Can you please explain Bernoulli's equation?

[Callmelucky]

Ok, well I'm trying to establish whether any of this explanation is landing before we keep moving. Does the diagram in #35 make sense to you?

I do understand that

 

[erobz]

I do understand that

Then that should answer your question about the existence of $F_2$?

 

[erobz]

If it's too complicated and way beyond high school curriculum then I accept that $F_2$ is there and I don't need to completly understand it , but I asked this question because I thought it's something simple that is not explained in tectbook

The existence of $F_2$ is not beyond high school curriculum. A mountain is being made of a mole hill. Why do you have no trouble believing $F_1$ exists?

 

[Callmelucky]

The existence of $F_2$ is not beyond high school curriculum. A mountain is being made of a mole hill. Why do you have no trouble believing $F_1$ exists?

Because that is force we are creating(actually pump) to move fluid around(then again you showed me that there is no work done which makes sense because there is no friction so all we need is initial push to keep fluid moving forever, but that is in pipes that have same diameter all around) but then again if energy is conserved, for pipes that do become narrow if some energy is taken there it will be given back when pipe become wide again, so I don't get where $F_2$ comes from, because if there i $F_2$ then we do need pump

 

[Callmelucky]

Then $F_1$ is used only to overcome air, but then again, air is fluid, and there is no friction, so taken mass of air into consideration the only thing that can happen is smaller acceleration of fluids(water and air in this case).

But that is if pipe has same diameter all the way around, there won't be any changes in kinetic, potential(in no difference in height) and pressure.

If pipe does have different diameters in different areas then pressure and kinetic energy will change but ultimately they will be conserved.

 

[Callmelucky]

So I don't get why would anyone want to apply force on both ends of pipe, the only thing that can happen is for pipe to explode eventually.

But yet again, what is the point of puttin that in textbook at the beginning where student is learning the concept.

 

[Callmelucky]

only thing $F_1$ can be used for is to overcome gravity.

Or maybe they didn't think that air outside the pipe is ideal fluid. Maybe that air that enters the pipe does have some friction with pipes so $F_1$ is used to overcome that.

But then again that should be mentioned.

 

[Lnewqban]

So I don't get why would anyone want to apply force on both ends of pipe, the only thing that can happen is for pipe to explode eventually.

But yet again, what is the point of puttin that in textbook at the beginning where student is learning the concept.

You are correct, excessive internal static pressure can make a pipe fail.

You can have a U-shaped vertical tube with a closed valve that keeps a height differential between left and right columns.
For that set up, fluid is not moving, therefore it has no dynamic energy, only potential and pressure.

After we suddenly open that valve, the volume contained between the two columns (the U of the arrangement) will be feeling a different amount of pressure between left and right ends or cross-sections.
That pressure differential will tend to naturally get balanced (due to energy loss through friction and turbulence), but it will give impulse to our volume of fluid initially inside the bottom of the U tube.

These additional links may help you:
http://hyperphysics.phy-astr.gsu.edu/hbase/press.html#ed

http://hyperphysics.phy-astr.gsu.edu/hbase/bercon.html

 

[Callmelucky]

You are correct, excessive internal static pressure can make a pipe fail.

You can have a U-shaped vertical tube with a closed valve that keeps a height differential between left and right columns.
For that set up, fluid is not moving, therefore it has no dynamic energy, only potential and pressure.

After we suddenly open that valve, the volume contained between the two columns (the U of the arrangement) will be feeling a different amount of pressure between left and right ends or cross-sections.
That pressure differential will tend to naturally get balanced (due to energy loss through friction and turbulence), but it will give impulse to our volume of fluid initially inside the bottom of the U tube.

These additional links may help you:
http://hyperphysics.phy-astr.gsu.edu/hbase/press.html#ed

http://hyperphysics.phy-astr.gsu.edu/hbase/bercon.html

can I access other topics as well from their site, as far I could see that is from Alabama University

edit: I was wrong it's hyper Physics. Mental maps got me confused, didn't know they were interactive.

Thanks for sharing.

 

[Callmelucky]

Pease, see:
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/14-6-bernoullis-equation/

This is awesome, thank you.

 

[Lnewqban]

This diagram shows that you can have pressure on both sides of the volume of fluid you are analyzing.
Let's assume that your book represents only the volume of oil contained in the tube and transition.

As you can see, nothing is moving as represented; therefore, the value of static pressure in cross-sections S1 and S2 must be equal to the height pressure created by the column of water on the left leg.

Once the valve is opened, the pressure on S2 is the atmospheric pressure, which is transferred through the volume of ethanol.
The higher value of the static pressure acting on S1 will move oil and ethanol up through the horizontal and right vertical tube.

As the water level descends, the pressure on S1 gets smaller, while the pressure on S2 increases.
Naturally, the levels of the open surfaces inside the left and right vertical tubes, will tend to equalize.

When that state of balance is eventually reached (after some time of back-and-forth oscillations of the fluid inside the U-shaped tube), pressure on S1 will have a greater value than the pressure on S2 due to the height difference between both sections.

 

[erobz]

Here is another example: The loop is initially charged to some desired pressure $P$ by the fill line. It is part of very commonly used hydronic heating systems in homes across the globe. They are also used heavily in industry as part of process cooling systems.

Any elemental slice you pick in the loop, there is a pressure acting on either side of it.

And furthermore, you don't need these special systems. In any piping system with fluid flowing there is a differential pressure across virtually any section you wish to examine, and that's because they all have what Bernoulli's doesn't have...friction.

So, if you are trying to determine head loss for a particular component, Bernoulli's still can be useful. If you are measuring pressures across a fitting (and flow rate), Bernoulli's says $X$ for the pressure differential, but we are measuring $Y$, the difference is...the head loss from friction.