Question

A gas charged accumulator is to provide an hydraulic system with 28 litres of oil from a maximum pressure of 40 MPa to a final pressure of 35 MPa. The accumulator will initially be charged to a pressure of 30 MPa. Determine the total volume of the accumulator. Assume expansion and compression takes place adiabatically and y 1,4

Answer 1

Answer:

total volume is 0.9125 m³

Explanation:

given data

oil = 28 litres

pressure p = 40 MPa

final pressure p2 = 35 MPa

initial pressure p1 = 30 MPa

y = 1,4

to find out

volume of accumulator

solution

so we here say that volume of oil

v3 - v2 = 28 litres

so v3 = 0.028 + v2          ......................a

and volume formula is

v1 = v2 $(p/p1)^{1/y}$   ...................1

so v2 = v3 $(p2/p)^{1/y}$    ..............2

put here value in equation  2

v2 = (0.028 + v2) $(35/40)^{1/1.4}$

v2 = 0.274 m³

and here v1 will be

v1 = 0.274  $(40/30)^{1/1.4}$

v1 = 0.3365 m³

and v3 will be

v3 = 0.028 + v2

v3 = 0.028 + 0.274

v3 = 0.302 m³

so

total volume is v1 + v2 + v3

total volume = 0.274 + 0.3365 + 0.302

total volume is 0.9125 m³