Looking at the Hyperphysics site, I see something that stops my mind, so I have to ask. It's about how Bernoulli's equation describes conservation of energy. It shows pressure energy, kinetic energy per unit volume, and potential energy per unit volume added together to make a constant.
Then it seems to be saying that pressure energy and kinetic energy trade places in a nozzle or tube of varying diameter. Other sources seem to say that pressure energy IS potential energy and a nozzle changes POTENTIAL and kinetic back and forth.
Are they trying to say there are two kinds of potential energy? With elastic potential energy as pressure energy and something else too that is another kind of potential energy?
Here's the equation. The first term is "pressure energy". The second term is "kinetic energy per unit volume". The third term is "potential energy per unit volume". The numbers in P1, P2, v1, v2 are subnotations.
P1 + 1/2 * rho * v1^2 + rho * g * h1 = P2 + 1/2 * rho * v2^2 + rho * g * h2
Thanks. Here's the link to the original article:
http://hyperphysics.phy-astr.gsu.edu/hbase/pber.ht...
Please relate this to flow of air in pipes if possible.
Thanks.
Answers & Comments
Verified answer
1. pressure energy is a silly term. there is no such thing. pressure = force/area = m/LT^2 (in dimensions of mass, length and time)
2. potential energy they talk about here is the 'gravitational potential energy'. for unit volume, it has the same units m/LT^2 it is also pressure due to gravity (pressure coming from the fluid above that unit volume)
3. the difference between P and \rho gz is that P is not from gravity ... it's there simply because there is a source supply fluid through that pipe and that flow has a separate pressure that does not depend on z (the vertical position of the unit volume)
4. and then there is KE per unit volume, which again has a same units : energy/volume = (force x distance)/volume = force/area = pressure.
5. so, essentially, for a unit unit volume of fluid, Bernoulli's equation is just the 'conservation of energy' equation, if you change grav. pot. energy (by changing height) and/or pressure (by changing the pipe aperture), the KE (or the velocity of the unit volume) changes automatically to adjust to keep the sum (KE + PE) constant.
Potential energy is simply the potential to have the capability to do work or cause a change. Both GPE and EPE do that; they both represent stored energy that can be released to do work or cause a change. And if you really want to ace your score, CPE, chemical potential energy, is also stored energy ready to be released to do work or cause a change. The energy stored in gasoline (petrol) is CPE. So at the abstract, GPE, EPE, and CPE are all the same. They are all stored energy that can be released to do work or cause a change. But there are differences. The differences are in the sources of that potential. For GPE, the force of gravity over a distance, which is GPE = Wh, is the source. When lifting somethings that weighs W = mg up to a height h, we do work on that something. And that's where the GPE comes from, the work we put into that something lifted. For EPE, the elasticity of the body, which is its tendency to return to a neutral size after being stretched or compressed, is the source. Again, we put work into the body by exerting a force F over some distance dX. But if the elasticity follows Hooke's Law, F = kdX and the average force over the distance dX is F/2 = kdX/2. So the work is average force over the distance = F/2 dX = kdX/2 dX = 1/2 kdX^2. And that's where EPE comes from, the work required to change the shape, dX. CPE is not as straight forward as work in = PE. But chemical potential energy comes from energy being transformed into chemicals that can later release that energy. Decaying biomass, dinosaurs and ferns, add their energies under ground under pressure and become petroleum, chock full of energy ready for release in your Ferrari for example. So the differences in PE are in the sources of that PE. Otherwise, they are all the same, stored energy ready to be released to do work or cause a change.