# Infinite hose?

## Main Question or Discussion Point

My teacher gave our class a hypothetical situation today, and asked if it was possible.
He asked if a hose were attached to a faucet, is it possible for the hose to be long enough so that the resistance in the hose causes the water to stop.

Is this possible?

From what I have thought through, the hose would have to be an infinate length in order for the water to not be able to pass through.
Am I way off?
Is there a real distance that a hose can be in order to stop water?

## Answers and Replies

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Danger
Gold Member
Welcome to PF, Cgrover.
The answer is 'yes' in practical terms; I'm not sure about theoretically, but I suspect so. Incidentally, you can't have an infinitely long hose, because there would be no place to put it. Once its coiled-up volume matches that of the universe, you're pretty much hooped.

mathman
My teacher gave our class a hypothetical situation today, and asked if it was possible.
He asked if a hose were attached to a faucet, is it possible for the hose to be long enough so that the resistance in the hose causes the water to stop.

Is this possible?

From what I have thought through, the hose would have to be an infinate length in order for the water to not be able to pass through.
Am I way off?
Is there a real distance that a hose can be in order to stop water?
I suspect that gravity could play a role. Put the faucet on top of a mountain and the hose going downhill. The water will come out the other end, no matter how long the hose is - at least till it reaches level ground.

rcgldr
Homework Helper
Both water and oil are pumped through hundreds of miles of pipelines without issue.

Danger
Gold Member
Jeff, what I'm wondering about is if there is a point at which the cross-section of the pipe would have to be so large that it wouldn't be practical. Pipelines are pretty humongus; could you force something for thousands of miles through an automotive brake line tube? (I mean actual fluid flow, as opposed to hydraulic pressure to work a remote cylinder.) It seems counter-intuitive to me, but I really don't know.

rcgldr
Homework Helper
As long as the length is longer than some small amount, it doesn't matter. You have zero flow at the walls of a pipe, and maximum flow at the center of the pipe. The maximum and overall flows don't diminish because of distance, as long as there's enough power to propel the fluid through the pipe. If the flow were to slow down, then there would be accumulation of fluid along the pipe, which could only happen if the fluid compressed and/or the pipe expanded. In the case of water or oil, the amount of compression would be very small.

Danger
Gold Member
Okay, I'm not familiar with fluid dynamics, so I was somehow thinking of the resitance rising with distance. What about the required pumping power, then? Does that increase with distance?

russ_watters
Mentor
The answer is 'yes' in practical terms; I'm not sure about theoretically, but I suspect so.
Not sure if you misread the direction of the question, but the answer is no in both practical and theoretical terms.

The OP asks specifically about the resistance of the hose, which means we are to disregard gravity here. Since friction and pressure resistance are dependent on velocity, no velocity would mean no resistance. Adding pipe makes resistance increase linearly (if velocity were held constant), and velocity to decrease hyperbolically, but never reaching zero.

russ_watters
Mentor
Jeff, what I'm wondering about is if there is a point at which the cross-section of the pipe would have to be so large that it wouldn't be practical.
Well, the OP's question was specific about if the flow would stop. Sure, it decreases as the pipe length increases.
Pipelines are pretty humongus; could you force something for thousands of miles through an automotive brake line tube?
Sure, as long as you don't need much flow. But it won't be zero.

Danger
Gold Member
Since friction and pressure resistance are dependent on velocity, no velocity would mean no resistance. Adding pipe makes resistance increase linearly (if velocity were held constant), and velocity to decrease hyperbolically, but never reaching zero.
Now I'm just totally confused. Wasn't he talking about flow? If so, that rules out the 'no velocity' scenario. You can't have a flow without a velocity. Or can you? Man, I'm out of my depth here.

rcgldr
Homework Helper
How can the flow slow down? Assume that there are 100 gallons per minute of flow at some point A on a long pipe. Further down along the pipe at point B assume that the flow is reduced to 50 gallons per minute. That means that between point A and point B, there is a net accumation of 50 gallons of fluid per minute. How is this possible for a sustained period? Where is this fluid accumulating in the pipe?

Danger
Gold Member
I never considered that it could slow down unsymmetrically. I just thought that at some point the pump might not be able to handle the flow and thus the entire system would slow to the point of not being able to move at all.
As mentioned repeatedly in the past, I have no formal education, so I'm just trying to get a handle on this. I dismissed the gravitational factor before responding, but I don't see how a, for instance, 1/2 hp motor/pump could force oil through a light-year of 1/8th" tubing.

rcgldr
Homework Helper
Alaskan pipe line, 800 miles long, 4 foot (48 inch) diameter, up to 11 pumps and drag reducing agent allow up to 2.1 million barrels per day flow (at over 1000psi), although 7 pumps and flow around 750,000 barrels a day is more common these days. New more efficient pumps may reduce the number of pumps required.

For water pipes 3/4 inch is good enough for a typical household with about 250 feet of pipe, although it's not one long length. Local water pipes run from 1 to 3 inch diameters, while water mains run from 8 inches to 48 inches.

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You would have to have either parallel paths (small leaks every ten feet, for example) or a non-steady flow for there to be such a length.

russ_watters
Mentor
Now I'm just totally confused. Wasn't he talking about flow? If so, that rules out the 'no velocity' scenario. You can't have a flow without a velocity. Or can you? Man, I'm out of my depth here.
Yes, no flow=no velocity. You can't have no flow (double negative!) because that would mean there would be no resistance to flow....which would then enable flow.

russ_watters
Mentor
How can the flow slow down? Assume that there are 100 gallons per minute of flow at some point A on a long pipe. Further down along the pipe at point B assume that the flow is reduced to 50 gallons per minute. That means that between point A and point B, there is a net accumation of 50 gallons of fluid per minute. How is this possible for a sustained period? Where is this fluid accumulating in the pipe?
The flow in the entire pipe is decreased by adding more pipe. Yes, conservation law applies - you can't have different flow rates in the same pipe.

Incidentally, there was an article in HPAC magazine last month about a similar scenario. A contractor wanted to run an air conditioning unit during construction to dry some paint, but the ductwork wasn't installed yet. This caused the fan to over-amp and trip it's breaker. No ductwork means less resistance, which means more flow, which means more horsepower is required of the fan.

Alaskan pipe line, 800 miles long, 4 foot (48 inch) diameter, up to 11 pumps and drag reducing agent allow up to 2.1 million barrels per day flow (at over 1000psi), although 7 pumps and flow around 750,000 barrels a day is more common these days. New more efficient pumps may reduce the number of pumps required.

For water pipes 3/4 inch is good enough for a typical household with about 250 feet of pipe, although it's not one long length. Local water pipes run from 1 to 3 inch diameters, while water mains run from 8 inches to 48 inches.
So if 10 pumps were removed does flow cease or become considerably slower?

Welcome to PF, Cgrover.
The answer is 'yes' in practical terms; I'm not sure about theoretically, but I suspect so. Incidentally, you can't have an infinitely long hose, because there would be no place to put it. Once its coiled-up volume matches that of the universe, you're pretty much hooped.
I don't think that suggesting an infinitely long hose is any different than examples of massless strings, ideal springs, frictionless inclines, infinite planes of charge, etc.

Indeed the answer in no:
We can use the Navier-Stokes equation to demonstrate that the flow rate (Volume of fluid flowing through the hose per unit time) is proportional to the pressure gradient: the output of the hose is atmosferic pressure P0 and the input is P1>P0. So, the only way not to have flow is that pressure gradient is 0, i.e., the hose is infinite (if we assume P1>P0). Of course, as the length of the hose increases, the pressure gradient decreases and so does the flow rate.

russ_watters
Mentor
So if 10 pumps were removed does flow cease or become considerably slower?
It does not cease, it just becomes slower.

rcgldr
Homework Helper
Is there a simple relationship between pipe diameter and fluid drag? I realise that there are other factor such as speed, viscosity, ..., but I was curious about diameter versus drag if the other factors are kept the same.

Nothing simple that I'm aware of. You usually end up using a table or graph.

Dale
Mentor
For laminar flow I believe that the resistance is related to the diameter to the fourth power. So doubling the diameter will increase the flow 16-fold for the same pressure gradient.

So there is a given length where the flow will cease from a faucet with standard pressure(it's a tap where I am) or does flow slow toward infinity.