I'm working on a problem that states :
"Methane enters a 3cm ID pipe at 30'C and 10 bar with an average velocity of 5m/s and emerges at a point 200 m lower than the inlet at 30'C and 9 bar"
The questions asks us to predict the signs for Kinetic and Potential energy. We were given the solutions which state that the kinetic energy is positive because when pressure decreases, volumetric flow rate increases and therefore the velocity. With constant temperature and diameter how is it possible for the pressure to decrease?
I'm trying having trouble trying to wrap my head around this concept. I don't understand what pressure they're referring to because from everything I read, kinetic velocity depends on the cross sectional area of a pipe.
Also, I'm struggling to understand the definition of shaft work and flow work in a process. The book explains shaft work as any extra work done that doesn't fall under the category of flow work but is it work done on a system or by a system?
Thanks a million in advance for any clarification regarding this.
Regarding the statement that kinetic velocity depends on the cross sectional area of a pipe, you need to be careful about the situation that statement applies to.
Think of a stable river where the water level at point A is constant and at point B the level is constant. Meaning the river's level, compared to flood stage, is the same as it was yesterday. At point A, the volume of water flowing past per minute is Va. At point B, the volume of water flowing past per minute is Vb. Assuming there are no streams adding water between A and B (or water plants taking water out) Va=Vb. So the volumetric flow rate is the same at both points. That has to be, if a certain amount of water goes past A, the same amount has to go past B. If the river at B is shallower, but still the same width, the water has to be going faster to get out of the way of the volume Va (per minute) that is coming from upstream.
But if water could be compressed, the volume Vb could be different from Va. Even then, the number of molecules would have to be the same.
I assume your question asks you to predict the signs for THE CHANGE IN Kinetic and Potential energy. I also assume that when the methane emerges, it is going into air at 1 bar. It is pressurized in the pipe, so it rushes to the outlet to escape. Regarding the relationship between pressure and velocity, check out this site:
About potential energy, see this site for a good discussion.
Shaft work and flow work are new terms to me. I tried searching but I couldn't identify a clear explanation. This one seems like a basic description.
I hope this helps,