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Physicist1011
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For a vertical pipe of water can the pipe length affect the velocity of the water?
note: the water is flowing through this vertical pipe.
note: the water is flowing through this vertical pipe.
Water is flowing through a pipe (where the water is being pumped up due to pressure). If the length of this pipe the water is flowing through is increased - how will this affect the water's velocity at the end of the pipe (which is open to the atmosphere).Orodruin said:Please be more specific in your question.
So you are pumping in water at the bottom and seeing how fast it squirts out the top? One answer is that it depends on the pump.Physicist1011 said:Water is flowing through a pipe (where the water is being pumped up due to pressure). If the length of this pipe the water is flowing through is increased - how will this affect the water's velocity at the end of the pipe (which is open to the atmosphere).
jbriggs444 said:So you are pumping in water at the bottom and seeing how fast it squirts out the top? One answer is that it depends on the pump.
If the pump is producing a constant flow rate then the flow rate out the top will be the same as the flow rate into the bottom, regardless of the pipe length.
If the pump is producing a constant pressure then the flow rate out the top will diminish and ultimately stop if the pipe is too tall. Roughly speaking, one psi will let you pump water up through two feet of vertical rise. That is because a one pound column of water with a cross section of one square inch is about two feet high (27 inches).
If the vertical tube has a constant cross-section [and if the water in the tube is not so saturated with dissolved gasses that bubbles form on the way up] then constant flow rate means constant stream velocity. The velocity of the water at the top is identical to that at the bottom.Physicist1011 said:Water is an incompressible liquid, it will have a constant flow rate in the tube. But what about the velocity of the water at the exit of the tube at the top. Also it works by air entering a container of water (via another tube) so that the pressure in the container of water increases - the water is then pumped up the tube (and exits this tube forming a fountain). I think that the pressure that causes the water to flow up the tube is not constant, but I am not completely sure.
Constant for one scenario, but different scenarios (different tube lengths) may have different velocities.Physicist1011 said:Water is an incompressible liquid, it will have a constant flow rate in the tube.
Exit velocity is tube velocity.But what about the velocity of the water at the exit of the tube at the top.
Basically in this scenario the pressure determines the velocity and total height of the fountain, largely independent of tube length for relatively short tubes.Also it works by air entering a container of water (via another tube) so that the pressure in the container of water increases - the water is then pumped up the tube (and exits this tube forming a fountain).
russ_watters said:Exit velocity is tube velocity.
russ_watters said:Basically in this scenario the pressure determines the velocity and total height of the fountain, largely independent of tube length for relatively short tubes.
No. This is impossible as long as the liquid can be regarded as incompressible and the tube cross sectional area is constant. It would violate conservation of mass. What happens is that the pressure gradient provides a force that acts against and exactly cancels the viscous forces and gravity.Physicist1011 said:Wouldn't the velocity decrease going upwards in height due to gravity acting downwards and friction of the tube walls on the water?
Thank you for your answer. Also I don't quite understand how conservation of mass would be violated?Orodruin said:No. This is impossible as long as the liquid can be regarded as incompressible and the tube cross sectional area is constant. It would violate conservation of mass. What happens is that the pressure gradient provides a force that acts against and exactly cancels the viscous forces and gravity.
jbriggs444 said:Yes, water pressure is responsible for this. The difference in pressure between the top and bottom of that parcel is the driving force.
If the flow velocity changed, there would be a net influx of mass into any test volume (mass would enter faster at the bottom than it exits at the top). This would mean that the mass inside the test volume would increase. This is incompatible with the density being constant.Physicist1011 said:Thank you for your answer. Also I don't quite understand how conservation of mass would be violated?
If pressure is higher on the bottom than the top of the parcel then that means that there is a net upward force on that parcel due to pressure, yes. [Which, if the parcel is at constant velocity, exactly matches the downward force from gravity and any viscous losses].Physicist1011 said:How is the difference in pressure between the top and bottom of the parcel the driving force. Is it because water will move from higher water pressure to lower water pressure?
The cause of the water pressure is not relevant. The behavior of the water in the tube is what it is regardless of whether the pressure at the inlet is caused by air pressure, pump pressure or someone squeezing a bladder.Also you said water pressure is responsible for this, what about air pressure since air pressure is what pushes the water up the tube?
jbriggs444 said:If pressure is higher on the bottom than the top of the parcel then that means that there is a net upward force on that parcel due to pressure, yes. [Which, if the parcel is at constant velocity, exactly matches the downward force from gravity and any viscous losses].
Yes.Physicist1011 said:Isn't the water traveling up at a constant velocity.
No, there are no net forces here.But now there is a net force due to pressure on it?
As already stated, the force from the pressure gradient exactly cancels the gravitational and viscous forces.Physicist1011 said:Isn't the water traveling up at a constant velocity. But now there is a net force due to pressure on it?
In perfect, frictionless situation with perfectly noncompressible liquids or perhaps superfluids this would not be a case, eg length of pipe would not affect velocity.Physicist1011 said:For a vertical pipe of water can the pipe length affect the velocity of the water?
note: the water is flowing through this vertical pipe.
Can you draw us a diagram of what you are describing? It isn't at all clear to me what this setup looks like.Physicist1011 said:What about a tube of air - if air was traveling from one container via a tube, because the pressure in the first container is increasing because water is entering there (via another tube). Would the length of the tube which air is traveling into another container matter?
Ok I am confused now. The users above wrote different answers and made sense. Doesn't the friction and weight force get balanced by the upward force due to pressure for the tube in which water is travelling. And why wouldn't this be the same for the tube of air?Martin0001 said:In perfect, frictionless situation with perfectly noncompressible liquids or perhaps superfluids this would not be a case, eg length of pipe would not affect velocity.
However real pipes, regardless how smooth, will impart some friction, if only due to intermolecular interaction water/tube material.
In any realistic pipe its length will affect velocity and with growth of pipe diameter departure from expected values will be more and more negligable.
Energywise we have conversion of part of mechanical energy of pump into heat dissipated in walls of pipe and in water.
Overal effect is that with increased length of pipe velocity would drop.
You should also read about laminar and turbulent flow. Former one is something what engineer would struggle for but the later is what he usually get for one or another reason. So the compromise is "as laminar as possible".
Equations are there, you can find them probably via wiki.
Regarding air, yes, length of tube would also matter. Situation there is getting even more complex because air is much more compressible than water is. This is adding "inertia" or time delay to air flow.
- There is a tube of air leading from one container to another. If I increase the tube length how will this affect pressure.russ_watters said:Can you draw us a diagram of what you are describing? It isn't at all clear to me what this setup looks like.
That isn't a diagram. Please provide a diagram.Physicist1011 said:- There is a tube of air leading from one container to another. If I increase the tube length how will this affect pressure.
- There is a container of water which a tube connects from here to another container (vertically), air pressure will increase in the container (as air is pumped in there) causing the water to flow up a vertical tube. How will the length of this tube affect the velocity of the water in the tube (basically how affects pressure that causes the water to move up the tube).
Ok, so there is no way I could have understood that from the description. This is just a complicated siphon and the length of the air tubes don't matter except that the pressure in them is determined by the height of the water tubes and reservoirs.Physicist1011 said:
I am not talking about the water reservoirs. I don't understand whether the length of the tubes affect the velocity of the water in tube from B to A.russ_watters said:Ok, so there is no way I could have understood that from the description. This is just a complicated siphon and the length of the air tubes don't matter except that the pressure in them is determined by the height of the water tubes and reservoirs.
In general longer pipes will have more friction loss, but which pipe are you referring to? For example, if you lower tank C, the flow rate will increase.Physicist1011 said:I am not talking about the water reservoirs. I don't understand whether the length of the tubes affect the velocity of the water in tube from B to A.
Before it was said that it does not matter because the pressure causes a force which cancels out friction and weight forces.
The question that I'd heard and answered was whether the length of the tube affected the difference between inlet velocity and outlet velocity. It does not. That's not the same as asking whether it affects velocity.Physicist1011 said:I am not talking about the water reservoirs. I don't understand whether the length of the tubes affect the velocity of the water in tube from B to A.
Before it was said that it does not matter because the pressure causes a force which cancels out friction and weight forces.
I do not understand that. So velocity will change with length then?jbriggs444 said:The question that I'd heard and answered was whether the length of the tube affected the difference between inlet velocity and outlet velocity. It does not. That's not the same as asking whether it affects velocity.
Lowering tank C will affect the water heights - that is why flow rate will increase.But will increasing the tube from B to A or C to A affect the velocity of the water at the top of the tube from B to A where the water comes out.russ_watters said:In general longer pipes will have more friction loss, but which pipe are you referring to? For example, if you lower tank C, the flow rate will increase.
Increasing tube lengths without increasing the height? That will reduce flow rates due to added friction lossPhysicist1011 said:Lowering tank C will affect the water heights - that is why flow rate will increase.But will increasing the tube from B to A or C to A affect the velocity of the water at the top of the tube from B to A where the water comes out.
The air tubes are generally considered unrestricted here so their length doesn't introduce added loss.Physicist1011 said:Ok, so this will happen to tubes B to A and C to A but not from B to C right? (why)