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Question:

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 m^{3}- Gas pressure:
p= 160 kPa- Compression index:
n= 1.4- Pressure/volume relationship:
pV=^{n}C- Work done = Integral sign top( V2) bottom= V1 pdV

You first need to work outC,the value of the pressure/volume relationship.

Calculate the work done in compressing the nitrogen from 0.8 m^{3}to 0.6 m^{3}using:

- integral calculus
- Simpson’s rule

Comment on the accuracy of the numerical method.

Note: if you wish, you may use a spreadsheet for the numerical method.

Update

Edited out the answer:

THANKS