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A new design of nitrogen charged accumulator, for use in a hydraulic circuit, (Hydropneumatic Accumulators - HydroTrole Limited) is being factory tested for certification purposes.
The following data has been collected by a technician:
- Gas volume: V = 0.8 m3
- Gas pressure: p = 160 kPa
- Compression index: n = 1.4
- Pressure/volume relationship: pVn = C
- Work done = Integral sign top( V2) bottom= V1 pdV
You first need to work out C, the value of the pressure/volume relationship.
Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:
- integral calculus
- Simpsonís rule
Comment on the accuracy of the numerical method.
Note: if you wish, you may use a spreadsheet for the numerical method.
Edited out the answer: