One principle given in Thermodynamics, Cengel is "The steady flow compression or expansion work is directly proportional to the specific volume of the fluid. Therefore, the specific volume of the working fluid should be as low as possible during a compression process and as high as possible during an expansion process."
Can anybody explain how it is been arrived?
I got to know about the below formula (applicable in some cases) from which we can get partly the answer for the question.
Work = specific volume * change in pressure
Any other conceptual explanation for the above statements known to you?
Just consider the equation for the total energy, you see a term
int[S] n.vp dS = int[V] div(vp )dV
this is the contribution of reversible work due to expansion/compression of a volume of fluid measured by the rate
int[S] n.v dS
For incompressible fluid this term vanishes
For steady-state, steady-flow process, the first law may written as
dq-dw=d(h)=d(u+pv)
Now if we neglected the heat transfer and the change in the internal energy, then
-dw=d(pv) = pdv+vdp
Since dv almost equal zero for liquid (v is almost constant for liquid), then the integration yields to:
w=v*( change in pressure)
�b�P�
The discussion now is about the compressible flow (Gases). The relation between pressure and volume is inversely proportional and governed by Boyle's law. In compression process minimum work is required to be added to the flow to be closer to the ideal work, hence lead increase the efficiency. In the expansion process reverse occurs, the maximum work needs to be extracted from the flow to improve the efficiency of the process.
The following discussion can be useful
https://www.researchgate.net/post/What_is_the_difference_between_internal_energy_and_kinetic_energy_for_gases
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering