Physics/Work & Energy
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.
It is possible for the pressure to decrease because velocity has increased. First off, a lower position on the piping means that potential energy decreased and kinetic must increase. This results in increased velocity, but also means that if you look at velocity as a function of pressure and think of the pressure as the result of collisions with the materials in front of a given volume of gas, then you can deduce that the number of collisions must be decreasing and that pressure must be lower.
Regarding kinetic velocity: It's a rather ugly way of describing flow rate. Don't get too hung up on it. You will notice that the kinetic velocity depends on the cross section alone,only when temperature, potential energy and pressure are constant, in truth any of them can vary.
While the beginning half of this page (http://udel.edu/~inamdar/EGTE215/Pipeflow.pdf
) is pretty basic, about half way through they work some problems where these are not held constant.
Shaft work and flow work: while it varies between disciplines such as engineering, chemistry and physics, I define shaft work as work done by the fluid/gas on a moving part or on the pipe itself. Flow work is a differential measurement: it represents the amount of work being done by the fluid/gas (work - out) minus whatever work was done on the fluid at the inlet (work in)... so for a flow work calculation you are actually looking at two parts, initial work on the fluid and final work by the fluid at the outlet.
I hope this helps.