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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.

The relevant relationship,here is given by the Bernoulli Relationship:
P + p*g*h + 1/2*p*v^2 = constant
Which is fundamentally an energy conservation statement. If you multiply each term by the volume this becomes:
P*V + p*V*g*h + 1/2*p*V*v^2 = constant
P - is the pressure within the fluid and P*V is the internal energy, p is the density of the fluid and p*V*g*h is the gravitational potential energy and 1/2*p*V*v^2 is the kinetic energy.
Since the energy content of the moving fluid must be conserved, as the speed of the fluid increases its kinetic energy also increases. Since the total energy remains constant one of the other two terms must decrease if the kinetic energy increases. That means that the internal energy P*V must decrease to compensate for the increase in kinetic energy.
As for the volumetric flow rate the law of continuity, a statement of matter conservation, states that the volume flow rate entering the closed system must be equal to,the volume flow rate exiting the closd system assuming that the fluid is essentially incompressible.
As the diameter of the pipe increases the volume flow rate will remain constant but  the velocity of the fluid will increase. Increasing the velocity increases the kinetic energy which in turn decreases the pressure.
I am unfamiliar with the term "shaft work".


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James J. Kovalcin


I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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