# What is the relationship between flow work and velocity of gas?

As we know that for open systems, we have energy conservation equation as $$h+\frac{v^2}{2}+zg=const.$$ $$h=u+pV$$ $$u+pV+\frac{v^2}{2}+zg=const.$$

Here $pV$ is flow energy. We know that all these different types of energies (internal energy, flow energy, kinetic energy and potential energy) are interchangeable.

My friend asked that when gas expands isothermally then the $pV$ (magnitude of flow work) remains the same before and after the expansion of gas (due to constant temperature the internal energy also remains constant and for horizontal flow, change in potential energy is zero).

When $pV$ is the same before and after the expansion, then from where the energy comes for the velocity of gas due to expansion.

I asked that first of all if the process is isothermal then it should be very slow and if the process is rapid then there must be a drop in the temperature of the gas. But it means a drop in internal energy provides energy for velocity. I want to know is there any relationship between flow work and velocity. Are these two energies (flow work and velocity) interchangeable?

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– user191954
Commented Jul 18, 2018 at 11:41