Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
w = (nc/(nc-1))*P2*V2*((P3/P2)^((nc-1)/nc)-1)
This formula uses 5 Variables
Variables Used
Work Done per cycle - (Measured in Joule) - Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.
Polytropic Index for Compression - Polytropic Index for Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.
Discharge Pressure of Low Pressure Compressor - (Measured in Pascal) - The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler.
Discharge Volume - (Measured in Cubic Meter) - Discharge volume is the volume of the refrigerant after compression or at the discharge.
Discharge Pressure of High Pressure Compressor - (Measured in Pascal) - The Discharge pressure of High pressure compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.
STEP 1: Convert Input(s) to Base Unit
Polytropic Index for Compression: 1.2 --> No Conversion Required
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)
Discharge Volume: 1.6 Cubic Meter --> 1.6 Cubic Meter No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
w = (nc/(nc-1))*P2*V2*((P3/P2)^((nc-1)/nc)-1) --> (1.2/(1.2-1))*700000*1.6*((1500000/700000)^((1.2-1)/1.2)-1)
Evaluating ... ...
w = 910180.461144918
STEP 3: Convert Result to Output's Unit
910180.461144918 Joule --> No Conversion Required
FINAL ANSWER
910180.461144918 910180.5 Joule <-- Work Done per cycle
(Calculation completed in 00.020 seconds)

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8 Work Done by a Two-Stage Reciprocating Compressor with Intercooler Calculators

Total Work done per cycle in Compressor during incomplete Intercooling given Temperature
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*((Suction temperature at Low pressure Compressor*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction temperature at Low pressure Compressor-Temperature at exit of Intercooler)
Total Work done per cycle in Compressor during Incomplete Intercooling given Volume
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction temperature at Low pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature at High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
Work done per cycle in Low Pressure Compressor during incomplete intercooling given Suction Temp
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction temperature at Low pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
Work done per cycle in Low pressure Compressor during incomplete intercooling given suction volume
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume Formula

Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
w = (nc/(nc-1))*P2*V2*((P3/P2)^((nc-1)/nc)-1)

Advantages of Multi-stage Compression.

1. The work done per kg of refrigerant is reduced in multi-stage compression with intercooler as compared to single-stage compression for the same delivery pressure.
2. It improves the volumetric efficiency for the given pressure ratio.
3. The sizes of the two cylinders (i.e. high pressure and low pressure cylinders) may be adjusted to suit the volume and pressure of refrigerant.
4. It reduces the leakage loss considerably.
5. It gives more uniform torque, and hence a smaller size flywheel is required.
6. It provides effective lubrication because of lower temperature range.
7. It reduces the cost of compressor.

How to Calculate Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume?

Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume calculator uses Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1) to calculate the Work Done per cycle, The Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume formula is defined as the amount of work done per cycle by the High-Pressure compressor in a Multistage compressor when Intercooling is incomplete and Suction Volume is given. Work Done per cycle is denoted by w symbol.

How to calculate Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume using this online calculator? To use this online calculator for Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume, enter Polytropic Index for Compression (nc), Discharge Pressure of Low Pressure Compressor (P2), Discharge Volume (V2) & Discharge Pressure of High Pressure Compressor (P3) and hit the calculate button. Here is how the Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume calculation can be explained with given input values -> 910180.5 = (1.2/(1.2-1))*700000*1.6*((1500000/700000)^((1.2-1)/1.2)-1).

FAQ

What is Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume?
The Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume formula is defined as the amount of work done per cycle by the High-Pressure compressor in a Multistage compressor when Intercooling is incomplete and Suction Volume is given and is represented as w = (nc/(nc-1))*P2*V2*((P3/P2)^((nc-1)/nc)-1) or Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1). Polytropic Index for Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index, The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler, Discharge volume is the volume of the refrigerant after compression or at the discharge & The Discharge pressure of High pressure compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.
How to calculate Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume?
The Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume formula is defined as the amount of work done per cycle by the High-Pressure compressor in a Multistage compressor when Intercooling is incomplete and Suction Volume is given is calculated using Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1). To calculate Work done per cycle in High pressure Compressor during incomplete intercooling given suction volume, you need Polytropic Index for Compression (nc), Discharge Pressure of Low Pressure Compressor (P2), Discharge Volume (V2) & Discharge Pressure of High Pressure Compressor (P3). With our tool, you need to enter the respective value for Polytropic Index for Compression, Discharge Pressure of Low Pressure Compressor, Discharge Volume & Discharge Pressure of High Pressure Compressor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Work Done per cycle?
In this formula, Work Done per cycle uses Polytropic Index for Compression, Discharge Pressure of Low Pressure Compressor, Discharge Volume & Discharge Pressure of High Pressure Compressor. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*((Suction temperature at Low pressure Compressor*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction temperature at Low pressure Compressor-Temperature at exit of Intercooler)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction temperature at Low pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature at High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction temperature at Low pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
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