Water Velocity Question: Impact of Pipe Length on Flow Rate

[Physicist1011]

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.

 

[Orodruin]

Please be more specific in your question.

 

[Physicist1011]

Please be more specific in your question.

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]

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).

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).

 

[Physicist1011]

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).

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.

 

[jbriggs444]

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.

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.

Consider a small parcel of water as it rises through the tube. As above, that parcel has the same velocity at top and bottom and every point in between. It is not accelerated. It follows that it is under zero net vertical force throughout its upward journey. But gravity acts on that parcel, pulling it downward. There must be some other force that acts opposite to gravity, driving it upward.

Yes, water pressure is responsible for this. The difference in pressure between the top and bottom of that parcel is the driving force. Pressure decreases all the way up the column. The pressure at any given point will be given by $P=\rho g h$ where P is the pressure, $\rho$ is the density of the fluid, g is the acceleration of gravity and h is the depth (height) below the top of the tube.

Now then, you speak of a "container of water" that is pressurized by air entering it. If we attach the vertical tube to the container so that water is allowed to leave the container and enter the tube under this pressure then we will notice something. The slowly moving water in the container will be at a pressure higher than $\rho g h$. Bernoulli explains why.

 

[russ_watters]

Water is an incompressible liquid, it will have a constant flow rate in the tube.

Constant for one scenario, but different scenarios (different tube lengths) may have different velocities.

But what about the velocity of the water at the exit of the tube at the top.

Exit velocity is tube velocity.

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).

Basically in this scenario the pressure determines the velocity and total height of the fountain, largely independent of tube length for relatively short tubes.

 

[Physicist1011]

Exit velocity is tube velocity.

Wouldn't the velocity decrease going upwards in height due to gravity acting downwards and friction of the tube walls on the water?

Basically in this scenario the pressure determines the velocity and total height of the fountain, largely independent of tube length for relatively short tubes.

What do you mean 'for relatively short tubes'?

 

[Orodruin]

Wouldn't the velocity decrease going upwards in height due to gravity acting downwards and friction of the tube walls on the water?

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]

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.

Thank you for your answer. Also I don't quite understand how conservation of mass would be violated?

 

[Physicist1011]

Yes, water pressure is responsible for this. The difference in pressure between the top and bottom of that parcel is the driving force.

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?
Also you said water pressure is responsible for this, what about air pressure since air pressure is what pushes the water up the tube?

 

[Orodruin]

Thank you for your answer. Also I don't quite understand how conservation of mass would be violated?

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.

 

[Orodruin]

You can actually observe this with a regular faucet. If you put a sufficiently low water flow, the column of water will be thicker at the top. Essentially the only force acting on the water is gravity (and surface tension), which means that the water will fall faster as it goes down. Since the flux is the same in all parts of the column, this means that the column's cross sectional area must decrease as the water falls. I am sure you have seen and noticed this phenomenon.

However, in your case, the cross sectional area is the same and therefore the velocity must be the same in order to keep the flux the same all along the column.

 

[jbriggs444]

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?

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].

Also you said water pressure is responsible for this, what about air pressure since air pressure is what pushes the water up the tube?

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.

 

[Physicist1011]

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].

Isn't the water traveling up at a constant velocity. But now there is a net force due to pressure on it?

 

[russ_watters]

Isn't the water traveling up at a constant velocity.

Yes.

But now there is a net force due to pressure on it?

No, there are no net forces here.

 

[Orodruin]

Isn't the water traveling up at a constant velocity. 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.

 

[Outhouse]

As water travels up said pipe, the pressure required increases due to atmospheric pressure.

Most pumps list head height ratings as flow lowers the higher fluid goes up, and electricity usage goes down with more head pressure on pump.

So yes the longer the pipe travels upward, the flow will decrease with length due to pump limitations upon atmospheric pressure.

If pipe is level sideways, length does not play a role, as your using/fighting atmospheric pressure.

sorry if I misunderstood the question.

 

[Physicist1011]

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?

 

[Martin0001]

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.

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.

 

[russ_watters]

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?

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]

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.

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?

 

[Physicist1011]

Can you draw us a diagram of what you are describing? It isn't at all clear to me what this setup looks like.

- 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).

 

[russ_watters]

- 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).

That isn't a diagram. Please provide a diagram.

 

[Physicist1011]

That isn't a diagram. Please provide a diagram.

 

[russ_watters]

View attachment 221133

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.

 

[Orodruin]

... and no, it will not give you a perpetual motion device ...

 

[Physicist1011]

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.

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.

 

[russ_watters]

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.

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.

 

[jbriggs444]

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.