Minimize supported weight of a water pipe

[RobertGC]

TL;DR Summary

Weight of water pipe.

I’m trying to calculate the weight I have to support at one end of a pipe with flowing water. So suppose you had a water pipe that extended from the ground upwards some distance away both horizontally and vertically, i.e., at an angle. Normally, you don’t have to worry about this issue because the entire length of the pipe would be on the ground going uphill:

But I’m envisioning a scenario with it being supported at only the end point, aside from the beginning point resting on the ground. If the pipe is straight, empty with one end on the ground, at most you would have to support is 1/2 the weight of the pipe, when horizontal, with this supported weight gradually decreasing to 0 as the angle went to to 90 degrees, i.e., vertically upwards.

Now suppose you had static water in the pipe it would be the same idea with the weight of the water included. But it seems to me if the water is flowing then the pressure/speed of the water would naturally cause the water to flow upwards anyway so the weight that needed to be supported should be less.

But the curve the water would want to go on its own would actually be parabolic. So the curve you should actually make the pipe be in is actually parabolic instead of straight if what you want to do is minimize the necessary supported weight. Now this would make the length of the curved pipe longer so the weight of the pipe itself would be more than for the straight pipe. Still, assuming the amount of flowing water is such that the pipe is continually filled, no empty space, then this should still reduce the total weight by reducing the weight of the water needing to be supported.

But there is another complication. With the water contacting the walls of the pipe and the friction that thereby arises the speed and/or direction of the water is altered so it wouldn’t really be going *naturally* in a parabolic path on its own. So the weight of the water would still need to be supported to some extent even with the pipe is in a parabolic shape.

In that case what would be the optimal shape of the pipe to minimize this supported weight of the water pipe?

 

[Dale]

Summary:: Weight of water pipe.

If the pipe is straight, empty with one end on the ground, at most you would have to support is 1/2 the weight of the pipe, when horizontal, with this supported weight gradually decreasing to 0 as the angle went to to 90 degrees, i.e., vertically upwards.

No, for an empty pipe you will need to support the full weight of the pipe regardless of the angle. If you don’t support the full weight then there will be a net force downward and therefore the pipe will accelerate down.

 

[RobertGC]

For the empty pipe case, if the pipe is vertically upwards then the ground is supporting the entire weight and you don’t have to support the weight at the top.

 

[Baluncore]

At the Ram pump you must have a solid fixing or concrete end-block at the bottom of the rising pipe. That block must counter two forces, the weight of the empty pipe, and the enclosed fluid pressure.
Empty pipe = weight of the pipe * Sin( slope angle).
The fluid = hydrostatic fluid pressure at bottom end of the pipe * cross-sectional area of the pipe.

The drive pipe must also be countered. But that is more tricky because of the pulse.
Assume the pressure in the drive pipe is the same as at the bottom of the riser pipe, because the valve opens during the pulse to connect the two pipes. Then compute the area of that pipe and multiply by that pressure.

In an ideal ram pump, the drive pipe will deliver in line with the output pipe so the pulse will not have to be countered in the pump mountings. But the continuous force in the riser must still be supported.

Remember for high lift ram pumps, the 10 metres of the driver pipe closest to the pump should be steel and not poly-pipe that will swell when the pulse occurs. The diameter of the entire driver pipe-line should be constant.

 

[jbriggs444]

For the empty pipe case, if the pipe is vertically upwards then the ground is supporting the entire weight and you don’t have to support the weight at the top.

That makes the unstated but reasonable assumption that the bottom support acts like a hinge and applies no torque while the top support acts like a freely sliding sleeve and applies force only at right angles to the pipe.

Edit: This is reasonably close to how teams of workmen deal with felling trees or standing up ladders and poles. You plant the one end (or notch the tree to make a hinge) and apply right-angle force as far up the tree/ladder/pole as can be managed.

 

[Dale]

For the empty pipe case, if the pipe is vertically upwards then the ground is supporting the entire weight and you don’t have to support the weight at the top.

I am not understanding the geometry. Could you sketch out what you are talking about. The picture you have is pretty, but not helpful

 

[anorlunda]

By the way, the pipe going uphill from the ram does not have to be rigid. A flexible pipe is inherently supported wherever it touches the ground.

Numerous videos on Youtube show ram pump installations using garden hose going up the hill.

 

[Baluncore]

The driver pipe and the delivery pipe have different mounting requirements.

The driver pipe need to be straight and of constant diameter. It can be held in place by the pump and pump mountings.

The air reservoir in the bulb at the pump maintains a reasonably constant pressure on the delivery pipe that runs up the hill to the storage tank. The delivery pipe can be a long thin polypipe since the water flow is slow and steady. If the delivery pipe is not buried half a metre underground, then it will be subjected to temperature changes. On a cold night the delivery pipe will shorten, then lengthen on a hot afternoon. Bends will be necessary to allow for the thermal length changes, apart from that, the route that the delivery pipe takes between the pump and the tank is not really important, except that it must be anchored to solid blocks at the bends, so it does not creep or slide down the hill.

 

[russ_watters]

With the caveat that a better diagram is needed (as others said)...

Now suppose you had static water in the pipe it would be the same idea with the weight of the water included. But it seems to me if the water is flowing then the pressure/speed of the water would naturally cause the water to flow upwards anyway so the weight that needed to be supported should be less.

No. If the speed is constant and the friction is low (which it usually is in relation to gravitational head), then there is no significant difference between the two cases. In both cases, *something* has to prevent the water from just flowing right back down and out of the pipe. It should be easy enough to identify what that device is in both cases.

 

[RobertGC]

At the Ram pump you must have a solid fixing or concrete end-block at the bottom of the rising pipe. That block must counter two forces, the weight of the empty pipe, and the enclosed fluid pressure.
Empty pipe = weight of the pipe * Sin( slope angle).
The fluid = hydrostatic fluid pressure at bottom end of the pipe * cross-sectional area of the pipe.

The drive pipe must also be countered. But that is more tricky because of the pulse.
Assume the pressure in the drive pipe is the same as at the bottom of the riser pipe, because the valve opens during the pulse to connect the two pipes. Then compute the area of that pipe and multiply by that pressure.

In an ideal ram pump, the drive pipe will deliver in line with the output pipe so the pulse will not have to be countered in the pump mountings. But the continuous force in the riser must still be supported.

Remember for high lift ram pumps, the 10 metres of the driver pipe closest to the pump should be steel and not poly-pipe that will swell when the pulse occurs. The diameter of the entire driver pipe-line should be constant.

Thanks for that. Actually, I only gave that pic of a ram pump, just to show the more common scenario of the ground supporting the entire weight. A ram pump might be used in my scenario though.

But the key feature of my scenario is that the pipe is not lying along the ground but is freely extending into the air, with a support only at the top.

This video might give an idea of where I’m going with this and why I need to minimize the supported weight at the top:

Drone Could Help Firefighters By Putting Out Fires.

Robert Clark

 

[RobertGC]

I am not understanding the geometry. Could you sketch out what you are talking about. The picture you have is pretty, but not helpful

The goal is to get to this:

Drone Could Help Firefighters By Putting Out Fires

Robert Clark

 

[russ_watters]

The goal is to get to this:

Drone Could Help Firefighters By Putting Out Fires

This is a very different scenario than the one you first presented. The video gives some clues as to the forces involved. Again: start by drawing a diagram of it and labeling as many forces as you can see.

 

[RobertGC]

Not really. The pipe or hose is only supported at the top. For this drone, at a 200 kg lifting capacity, it’s powerful enough to support the entire weight of the water up to close to 1,000 ft and the weight of the hose.

But for the application I’m envisioning I want the the hose or pipe to be much, MUCH longer. Then it would be unfeasible for the hovering vehicle to support the entire weight of the water column.

For fully vertical non-flexible pipe, you would not need to support any weight at all at the top and the water would extend all the way to the top given sufficient pressure. But suppose this pipe is at an angle, that’s when you have the issue of supporting the weight of the water and the pipe.

In addition to the previous video I linked, see also this:

JetLEV water propelled jet pack.
.

You see with sufficient pressure at the bottom and the opening at the top angled downward, the flowing water exiting at the top, can support the weight of the water, the weight of the pipe, and even extra weight.

Now envision much longer pipes, and the possible applications. Again, for a very long distance you don’t want to have to support the weight of the water column in the pipe/hose, either by a hovering vehicle or by the force supplied by the exiting pressurized water because that would require too much force to be applied.

Robert Clark

 

[anorlunda]

Hydrostatic pressure is the problem. Given a tall enough pipe, the hydrostatic pressure at the bottom will burst the pipe, not to mention overcome the maximum pressure of the supply pump. Figure roughly 450 psi per 1000 vertical feet of height.

 

[berkeman]

Hydrostatic pressure is the problem. Given a tall enough pipe, the hydrostatic pressure at the bottom will burst the pipe, not to mention overcome the maximum pressure of the supply pump. Figure roughly 450 psi per 1000 vertical feet of height.

Yeah, it looks like you can see that in the drone demo video. As it climbs higher the output pressure and flow go way down...

 

[Dale]

The goal is to get to this:

Drone Could Help Firefighters By Putting Out Fires

Robert Clark

Summary:: Weight of water pipe.

at most you would have to support is 1/2 the weight of the pipe, when horizontal, with this supported weight gradually decreasing to 0 as the angle went to to 90 degrees, i.e., vertically upwards.

So, with the clarified geometry this is not correct. Since the pipe is flexible there will be no support from the ground. The entire weight of the pipe and water must be supported by the drone.

 

[RobertGC]

Hydrostatic pressure is the problem. Given a tall enough pipe, the hydrostatic pressure at the bottom will burst the pipe, not to mention overcome the maximum pressure of the supply pump. Figure roughly 450 psi per 1000 vertical feet of height.

Yes. But consider this:

https://www.webstaurantstore.com/si...ne-and-50-hose-4200-psi-4-0-gpm/36660456.html

At about 10 times higher pressure at 4,200 psi get 10,000 ft(!) But then remember for a parabolic arc if you want to maximize horizontal distance given the same initial speed, or pressure, angle it at 45 degrees, then the horizontal distance will be twice as far, 20,000 ft, nearly 4 miles!

Obviously, at such very long distances you don’t want to support the weight of the water column, as it would take too much force. You want the water to travel that far due to its own pressure and velocity.

Robert Clark

 

[RobertGC]

So, with the clarified geometry this is not correct. Since the pipe is flexible there will be no support from the ground. The entire weight of the pipe and water must be supported by the drone.

Perhaps. For the scenario I’m envisioning with the water transported long distances. You might want the pipe to be fixed, non-flexible In a parabolic curve. But on the other hand if the water is flowing in a parabolic arc and the flexible hose material is quite lightweight the hose material might yet be supported by the water in a parabolic arc also.

Robert Clark

 

[Dale]

It is VERY difficult to answer a question where it is so vaguely described and every time I answer, the scenario is changed.

I, for one, am done. Best of luck.

 

[RobertGC]

The scenario with the drone supported fire hose might actually be feasible for the long distances I’m envisioning. Say you wanted to transport the water to a fire 20,000 feet horizontal distance away, about 4 miles, 6.4 kilometers. Calculate the length of the parabolic arc. At a 45 degree starting angle, the height will be 1/4th the range or 5,000 feet. This page has a calculator for parabolic arc length:
https://www.vcalc.com/wiki/vCalc/Parabola+-+arc+length

For a 20,000 foot range and 5,000 foot height, the length along the arc is about 23,000 feet. So you would need 23 of these drones placed at 1,000 feet apart to support that weight.

You would though need higher pressure at the start to get to the greater height of 5,000 feet, 5 times higher or about 2,250 psi. Many pressure washers get to those pressures and above.

Robert Clark

 

[berkeman]

Say you wanted to transport the water to a fire 20,000 feet horizontal distance away, about 4 miles, 6.4 kilometers.

What is the pressure loss in 4 miles of 3" flexible fire hose?

 

[RobertGC]

While we’re on the topic of how far we can send the stream of water you might want to see this video:

This could send a stream of water 100,000 feet into the air, 20 miles, or a 40 mile horizontal distance!

Robert Clark

 

[berkeman]

What is the pressure loss in 4 miles of 3" flexible fire hose?

https://www.firerescue1.com/fire-pr...-and-overcome-friction-loss-k79PfBh4sTCRaWZr/

 

[RobertGC]

What is the pressure loss in 4 miles of 3" flexible fire hose?

Good point. And the hose would also have to be heavier to resist the greater pressure.
There are a few formulas for pressure loss by distance such as:

https://en.m.wikipedia.org/wiki/Poiseuille's_law

Robert Clark

 

[russ_watters]

Not really. The pipe or hose is only supported at the top. For this drone, at a 200 kg lifting capacity, it’s powerful enough to support the entire weight of the water up to close to 1,000 ft and the weight of the hose.

No way. I'm sure you've miscalculated; show us your calculations.

Also, the the dynamics of this are complicated. A pressurized hose is somewhat self-supporting.

This could send a stream of water 100,000 feet into the air, 20 miles, or a 40 mile horizontal distance!

No it could not.

The bottom line of all of this is that you need to pick a specific scenario and start trying to solve it. Otherwise this is just pointless handwaving and we'll have to close it as being non-productive.

 

[RobertGC]

No way. I'm sure you've miscalculated; show us your calculations.
Also, the the dynamics of this are complicated. A pressurized hose is somewhat self-supporting.
No it could not.
The bottom line of all of this is that you need to pick a specific scenario and start trying to solve it. Otherwise this is just pointless handwaving and we'll have to close it as being non-productive.

About the fire fighting drone, I’m going by what was given in the video,

The drone could be used to fight fires to nearly 1,000 feet, 300 meters, and later in the video it was shown having a lifting capability of 200 kg. You’re probably right about the weight of the water being partially supported by the upward flow of the water, which is good for this scenario since it reduces the weight that needed to be supported by the drone.

For calculating the pressure loss by length of hose, we‘ll probably want to use more practical formulas than the Poiseuille formula. Ones in common use are Hazan-Williams:

https://en.m.wikipedia.org/wiki/Hazen–Williams_equation

and Darcy-Weisbach:

https://en.m.wikipedia.org/wiki/Darcy–Weisbach_equation

I’ll take a look at those numbers.

Robert Clark

 

[russ_watters]

About the fire fighting drone, I’m going by what was given in the video...

The drone could be used to fight fires to nearly 1,000 feet, 300 meters, and later in the video it was shown having a lifting capability of 200 kg. You’re probably right about the weight of the water being partially supported by the upward flow of the water, which is good for this scenario since it reduces the weight that needed to be supported by the drone.

Do. The. Math.

Or this thread will be closed.

A video making unsupported claims about a device that is still under developmentnent (translation: doesn't "yet" do what they claim) means very little. Even worse, some of your claims are not in the video.

 

[gmax137]

What is the intended flow rate? Did I miss it? This is probably the most important number in the "design" of the system being discussed here. The pictured pressure washers are nice but they deliver 2 to 5 gpm. Firefighting involves more like 100 to 200 gpm per hose.

What is the pressure loss in 4 miles of 3" flexible fire hose?

Exactly the question; the answer of course depends on the flow rate.

 

[RobertGC]

What is the intended flow rate? Did I miss it? This is probably the most important number in the "design" of the system being discussed here. The pictured pressure washers are nice but they deliver 2 to 5 gpm. Firefighting involves more like 100 to 200 gpm per hose.Exactly the question; the answer of course depends on the flow rate.

Right. The firefighting drone video does not give the flow rate. By the way, looking at that video it looks like they are using two different hose sizes. The smaller size one is probably the one where it could reach 1,000 feet:

This may be a 1-1/4” standard size fire hose, rather than a 3” size hose mentioned in a comment above. This would mean a lower water weight it would have to support.

The larger hose, is seen here in the video:

This likely would be used for the far more common scenarios of apartment building fires, likely 100 feet high and less.

Here is a pressure loss calculator by flow rate, diameter, and hose length:
https://frictionlosscalculator.com/?hosesize=1.25&length=1000&gpm=30

Trying different values for GPM the pressure loss does indeed get worse for higher flow rates. For 1,000 feet, 30 GPM, and 1.25” diameter it gives the loss as 72 PSI. Acceptable for a 450 PSI (30 bar) starting pressure to reach a 1,000 feet (300 meter) height.

For a 5,000 ft. height, the needed pressure would be 5 times as high, 2,250 PSI. Typing 5,000 ft., 30 GPM, and 1.25” into the calculator gives a pressure loss of 360 PSI, acceptable for a 2,250 PSI starting pressure.

For the pressure washer scenario, these typically only give flow rates at the low single digits. Furthermore, the hose diameters are commonly only in the 1/4” range. Still, because of the low cost of the pressure washers and of the drones needing to support a much smaller weight, this is something amateurs could probably do as a proof-of-concept demonstration.

Robert Clark