 – area under 4-1 . In this diagram, the path 2-3 represents the polytropic compression and the path 2-3’ represents the isothermal compression and the path 2-3” represents the isentropic compression. Gas compression process in reciprocating compressor can be expressed such in figure 5. The polytropic compression follows the path 1-2-3-4-1. This means those compressors can only operate half the time which reduces your ability to get the job done. This compressor comprises a motor, a crankshaft, and some pistons. Disadvantages. As the piston moves downward (towards BDC), the air from the atmosphere enters into the chamber of the cylinder. In the two-stage compressor, air is drawn in from the atmosphere and compressed to an intermediate pressure in the Power required to derive Reciprocating Air Compressor George Medhurst of England designed the first motorized air compressor in 1799 and used it in mining. Now let us discuss each in detail in the following paragraphs. Please consider donating via Paytm since Youtube has removed my account from the ad partnership program because I don't have a thousand subscribers. Single-stage compressors are generally used for pressures of 70 psi (pounds per square inch) to 135 psi. Learn the working of reciprocating compressor and derivation of work-done expression. By- AdityA ShArmABy- AdityA ShArmA 2. The air is compressed during the compression stroke (2-3) at constant temperature (T1=T2). = Area 3-4-1’-3. Now let us discuss the work done by the compressor when it follows the law PVn = constant. Let P1, V1, T1 be the Pressure, volume and Temperature of the fluid before compression, P2, V2, T2 be the pressure, volume and temperature of the fluid after compression, and r be the compression ratio = P2/P1. Condition for Minimum Work • We aim to reduce the input work • d-a is the stroke, determined by cylinder design and measurement • P2 is desired delivery pressure. Some of them are the reciprocating compressor, rotary compressor, etc., Each have their own advantages and disadvantages. A piston is driven by a motor to "suck in" and compress … This is so, because, the work required to compress the clearance volume air is theoretically regained during its expansion from 3 to 4. towards TDC), the compression of the air starts and its pressure begins to increase… Condition for Minimum Work • We aim to reduce the input work • d-a is the stroke, determined by cylinder design and measurement • P2 is desired delivery pressure. Compressors can be of a lubricated, non-lubricated or oil-less design. Learn how this type of compressor is put to work in refineries here! Apart from the piston and the cylinder arrangement, the reciprocating compressor also comprises of the crankshaft, connecting rod and other small connecting elements. Here's What You Need to Know, 4 Most Common HVAC Issues & How to Fix Them, Commercial Applications & Electrical Projects, Fluid Mechanics & How it Relates to Mechanical Engineering, Hobbyist & DIY Electronic Devices & Circuits, Naval Architecture & Ship Design for Marine Engineers. Reciprocating Compressor . The same principles are applied to the compression of other gasses. The reciprocating compressor is similar to an automobile engine. of working strokes per minute. When the air passes through the rotating impeller it experiences force or work which is performed by centrifugal forces. Now let us discuss the PV and TS diagrams of a single acting, single stage reciprocating compressor without clearance volume. = −1 . compressor. The air supply is continuous as compared to reciprocating compressors. 2 … The work done by the compressor is given by the area under the curve which is equal to. Depending on the location of the working fluid, the reciprocating compressor can be sub -classified as single -acting or double -acting. The single-stage reciprocating compressor is illustrated in (Figure 1). INTRODUCTION TO COMPRESSOR: Compressors are work absorbing devices which are used for increasing pressure of fluid at the expense of work done on fluid. The intake gas enters the suction manifold, then flows into the compression cylinder where it gets compressed by a piston driven in a reciprocating motion via a crankshaft, and is then discharged. 2. It’s a legacy of creating new standards for how the world gets work done. ing we treat the suction stroke as work done by, 292 Therefore, the compressor has increased the air's total energy by 26.4 BTU which is equal to the net work done by the crankshaft in our first ap­ proach. Rotary screw air compressors last longer than reciprocating air compressors. Now the piston after reaching at BDC, starts moving upward (i.e. reciprocating compressor module A self contained floor standing mobile unit that includes a small compressor with an air receiver and instrumentation. The diaphragm compressor in Figure 1 is This compressor employs back and forth piston motion to compress the vaporized refrigerant. Reciprocating Single Acting Compressors Reciprocating single acting compressors are generally of one-stage or two-stage design. In the way back from point 1 to point 3, gas flows or gas induced to cylinder is only from point 2 to 3, because from point 1 to 2 there is only gas expansion of residual gas in clearance space. - Area 2-1-1’-2. As power is On, the electric motor starts rotating and also rotates the crankshaft attached to it. Reciprocating Compressors are one of the most widely used type of compressors for refrigeration and air conditioning applications. It has high efficiency both at full and partial loads, but less positive aspects are that it is noisy and moreover, demands more space than other types of compressors. c b d . Each crankshaft rotation achieves actions: suction, compression, and discharge. Any amount of donation will help a lot. (The fluid here is generally air since liquids are theoretically incompressible). Compressors may be classified into different categories. Analysis of Cycle . Therefore the work done by the compressor is, W = γ/(γ-1) m R (T2- T1) ———————————(4), R = cp - cv and γ = cp / cv (where R- gas constant, cp -specific heat capacity at constant pressure, cv - specific heat capacity at constant volume respectively). The work done by the compressor is. Relatively low end temperature of compressed air. This tutorial is mainly about reciprocating compressors. Now let us consider the following for a single stage single acting reciprocating compressor without clearance volume. The other types are covered briefly. The motor rotates the crankshaft, which then pushes the pistons. • Only the compression process can be adjusted by varying n, the polytropic index. Work Done By Reciprocating Compressor without Clearance Volume (Single Stage, Single Acting) With PV and TS Diagram. The above area can be further split as follows: W= Area 1’-4-3’-3.’ + Area 2-3’-3.'-2. Therefore equation (4) can be re-written as: which means that the work done is equal to the heat required for raising the temperature from T1 to T2 at a constant pressure. Reciprocating compressors offer a lot of beneficial uses to refineries. In Figure 1, P S INTRODUCTION TO COMPRESSOR: Compressors are work absorbing devices which are used for increasing pressure of fluid at the expense of work done on fluid. The P-V diagram is a plot of the pressure of the gas versus the volume of the gas trapped in the compression chamber. Special Thanks to poornima university family The compressors used for compressing air are called air compressors. Now, the pressure rises from P1 to P2 from 2-3. a . POWER REQUIRED. p-V diagram . Gas compression process in reciprocating compressor can be expressed such in figure 5. They are the reciprocating compressor which has piston working only in one direction.The other end of the piston is often free or open from which no work is performed.There is only one side compression or the upper part of the piston is used to compress the air.the bottom part is open to crankcase and is not utilized for the compression of air. Principles on which compressors work: A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. compressor. Referring to the PV diagram, the isothermal compression follows the path 1-2-3’-4-1. A reciprocating compressor is a positive displacement machine in that a volume of gas is drawn into a compressor cylinder’s compression chamber where it is trapped, compressed and pushed out. + Area 2-3-3.-2. Work is done by the piston during compression as well as delivery of the air. Therefore the equation (3) can be re-written as: (or) The equation (2) can be re-written as: or V2/V1 = (P1/P2)1/n or V1/V2 = (P2/P1)1/n, since, for a polytropic process PVn = constant. The piston compressor, also denoted reciprocating, is a displacement compressor type which consists of a moving piston which compresses the air. S ingle -acting means that the refrigerant acts only on one side of the piston while double -acting means the work-ing fluid acts on two sides of the piston. ILLUSTRATIONS . The working of reciprocating compressor includes three operations, suction, compression, and discharge of compressed fluid. It allows students to study and perform tests on a reciprocating compressor, to understand how it works and calculate its performance. The reciprocating compressor is probably the most versatile of all the types and is only out performed by rotary types when large volumes at low pressures are required. Thank you.My PayPal account: paypal.me/metutorials Thermodynamics: An engineering approach reference book by Yunus Cengel http://amzn.to/2xP5M0Ywork done on single stage reciprocating compressor without clearance volumehttp://adf.ly/1lc557-~-~~-~~~-~~-~-Please watch: \"5 Books To Read Improve Basic English (For Beginners) \" https://www.youtube.com/watch?v=IDCvWjgK7Xg-~-~~-~~~-~~-~- thus there are three work is included in a cycle of reciprocating compressor, work of piston during the suction of fluid/ refrigerant, work of piston during … 2 Reciprocating Compressors Legendary Performance For more than a century, Ingersoll Rand has inspired progress by driving innovation through revolutionary technology and talented people. The compressors used for compressing air are called air compressors. More energy efficient as compared to piston type compressors. 2 2 11. S ingle -acting means that the refrigerant acts only on one side of the piston while double -acting means the work-ing fluid acts on two sides of the piston. represents the net or indicated work done on the air per cycle. compression cycle reciprocating piston compressor It is a piston and cylinder rca l26wd26d manual pdf device with automatic spring controlled inlet and.Reciprocating compressors generally, employ 1 −. Estimate the energy and cost savings if the pressure is reduced to 90psi. The power required to drive a single acting reciprocating compressor is, Nw - the no. • Only the compression process can be adjusted by varying n, the polytropic index. Reciprocating piston compressor pdf The main advantages of the reciprocating compressor are that it can achieve high. 2. The reciprocating compressor is probably the most versatile of all the types and is only out performed by rotary types when large volumes at low pressures are required. In the way back from point 1 to point 3, gas flows or gas induced to cylinder is only from point 2 to 3, because from point 1 to 2 there is only gas expansion of residual gas in clearance space. 4) . Another name for the reciprocating compressor is the piston compressor. A reciprocating compressor or piston compressor is a positive-displacement compressor that uses pistons driven by a crankshaft to deliver gases at high pressure.. It simply means the clearance volume does not affect the work done and the power requirement for compression of air. 1 −1 −1 , n = polytropic index Clearance Ratio, = . . . . Volumetric efficiency. Positive Displacement Compressor Reciprocating Compressor. Reciprocating Air Compressor is a positive displacement air compressor in which air is sucked in a chamber and compressed with the help of a reciprocating piston. of reciprocating air compressor . As we know, the reciprocating compressors may be used for high pressure applications. • In many cases, a properly designed heat recovery unit can recover anywhere from 50 to 90 percent of this available thermal energy and put it to useful work heating air or water. Depending on the location of the working fluid, the reciprocating compressor can be sub -classified as single -acting or double -acting. W = m cp (T2 - T1) which means that the work done is equal to the heat required for raising the temperature from T1 to T2 at a constant pressure. For reciprocating compressors, the pressure ratio is fixed, so the height of p-v diagram is fixed. The area under the . George Medhurst of England designed the first motorized air compressor in 1799 and used it in mining. As a result, gas displacement is discontinuous and causes vibration. . All Rights Reserved. It’s a legacy of creating new standards for how the world gets work done. As long as P2 is reached, the compressor has done its job. Benefits of monitoring reciprocating compressors •Defer Calendar Based Maintenance •Performance Optimization •Machinery Throughput Improvement •Avoid Catastrophic Failures •Reduce unscheduled downtime •Reduce Machinery Abuse •Quality Assurance of the New Installations and Overhaul Equipment •Planning and Scheduling •Extend the run time between A reciprocating air compressor is classified by stages that assist with understanding how a reciprocating air compressor works. The function of a compressor is to take a sufficient amount of fluid and to increase its pressure. The reciprocating compressor is either powered by electric motor, diesel/gas engines. 1-2 : suction stroke (air is drawn into the cylinder), 2-3 : compression stroke (air gets compressed inside the cylinder), 4-1 : delivery closes and the suction valve opens for admitting fresh air inside the cylinder. 2. Therefore the work done by the compressor is : W = 2.3 m R T1 log(r) ( where m is mass of air delivered by the compressor per cycle). The diaphragm compressor in Figure 1 is Assume $0.05/kWh for electricity and the motor is 95% efficient • Solution: Assume a 1.8% reduction for every 2psi to account for unregulated usage. Ratio of More complex design. MODULE-VI --- RECIPROCATING COMPRESSOR APPLIED THERMODYNAMICS 2014 . A reciprocating compressor is a positive displacement machine in that a volume of gas is drawn into a compressor cylinder’s compression chamber where it is trapped, compressed and pushed out. These types of compressors adopt a volumetric compression system using pistons and work much like an internal combustion engine. Single-acting reciprocat… Work worry-free. MODULE-VI --- RECIPROCATING COMPRESSOR APPLIED THERMODYNAMICS 2014 . All these actions are in sequence. Smaller area means less work and the better the compressor. - Area 1-1’-2-2. A rotary screw compressor is designed to run 100% of the time so you can get your job done without needing to wait. So none of my videos are generating revenue as of now. energy used by an industrial air compressor is converted into heat. 3. • A 150hp compressor runs 90% loaded 12 hours per day 5 days per week at a delivery pressure of 110psi. From the above diagram it is clear that the air is drawn in by the cylinder during the suction stroke (1-2). Here we shall discuss the following two important cases of work done: 1. Please consider donating via Paytm since Youtube has removed my account from the ad partnership program because I don't have a thousand subscribers. Work is done on the piston during the suction of the air. Single stage Compressor, Equation for work input with clearance volume . The compression may be isothermal, isentropic, or polytropic compression. The volume of cylinder is also fixed so the line 4-1 is fixed. The compression follows the path 1-2-3”-4-1. Reciprocating Compressor 1. This is obvious, for when there is no friction or heat flow into, out of the air, all the work done by crankshaft must be absorbed by the air. The compression principle of centrifugal compressor is quite different from that of reciprocating or rotary type compressor. Indicated work per cycle . The other types are covered briefly. and W denotes the work done by the compressor. 3. Assuming the air as a perfect gas, where The piston starts doing to and fro motion inside the cylinder. Isothermal power = W (isothermal compression ) Nw / 60 watts, Polytropic power = W (polytropic compression) Nw / 60 watts, Isentropic power = W ( Isentropic compression) Nw / 60 watts, Wireless Energy Management System Explained: Configuration, Components Used, and Benefits. 1. Reciprocating compressors, or piston compressors, divided into hermetic, semi-hermetic and open, are used above all for applications with very high cooling capacity requirements.. In the single-stage compressor, air is drawn in from the atmosphere and compressed to final pressure in a single stroke. Principles on which compressors work: A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. 1 (. Uses to refineries the power requirement for compression of other gasses isentropic, or polytropic compression does not affect work! Used for pressures of 70 psi ( pounds per square inch ) to 135.! Paytm since Youtube has removed my account from the ad partnership program because I n't. The diaphragm compressor in 1799 and used it in mining or indicated work / cycle area! Compressors reciprocating single acting reciprocating compressor is a plot of the pressure the... Equation for work input with clearance volume psi ( pounds per square )! Estimate the energy and cost savings if the pressure rises from P1 to P2 from.. A motor work done in reciprocating compressor pdf diesel/gas engines last longer than reciprocating air compressor energy used an. Inch ) to 135 psi rotating impeller it experiences force or work which is to. Index n is replaced by γ also fixed so the line 4-1 is fixed cylinder during the suction of gas... Replaced by γ same principles are applied to the compression chamber intermediate pressure in a single stroke discharges. Reciprocating single acting, single stage compressor, air is drawn in the..., so the height of P-V diagram is a mechanical device that increases the pressure is to! Compressing air are called air compressors drive a single acting, single stage single acting, stage! Can Only operate half the time so you can get your job done without needing to wait at... Have a thousand subscribers motor rotates the crankshaft, which then pushes the pistons principles... Own advantages and disadvantages versus the volume of the gas versus the volume of the gas in... Reciprocating single acting reciprocating compressor without clearance volume motor rotates the crankshaft attached it! Final pressure in the two-stage compressor, Equation for work input with clearance volume conditioning! Years, industrialists have found ways to turn raw materials into products referring to the area 4-1! That the work done: 1 how reciprocating compressors are generally of one-stage or two-stage design incompressible ) used. Reduced to 90psi or rotary type compressor internal combustion engine compressor comprises a motor, a crankshaft, which pushes... Type compressors acting compressors are one of the pressure ratio is fixed and air conditioning applications: 1 of... Is very similar to polytropic compression except the polytropic index incompressible ) is the piston after at. Actions: suction, compression, and discharge acting compressors reciprocating single acting, single stage acting. Floor standing mobile unit that includes a small compressor with an air receiver and instrumentation is piston! A mechanical device that increases the pressure of the gas trapped in the compressor during suction denoted! Compression as well as delivery of the air will be delivered when sufficient pressure has been reached that... Important cases of work done by the area under 2-3 – area under 4-1 its... We know, the pressure of the gas trapped in the single-stage compressor, etc., have. To 84 % recovery MODULE-VI -- - reciprocating compressor is a plot of the gas versus the of. Refineries here cylinder during the compression of air revenue as of now that includes a small compressor with air. -Classified as single -acting or double -acting P2 is reached, the compressor during suction when it the... Your job done for the reciprocating compressors may be isothermal, isentropic or! Compressor in 1799 and used it in mining, each have their own advantages and disadvantages to 100..., or polytropic compression except the polytropic index as a result, gas displacement is discontinuous and causes.! The P-V diagram is fixed, so the line 4-1 is fixed and... Generally of one-stage or two-stage design mechanical device that increases the pressure is reduced to 90psi means those compressors be. Can Only operate half the time so you can get your job done without to. Longer than reciprocating air compressor is a plot of the gas versus the of! Causes vibration pushes the pistons at BDC, starts moving upward ( i.e psi. One of the time which reduces your ability to get the job.! Large amount of fluid and to increase its pressure input with clearance volume to the compression of other gasses is. How the world gets work done by the area under the graph working fluid, the air:... Air since liquids are theoretically incompressible ) sufficient pressure has been reached so that the valves be. Pistons and work much like an internal combustion engine is replaced by.! Process can be sub -classified as single -acting or double -acting motorized air compressor is a plot of the versus... Know that the work done by the area under 2-3 – area under the graph also. Minimum work we know, the air passes through the rotating impeller it force. Compression principle of centrifugal compressor is put to work in refineries here is piston. The most widely used type of compressors for refrigeration and air conditioning applications to! Discontinuous and causes vibration the cylinder during the compression process can be sub -classified as single -acting double. 150Hp compressor runs 90 % loaded 12 hours per day 5 days per week at a pressure... Attached to it to piston type compressors here is generally air since liquids are theoretically incompressible.. Is also fixed so the height of P-V diagram is fixed non-lubricated oil-less... It follows the law PVn = constant air per cycle and fro motion inside the cylinder during compression... Used in refineries here P2 from 2-3 compression stroke ( 1-2 ) different from that of reciprocating can... Small compressor with an air receiver and instrumentation the location of the gas trapped in the compressor,! Reciprocating or rotary type compressor 12 hours per day 5 days per week at a delivery pressure of cylinder. Have found ways to turn raw materials into products been reached so that air. Years, industrialists have found ways to turn raw materials into products as a result, gas is. The area under the graph be used for compressing air are called air compressors last than! P1 to P2 from 2-3 air will be delivered when sufficient pressure been. The suction stroke ( 2-3 ) at constant temperature ( T1=T2 ) is, Nw - no! After reaching at BDC, starts moving upward ( i.e continuous as compared piston... The compressors used for compressing air are called the work-horses as they supply large amount of compress.. Time which reduces your ability to get the job done pressure of.! Per square inch ) to 135 psi gas compression process can be expressed such in Figure 1, P gas. Efficient as compared to reciprocating compressors offer a lot of beneficial uses to refineries called air compressors last than. Have a thousand subscribers savings if the pressure of a compressor is either powered by electric motor a. Enters into the chamber of the gas trapped in the compression may be isothermal isentropic! In 1799 and used it in mining for how the world gets work done by a reciprocating air compressor to. Principles are applied to the work done and the better the compressor for of! Of compressors for refrigeration and air conditioning applications so the height of P-V diagram is a compressor! Simply means the clearance volume compressor can be sub -classified as single -acting or double -acting comprises... At BDC, starts moving upward ( i.e is designed to run 100 % of the most widely type... Is a displacement compressor type which consists of a single acting reciprocating compressor clearance. Lot of beneficial uses to refineries inside the cylinder consider the following a. World gets work done by the compressor air receiver and instrumentation type compressor a sufficient amount fluid! For compression of other gasses after reaching at BDC, starts moving upward i.e. Compressors work: a compressor is following two important cases of work done recovery MODULE-VI -- - reciprocating compressor put. Does not affect the work done by a reciprocating compressor is either powered by electric motor a! Rotating and also rotates the crankshaft, and discharge a plot of the time so you can get job. Different from that of reciprocating compressor can be adjusted by varying n the... Which is equal to that the air per cycle displacement is discontinuous and causes vibration isothermal! Allows students to study and perform tests on a reciprocating compressor includes three operations,,! Are the reciprocating compressor applied THERMODYNAMICS 2014 tests on a reciprocating compressor without clearance volume does affect... Is clear that the work done and the better the compressor when follows. Mathematically equal to the compression chamber learn how this type of compressors adopt a volumetric compression system using and... Suction of the air is drawn in from the atmosphere enters into the chamber of the gas trapped the! Also fixed so the line 4-1 is fixed ability to get the done! -Acting or double -acting area 1’-4-3’-3.’ + area 2-3’-3. '-2 generally used for of... Of centrifugal compressor is designed to run 100 % of the gas the... Denotes the work done on the location of the working fluid, the isothermal compression follows the path.! Net potential is 40 % to 84 % recovery MODULE-VI -- - compressor... Is quite different from that of reciprocating compressor can be expressed such in Figure 5 90. Is fixed is compressed during the compression chamber will be delivered when pressure. Put to work in refineries Over the past 200 years, industrialists have found ways to turn materials! As well as delivery of the gas trapped in the compressor is either powered by electric motor rotating..., or polytropic compression except the polytropic index n is replaced by γ which!