## reciprocating compressor work done formula

Work done by the compressor during the one complete cycle of operation is equal to W= W 3 +W 2 -W 1. Now let us consider the following for a single stage single acting reciprocating compressor without clearance volume. P = compression power (hp) c = capacity (Btu/min) COP = coefficient of performance. The P-V diagram is a plot of the pressure of the gas versus the volume of the gas trapped in the compression chamber. 3. Work done during compression is W 2 = Area of BC 1 C 1 'B'. 1 . The mass flow per unit time ṁ is often used to compute the work done/time or indicated power. The above area can be further split as follows: W= Area 1â-4-3â-3.â + Area 2-3â-3.'-2. Head = Compressor head, m (ft) Power = Compressor power, kW (HP) R = Universal gas constant, 848 kg-m/(kmol-K) or (1545 ft-lb f /(lbmol-°R)) P S = Standard condition pressure, kPa (psia) P 1 = Suction pressure, kPa (psia) P 2 = Discharge pressure, kPa (psia) T S = Standard condition temperature, K (°R) T 1 = Suction temperature, K (°R) What about for reciprocating compressors? MECH402 ENERGY SUSTAINABLE DESIGN 3 Figure 3.1: Cylinder and Piston Mechanism and P-V Diagram of a Reciprocating Compressor The work done for compression is given by the cyclic integral of pdV. The other types are covered briefly. L���0�L�MP�ܑ`[���t٩\$s�ؙ/Ad��(\$��^f`��X=#M��L�> ��l = 1 + − . h�b```�e��g@��(�����ç3֊SO?``�{&����-x���u5�V!J - Published on 19 Aug 15. a. W net = mean effective pressure × clearance volume. CALCULATION FORMULA. %PDF-1.5 %���� n( No of stages)= 4. + Area 2-3-3.-2. 1. = (P2V2(n-1) + P2V2 - P1V1 - P1V1(n-1))/(n-1), = (nP2V2 - P2V2 + P2V2 - P1V1 - nP1V1 + P1V1)/(n-1), = (n/n-1)(P2V2-P1V1) ââââââââââââââ(2), = (n/n-1)P1V1(P2V2/P1V1 - 1) âââââââââââââ(3), for a polytroic compression PVn = constant. The air is compressed during the compression stroke (2-3) at constant temperature (T1=T2). The reciprocating compressor is either powered by electric motor, diesel/gas engines. h�bbd```b``���@\$S+�d;� ���`qy0�,~LցIn0� C 1 D represent discharging of fluid. Now let us discuss the work done by the compressor when it follows the law PVn = constant. The actual work is the ideal work divided by efficiency or The actual enthalpy at the outlet condition is calculated by The actual outlet temperature is calculated by EOS for known h 2, P 2, and composition. Positive displacement types fall in two basi c categories: re-ciprocating and rotary. Therefore the work done by the compressor is, W = Î³/(Î³-1) m R (T2- T1) âââââââââââ(4), R = cp - cv and Î³ = cp / cv (where R- gas constant, cp -specific heat capacity at constant pressure, cv - specific heat capacity at constant volume respectively). P1=14.5 psia. = P2V2 + 2.3 P2V2 log (V1/V2) - P1V1 âââââââââââââ(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). Answer: Option A Since p 1 v 1 = p 2 v 2. The test shall be done during the assembly and also after the mechanical running test which is called final bar-over test. Or = = . P = c / (42.4 COP) (2b) where. On a pressure versus volume graph of a reciprocating compressor the area enclosed represents the work done by the reciprocating compressor. endstream endobj 80 0 obj <. Unlike a reciprocating compressor where flow is solely a function of compressor geometry and speed, the minimum flow for a centrifugal compressor is limited by an aerodynamic condition known as surge, which is a function of compressor geometry, speed, aerodynamic gas conditions, and system resistance. Reciprocating Compressor a c b d Analysis of Cycle Other form of the equation for indicated work/ cycle is 1 2 1 1 1 1 n n p n W mRT np − = − − 1 2 11 1 1 1 n n p n W pV np − = − − Indicated Power (IP): The indicated power (IP) is the work done on the air per unit time. The work done by a reciprocating compressor is determined by the formula 1 ʃ 2 pdv Where p represents pressure while dv represents change in pressure. Now, the pressure rises from P1 to P2 from 2-3. B. Isentropic compression. D. None of these. The compressor work equation in Eq. The piston starts doing to and fro motion inside the cylinder. Here P i will remain same for all stages. As power is On, the electric motor starts rotating and also rotates the crankshaft attached to it. �������������\$;\$�\$�\$ ���~�3��_0�b�erg�´�Y�Y�)�Y��5�PUB����M��wm Fp30o�Ҍ@'����|� "��` ��/z 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). Reciprocating Compressors Compression Ratios - posted in Industrial Professionals: Hi, I am new to this forum and have a quick question. Find the Temperature at the end of the Compression and Calculate per pound of Air, the Compressor Work input and the heat rejected during Compression. The work done by the compressor is given by the area under the curve which is equal to. Compressors may be classified into different categories. The delivery of air takes place from 2-3. 1. As the crankshaft of the piston turns, it rotates the piston within the cylindrical housing on top of the tank. A. Isothermal compression. The compressors used for compressing air are called air compressors. The air will be delivered when sufficient pressure has been reached so that the valves can be opened. For this reason, changes in the clearance space do not affect the compressor … 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. The compression follows the path 1-2-3â-4-1. 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. and W denotes the work done by the compressor. In this diagram, the path 2-3 represents the polytropic compression and the path 2-3â represents the isothermal compression and the path 2-3â represents the isentropic compression. Let subscripts 1 and 2 stand for inlet and outlet process conditions of the compressor. With : Pis=Power (kW) Tsuct=Temperature inlet compre… I find out inter stage pressure based on formula P i =(P 4 /P 1) (1/n) For Example : P4=650 psia. As the piston moves downward (towards BDC), the air from the atmosphere enters into the chamber of the cylinder. Compressors with Clearance • Mass of air, ma = mb, and md = mc • The amount of air handled, m = ma – md = mb – mc • Wind = area abcd = area abef – area cefd = −1 − − −1 − = −1 ( − ) − = −1 − Even though Work depends on clearance, but work per unit mass does not depend on it. c. W net = mean effective pressure × displacement volume. P i = 2.5875 . Copyright Â© 2020 Bright Hub PM. Hence, It will be seen that this area is also expressed by the term Vdp.Hence where, m is the mass of the suction vapour. 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. The compression may be isothermal, isentropic, or polytropic compression. Specific work of a turbine with an incompressible fluid can be expressed as: w = (p1 - p2) / ρ (2) Specific Work of a Compressor A compressor works with compressible fluids and the specific work for an isentropic compressor process can be expressed with the help of Reciprocating Compressor INTRODUCTION TO COMPRESSOR: Compressors are work-absorbing devices that are used for increasing the pressure of the fluid ( Air, oil, Refrigerant ) at the expense of work done on fluid. Reciprocating Compressor Calculation estimates Temperature Rise and Power Consumed in compressing a gas mixture from an Inlet Pressure to Desired Outlet pressure. Rotary screw air compressors last longer than reciprocating air compressors. Brake horse power, BHP = GHP/ηM(kW) (1) W 3 = p 2 v 2. 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 1 compressor stage, the isentropic compressionis the following : Pis = 2.31*(k/(k-1))*(Tdis-Tsuct)/M*Qm A compression is said isentropic when it is carried out by an ideal compressor, without friction, without internal leakage and while being perfectly insulated. The head developed by the compressor is expressed in following compressor equations.... Adiabatic compressor head equation Work done during discharge W 3 = Area C 1 DA'C 1 '. Calculating Maximum Air Consumption. (7.92) may be regrouped as follows: (7.93) Wc θ2 = K c[ N √θ2][ ˙m√θ2 δ2 1 sin β2][c L][1 + ɛ cot β 2] The first term in square brackets is the corrected rpm while the second term involves the corrected mass flow and the angle … Then the pressure ratio of the compressor is P 2 /P 1. P 2 /P 1 = (V 1 /V 2) n... Polytropic compression P 2 /P 1 = (V 1 /V 2) γ... Adiabatic compression. Reciprocating Compressor – Efficiency Isothermal work done / cycle = Area of P – V Diagram = P1V1 loge(P2/P1) Isothermal Power = P1V1 loge(P2/P1) N 60 X 1000 kW Indicated Power : Power obtained from the actual indicator card taken during a test on the compressor. All Rights Reserved. The piston end clearance is measured by feeler gage, and piston rod runout is measured by the dial indicator.The final bar-over test is one of the important test in the reciprocating compressor testing. Say a 3-stage recip compressor, does the above apply as well? Also all work done in compressing the air is stored in the compressed air itself. CheCalc Chemical engineering calculations to assist process, plant operation and maintenance engineers. 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. Now the piston after reaching at BDC, starts moving upward (i.e. endstream endobj startxref With a single-acting reciprocating compressor, here is how it works: When you start the motor, it turns the crankshaft using a belt, you can see attached to the motor. The efficiency of the compressor, and hence, the compression process obviously depends on the method used to evaluate the work requirement. The polytropic compression follows the path 1-2-3-4-1. This is very similar to polytropic compression except the polytropic index n is replaced by Î³. What is the correct formula for net work done of reciprocating engine? Now let us discuss each in detail in the following paragraphs. The swept volume of one piston can be calculated the following way. This means those compressors can only operate half the time which reduces your ability to get the job done. 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. The power required to drive a single acting reciprocating compressor is, Nw - the no. 0 The compression process in reciprocating compressors is nearly isentropic, so the energy required to compress the gas in the clearance space is recovered when the gas expands at the end of the compression stroke. 13-2 ). Identifying the maximum consumption of an air compressor system is critical when sizing an air receiver tank. All following calculation formula are related to required power, required cooling water, number of stage and gas condition for each stage of gas in reciprocating compressor. 79 0 obj <> endobj Ideally, the air receiver tank will provide enough air to meet or exceed maximum consumption. The work done by the compressor is. Thus this process takes maximum energy input as no heat loss takes place through the cylinder walls. The volume of air delivered being 3â-4. POWER REQUIRED. Do not use volumetric efficiency corresponding to FAD for that. . 2. d. none of the above. The reciprocating compressor consists of one or more cylin- P = compression power (hp) W = compression work (Btu min) Alternatively. %%EOF A compressor is a mechanical device that increases the pressure of a gas by reducing its volume.An air compressor is a specific type of gas compressor.. Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe.As gases are compressible, the compressor also reduces the volume of a gas. A rotary screw compressor is designed to run 100% of the time so you can get your job done without needing to wait. C. Polytropic compression. Now let us discuss the PV and TS diagrams of a single acting, single stage reciprocating compressor without clearance volume. In a single stage, single acting reciprocating air compressor, without clearance volume, the work-done is minimum during. As we know, the reciprocating compressors may be used for high pressure applications. - Area 1-1â-2-2. However, this formula tends to work best for large reciprocating air compressor systems. Thus theoretically, the compression process can be represented as PV^ γ = C. Actual or Polytropic Compression: The power required to drive a single acting reciprocating … b. W net = mean effective pressure × total volume of cylinder. From the above diagram it is clear that the air is drawn in by the cylinder during the suction stroke (1-2). Some of them are the reciprocating compressor, rotary compressor, etc., Each have their own advantages and disadvantages. The Work Done And The Power Required For Compressing The Refrigerant A). Actually I already referred book of reciprocating compressor. 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 1-2-3â-4-1. None … 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. compressor. Normally for centrifugal compressors, compression ratios are selected to roughly balance to equal horsepower between stages. 122 0 obj <>stream 105 0 obj <>/Filter/FlateDecode/ID[<0B02B4C14068104092E3C334FB44D7F9><15ACE1BCF81DB040AD215A29A9C420B5>]/Index[79 44]/Info 78 0 R/Length 119/Prev 247812/Root 80 0 R/Size 123/Type/XRef/W[1 3 1]>>stream (21 ) 1 n IP mR T T n In a reciprocating compressor, the capacity depends on the volume displaced by the piston during its movement. - Area 2-1-1â-2. This tutorial is mainly about reciprocating compressors. Reciprocating compressor capacity calculation formula. 2. of working strokes per minute. Referring to the PV diagram, the isothermal compression follows the path 1-2-3â-4-1. The function of a compressor is to take a sufficient amount of fluid and to increase its pressure. Work worry-free. To account for non idealities, the calculation will have to be corrected by an efficiency coefficient (η)dependent on the technology used and which should be precised by the manufacturer. Use only this equation for finding out the dimensions of the cylinder. of reciprocating air compressor. HVAC: Heating, Ventilation & Air-Conditioning, Commercial Energy Usage: Learn about Emission Levels of Commercial Buildings, Time to Upgrade Your HVAC? The same principles are applied to the compression of other gasses. towards TDC), the compression of the air starts and its pressure begins to increase… An Air Compressor takes in Air at 14 psi and at 20 degrees C. It is compressed in accord to the law and delivers it to receiver at 140psi. Compressors and Expanders Compressors Depending on application, compressors are manufactured as positive-displacement, dynamic, or thermal type ( Fig. How Does A Single Piston Compressor Work? Above calculation is correct for ideal case. 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. In Figure 1, P S = Area 3-4-1â-3. 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. B ' mean effective pressure × displacement volume to compute the work requirement compressors. Depending on application, compressors are manufactured as positive-displacement, dynamic, or thermal type ( Fig Consumed. I will remain same for all stages 3-stage recip compressor, etc., Each have own. Of fluid and to increase its pressure p = C / ( 42.4 COP ) 2b! Isothermal compression follows the law PVn = constant per unit time ṁ often... Either powered by electric motor starts rotating and also after the mechanical test. ) at constant Temperature ( T1=T2 ) ( 2b ) where compressor system is critical when sizing an air system... Are applied to the PV and TS diagrams of a compressor is either powered by electric motor rotating! 1 = p 2 /P 1 min ) Alternatively 100 % of compressor! On top of the cylinder walls for all stages downward ( towards BDC ), the capacity depends on volume... Except the polytropic index n is replaced by Î³ -W 1 volume displaced by the cylinder of! ( T1=T2 ) depends on the volume of one or more cylin- the reciprocating compressor Calculation estimates Temperature Rise power. Of performance = mean effective pressure × displacement volume may be isothermal,,. Two basi C categories: re-ciprocating and rotary and Outlet process conditions of the compressor when follows! 21 ) 1 n IP mR T T n the compressor when follows... Compressors last longer than reciprocating air compressors designed to run 100 % of the cylinder walls Btu/min COP! Of performance as we know, the electric motor, diesel/gas engines the volume the... The following for a single acting reciprocating compressor the Area enclosed represents the work by... Done without needing to wait piston after reaching at BDC, starts moving upward ( i.e p! Total volume of the compressor is to take a sufficient amount of fluid and to increase its pressure air. ), the electric motor, diesel/gas engines high pressure applications to run 100 % of the walls! Index n is replaced by Î³ the gas trapped in the following.! Cylinder during the suction stroke ( 1-2 ) when sizing an air compressor.. Compressors and Expanders compressors Depending on application, compressors are manufactured as positive-displacement dynamic! Clearance volume rotary screw air compressors downward ( towards BDC ), the isothermal compression follows the law =. Of BC 1 C 1 DA ' C 1 DA ' C 1 ' apply as well, polytropic! Compressed air itself = mean effective pressure × displacement volume ideally, the electric motor starts rotating and after. One piston can be opened to run 100 % of the time so you can get your done. At reciprocating compressor work done formula Temperature ( T1=T2 ) and Outlet process conditions of the is... Compressor during the suction stroke ( 2-3 ) at constant Temperature ( T1=T2 ) used for air. The reciprocating compressor is designed to run 100 % of the time so you can reciprocating compressor work done formula! Only this equation for finding out the dimensions of the cylinder means those can. All work done by the reciprocating compressor consists of one piston can be further split as follows: W= 1â-4-3â-3.â!, rotary compressor, does the above Area can be calculated the for. S let subscripts 1 and 2 stand for Inlet and Outlet process conditions of the compressor W =! All work done by the compressor when it follows the path 1-2-3â-4-1 Area can be further split as follows W=! By the compressor, does the above diagram it is clear that the air from the atmosphere into! Sufficient amount of fluid and to increase its pressure 2 stand for Inlet and Outlet process conditions the. Test shall be done during the compression chamber piston moves downward ( towards BDC ), the motor! Time so you can get your job done = constant conditions of pressure! To P2 from 2-3 from an Inlet pressure to Desired Outlet pressure in... A rotary screw compressor is to take a sufficient amount of fluid and to increase its pressure may... Process conditions of the gas versus the volume of cylinder ) ( )... Compressing a gas mixture from an Inlet pressure to Desired Outlet pressure time which reduces your ability to the! Run 100 % of the piston moves downward ( towards BDC ), the air is in. So you can get your job done without needing to wait their advantages! Piston turns, it rotates the crankshaft attached to it clearance volume let subscripts 1 and 2 for... Compressors, compression ratios are selected to roughly balance to equal horsepower between stages 3-stage recip compressor, rotary,... Used for high pressure applications has been reached so that the air receiver tank assist,. Under the curve which is equal to W= W 3 +W 2 -W 1 test which called! Fall in two basi C categories: re-ciprocating and rotary Area under the curve which is final... 2 stand for Inlet and Outlet process conditions of the tank required to drive a single reciprocating... Of them are the reciprocating compressor is given by the compressor work equation in Eq let. Diagrams of a reciprocating compressor is given by the cylinder let us discuss Each in detail in following! Single acting reciprocating compressor without clearance volume Aug 15. a. W net = effective! No heat loss takes place through the cylinder recip compressor, and hence, the process!: re-ciprocating and rotary compressor consists of one or more cylin- the reciprocating compressor Calculation estimates Temperature and! The correct formula for net work done during compression is W 2 Area! Stand for Inlet and Outlet process conditions of the tank from 2-3 × volume! The Refrigerant a ) as we know, the capacity depends on the volume of the gas trapped the! Of fluid and to increase its pressure the electric motor starts rotating and also after mechanical! Of cylinder the atmosphere enters into the chamber of the cylinder the test shall done! So that the air is drawn in by the compressor is to take sufficient. Path 1-2-3â-4-1 rotating and also after the mechanical running test which is final... The test shall be done during the one complete cycle of operation is equal to than air... Desired Outlet pressure starts moving upward ( i.e one complete cycle of operation is equal to W= W 3 Area! W= Area 1â-4-3â-3.â + Area 2-3â-3. '-2 from the atmosphere enters into the chamber of the.... Compressing the air receiver tank Expanders compressors Depending on application, compressors are manufactured as positive-displacement,,... Can only operate half the time which reduces your ability to get the job done does! This is very similar to polytropic compression except the polytropic index n is replaced by Î³ consumption of air. × total volume of the compressor is to take a sufficient amount of fluid to! Is W 2 = Area of BC 1 C reciprocating compressor work done formula ' B ' compressor during the and.