Find Best Water Nozzle Type & Pressure for Longest Distance

[Mahonroy]

TL;DR Summary

I am experimenting with garden hose and pumps, to achieve furthest water spray distance. I hit a wall and am currently stuck on the problem.

Hello, I am trying to throw water the furthest distance possible from a garden hose and an inline water pump. The amount of water is not important - e.g. a tiny stream is perfectly fine, so long as it reachest a really far distance. I understand wind severely messes this up, so lets not worry about wind for now.

My goal is to reach a minimum of 100 feet, utilizing one pump is no problem, and utilizing 2 pumps in series only if absolutely necessary.

A quick overview:
My water pressure out of the garden hose is roughly 50psi with the end completely blocked off. Fully open I am getting about 5 gallons per minute of flow.

The pumps I have are 1.6HP, 1300GPH.

I tried a bunch of different "jet" style nozzles, and this one seemed to perform the best as far as distance is concerned. The hole is 3.7mm in diameter:

As a test, I drilled the same 3.7mm hole in a brass garden hose plug, and it performed pretty much exactly the same (to my surprise):

Initial testing using the above nozzles. I have a pressure gauge right before the nozzle:
Garden hose reads 50psi when closed at the nozzle. When fully open, pressure reads 0 psi and water shoots about 20 feet.

Using 1 pump, pressure reads 115psi when closed at the nozzle. When fully open, pressure reads 30-40psi, and water shoots about 65 feet.

Using 2 pumps in series, pressure reads 150psi when closed at the nozzle. When fully open, pressure reads about 100psi, and water shoots about 90 feet.

There is a decent amount of misting/spraying surrounding the stream - it sort of resembles those large sprinklers at parks and golf courses.

I decided to do some more testing with different diameter holes, just on the garden hose with no pump:

I mentioned above, the 3.7mm hole yielded a distance of about 20 feet. To my surprise, the 1.7mm hole performed the best, and gave a fairly steady stream (not much mist) and got 30 feet. Pressure guage read 20 psi right before the nozzle. I tried this same 1.7mm nozzle with a single pump, and the distance actually went down slightly to 25 feet, with a lot more water spray and mist. The pressure guage read 60psi. It looks like a lot more water volume is flowing out of the nozzle, but its less controlled.

The 1.2mm got about 25 feet with the garden hose (lots of spray/mist), and about 20 feet with the single pump (a lot more spray/mist). Pressure gauge read 80psi.

So now I am not sure which way to go with this. It seems more of a laminar flow is the way to get better distances, but if I achieve a nice stream at one pressure - as I increase pressure the stream is not so nice anymore - and in most cases it reduces the distance.

I considered attempting to build a liminar flow canister similar to "The King of Random" youtube video:


But he even mentioned that as he increased pressure it started to perform bad. So I am not confident that my canister would help things.
Another option is to just keep throwing pumps at the problem, as I am getting further and further distances with more pumps.... but each one draws 10 amps of current, so I won't even be able to put all of those on a single circuit. Ideally I want to accomplish this with a single pump.

Is there a way I can calculate this? E.g. mathematically arrive at some diameter hole at X pressure. Or some other type of nozzle design I should try?

Any help or advice is greatly appreciated, thanks!

 

[erobz]

Is there a way I can calculate this? E.g. mathematically arrive at some diameter hole at X pressure. Or some other type of nozzle design I should try?

You have to analyze the entire system. The pump has a head vs discharge curve, the nozzles and hose have viscous losses to consider. You can only just keep adding pumps to the system up to a certain point, and there are performance implications for that as well. The main equation is "The Energy Equation" encountered early in the study of fluid mechanics:

Between any two points in the (steady - not changing in time ) flow:

$$ \frac{P_1}{\rho g } + z_1 + \frac{V_1^2}{2g} + h_p = h_t+\frac{P_2}{\rho g } + z_2 + \frac{V_2^2}{2g} + \sum_{1 \to 2} h_l $$

If you are interested, I can show you how to apply this equation to model the system, I just need to get some information about that system.

 

[Mahonroy]

You have to analyze the entire system. The pump has a head vs discharge curve, the nozzles and hose have vicious losses to consider. You can only just keep adding pumps to the system up to a certain point, and there are performance implications for that as well. The main equation is "The Energy Equation" encountered early in the study of fluid mechanics:

Between any two points in the (steady - not changing in time ) flow:

$$ \frac{P_1}{\rho g } + z_1 + \frac{V_1^2}{2g} + h_p = h_t+\frac{P_2}{\rho g } + z_2 + \frac{V_2^2}{2g} + \sum_{1 \to 2} h_l $$

If you are interested, I can show you how to apply this equation to model the system, I just need to get some information about that system.

Thanks for the response! And yes I am interested in figuring out how to model this and figure out what to do.

 

[erobz]

A sketch of the components pipes, fittings, pump, and valves in your system from the source ( main water line? ) to the nozzle is a start. The inside diameters of the various conduit components are relevant, as well a length. It might take a couple replies to work through all the necessary data.

You are going to need to be comfortable with algebra for the basic analysis where we aren't trying to precisely model the nozzle. If we try to dive into that, it will get more complex quite rapidly, but we can cross bridge if we get there.

 

[jrmichler]

A nozzle is more than just a hole drilled in a piece of metal. It is also the entrance to that hole. A square edge entrance, or worse yet a burr at the entrance, reduces the flow while adding turbulence. The effect of entrance edge shape on flow coefficient K is shown in this figure from Crane Technical Paper No. 410:

The sharp edge case, r/d equals 0, is the case of a hole drilled without burrs. A square edge causes a vena contracta (search the term). The vena contracta not only reduces the flow, but causes turbulence. That turbulence is probably the cause of the spray and mist. The entrance radius is made large in pipe flow nozzles (search the term), which are used in pipe flow measurements. A typical flow nozzle (screen grab from https://www.wermac.org/specials/flownozzle.html) is shown below:

I expect that rounding the entrance to your drilled holes will deliver less spray and mist along with greater distance. If you still get spray and mist, I suggest connecting the garden hose to a 5 to 10 foot length of straight pipe. The length of straight pipe reduce flow turbulence entering the nozzle. Then experiment with hole diameters.

It sounds like a fun project. Let us know what you find.

 

[Mahonroy]

A nozzle is more than just a hole drilled in a piece of metal. It is also the entrance to that hole. A square edge entrance, or worse yet a burr at the entrance, reduces the flow while adding turbulence. The effect of entrance edge shape on flow coefficient K is shown in this figure from Crane Technical Paper No. 410:
View attachment 328510
The sharp edge case, r/d equals 0, is the case of a hole drilled without burrs. A square edge causes a vena contracta (search the term). The vena contracta not only reduces the flow, but causes turbulence. That turbulence is probably the cause of the spray and mist. The entrance radius is made large in pipe flow nozzles (search the term), which are used in pipe flow measurements. A typical flow nozzle (screen grab from https://www.wermac.org/specials/flownozzle.html) is shown below:
View attachment 328513

I expect that rounding the entrance to your drilled holes will deliver less spray and mist along with greater distance. If you still get spray and mist, I suggest connecting the garden hose to a 5 to 10 foot length of straight pipe. The length of straight pipe reduce flow turbulence entering the nozzle. Then experiment with hole diameters.

It sounds like a fun project. Let us know what you find.

Thanks a lot for this information, very helpful!

I can easily countersink the back of the hole at an angle, such as 45 degrees. Rounding it as in putting a radius on it will be a little trickly. I'll see what I can come up with here.

I will also try a length of straight pipe (same inner diameter as the hose I am assuming?). What about the length of the nozzle? E.g. the length after the radius. Is there any benefit to adding length to that 1.7mm hole?

 

[hutchphd]

Maybe do some rough prototypes with plastic pipeand plexiglas. Shaping would be a lot easier. I would start small and then figure the way the result should scale (Reynalds Number?.....Clearly I'm no expert) Should be very interesting. I don't think anyone would mind seeing some data! Irts all magic to me.
I once built an artsy fountain that used a laminar vertical flowing stream as a "light pipe". Made interesting light patterns where it "delaminated". Not quite a Lava Lamp, but what the heck

 

[sophiecentaur]

You have to analyze the entire system. The pump has a head vs discharge curve, the nozzles and hose have vicious losses to consider. You can only just keep adding pumps to the system up to a certain point, and there are performance implications for that as well. The main equation is "The Energy Equation" encountered early in the study of fluid mechanics:

Between any two points in the (steady - not changing in time ) flow:

$$ \frac{P_1}{\rho g } + z_1 + \frac{V_1^2}{2g} + h_p = h_t+\frac{P_2}{\rho g } + z_2 + \frac{V_2^2}{2g} + \sum_{1 \to 2} h_l $$

If you are interested, I can show you how to apply this equation to model the system, I just need to get some information about that system.

There is a fundamental limit to the range, whatever nozzle design you use. From a simple viewpoint and ignoring the dynamics of the fluid flow it seems to me to be a 'matching problem'. The power output of the pump sets the maximum velocity (v) from a nozzle. Simple Ballistics (assuming we have a series of small cannon balls) would suggest that the maximum range is at an elevation of 45° and is R=v²/g. (How near 45° is your optimum elevation? I'd bet that the water falls pretty steeply at that point.) So the velocity of the exit stream has to be at least this value. If that value can't be achieved then you'll never get there.
Did the OP consider trying the pumps in parallel, btw? They would both be working at their design input pressure. Just a thought, based on using two batteries for high current drain applications. (Entirely different units and impedances, of course and I'm not familiar with the analogy between pumps and batteries.)

the nozzles and hose have vicious losses to consider.

I think you mean viscous losses here - but those losses can often be described as 'vicious' when you are after maximum performance.

 

[Baluncore]

(How near 45° is your optimum elevation? I'd bet that the water falls pretty steeply at that point.)

A laminar flow nozzle will generate a "solid rod" of water that does not break up.

Because the water is travelling through the air as a continuous cylinder, air resistance will be less. It is only the boundary layer of air, against the surface = "wetted area" of the stream, that slows the water down. The path taken will be much closer to the parabola, than a ball that runs out of puff.

The maximum range will be achieved with a continuous flow from a laminar flow nozzle.

 

[sophiecentaur]

A laminar flow nozzle will generate a "solid rod" of water that does not break up.

Because the water is travelling through the air as a continuous cylinder, air resistance will be less. It is only the boundary layer of air, against the surface = "wetted area" of the stream, that slows the water down. The path taken will be much closer to the parabola, than a ball that runs out of puff.

The maximum range will be achieved with a continuous flow from a laminar flow nozzle.

That's interesting. I would expect a 2mm wide 30+m arc of water to break up long before the the end, though. But the best performance would be better than what I've ever achieved from a garden hose, no doubt.

 

[jbriggs444]

There is a fundamental limit to the range, whatever nozzle design you use.

Well, if you jack the pressure up just a bit, you can create a space gun. Once you reach orbit or escape velocity, the available range increases nicely.

Tongue firmly in cheek.

 

[erobz]

Did the OP consider trying the pumps in parallel, btw? They would both be working at their design input pressure. Just a thought, based on using two batteries for high current drain applications. (Entirely different units and impedances, of course and I'm not familiar with the analogy between pumps and batteries.)

They are similar. With pumps in series you add the head from each pump at a given volumetric flowrate to get the effective pump curve. In parallel you add flowrates at a particular head to get the effective curve pump curve. I think the analog is fine, its just with pumps you have that the head (voltage) is a function of the flowrate ( current ). I'd imagine that is true with batteries as well when we look past their common idealization in elementary circuits, maybe not quite as dramatically though. I don't know.

I think you mean viscous losses here - but those losses can often be described as 'vicious' when you are after maximum performance.

Yes, the AI that was supposed to correct me apparently didn't see the context of the statement.

 

[sophiecentaur]

Well, if you jack the pressure up just a bit, you can create a space gun. Once you reach orbit or escape velocity, the available range increases nicely.

Tongue firmly in cheek.

Lol. I meant with a given pump.

 

[erobz]

ignoring the dynamics of the fluid flow it seems to me to be a 'matching problem'.

To me it seems like there is going to be an optimum nozzle length that maximizes the outlet velocity based on the remaining system/pump curve characteristics.

I'm imagining a linearly converging nozzle (truncated cone):

Aplying Newton Second to the differential element:

$$ -\frac{dP}{dx}A - P\frac{dA}{dx} - \tau (x)\frac{dA_s}{dx} \cos \alpha = \rho A v \frac{dv}{dx} $$

With
$A(x)v(x) = Q = \text{const.}$ incompressible flow

$D(x) = D_i - \frac{D_i - D_o}{L}x$

$A(x) = \frac{\pi}{4}{D(x)}^2$

$\frac{dA}{dx} = -\frac{\pi}{2} \frac{D_i - D_o}{L} D(x)$

$\frac{dA_s}{dx} \cos \alpha = \pi D(x)$

$\frac{dv}{dx} = Q \frac{ \frac{\pi}{2} \frac{D_i - D_o}{L} }{{A(x)}^2}D(x)$A first order ODE with non-constant coefficients. I haven't taken that part any further yet, but the idea is to describe the pressure gradient as a function of $Q$ using that result and sweep the other parameters $D_o, L$ in concert with post #2 for the rest of the system to find the maximum discharge velocity.

Keeping the flow non turbulent at the exit pigeonholes the velocity for a certain outlet diameter via the Reynolds Number, and I'm not sure if that is good if the sole objective is just to get water to land as far away as possible?

 

[sophiecentaur]

With pumps in series you add the head from each pump at a given volumetric flowrate to get the effective pump curve.

Is that necessarily true? I would have thought that they would need to be coupled with a suitable 'chamber' to iron out pressure and flow variations between output one and input two or they would 'see each other'. as the saying goes. It could be analogous to connecting two alternators in series and expecting to get twice the AC volts.
But what do I know? It may be that it's never an issue in practice.

 

[erobz]

Is that necessarily true? I would have thought that they would need to be coupled with a suitable 'chamber' to iron out pressure and flow variations between output one and input two or they would 'see each other'. as the saying goes. It could be analogous to connecting two alternators in series and expecting to get twice the AC volts.
But what do I know? It may be that it's never an issue in practice.

I could see some issues with very different pumps in certain systems, but I can't see any issues that a check valve wouldn't take care of other than perhaps one or both of the pumps running at a point of low flow or low efficiency and perhaps heating up. Obviously the absolute pressure in the system should not exceed the rating of the pump ( we don't want to split the casing, ect...), so adding in series has limits there. Is this what you are thinking can go wrong or did you have something else in mind?

 

[erobz]

For instance, the red and blue curves are different pumps. When added in series they form the composite purple dashed curve. You aren't going to be running both in system 2 as the red pump just becomes a load on the blue pump, while consuming power on its own for nothing.

So in practice the engineer would not specify this series combination for system 2.

There is probably a no-fly zone a dozen other ways, but in general for a system of pumps in series adding the heads at a given flow is the model for the composite pump curve. That is what I was saying, not that anything can (should) be done without consideration of the final result.

 

[sophiecentaur]

For instance, the red and blue curves are different pumps.

I need a bit of help here, please because something seems to be missing to get from this to the height / distance reached by the jet. The exit v needs to be enough for the wanted trajectory but the graphs appear to correspond to filling a reservoir at the level of the top of the hose. Is there enough information to infer the exit velocity of the actual nozzle

I assume the H value is the height achieved with a particular hose. It implies that the max value of pressure at the nozzle will be zero so the velocity of the water will be zero. To get a jet to go higher than this then you need to have the nozzle below H max and the flow rate needs to be enough so that the exit velocity (end of the taper) . The pressure at the start of the taper needs to be enough to give the required exit v whilst keeping the volume flow constant. You're operating further out from the y axis, on an increasingly negative slope/

Do you see my problem? It may only need a few words to reassure me it's all OK.

 

[erobz]

I need a bit of help here, please because something seems to be missing to get from this to the height / distance reached by the jet. The exit v needs to be enough for the wanted trajectory but the graphs appear to correspond to filling a reservoir at the level of the top of the hose. Is there enough information to infer the exit velocity of the actual nozzle

I assume the H value is the height achieved with a particular hose. It implies that the max value of pressure at the nozzle will be zero so the velocity of the water will be zero. To get a jet to go higher than this then you need to have the nozzle below H max and the flow rate needs to be enough so that the exit velocity (end of the taper) . The pressure at the start of the taper needs to be enough to give the required exit v whilst keeping the volume flow constant. You're operating further out from the y axis, on an increasingly negative slope/

Do you see my problem? It may only need a few words to reassure me it's all OK.

It's just a case of mistaken identity. $h$ is the “head”, (pressure per unit specific weight of the fluid being pumped through the system). That graph was directed to your last response about the effect of different pumps "seeing each other", not about the solution.

 

[sophiecentaur]

That graph was directed to your last response about the effect of different pumps "seeing each other", not about the solution.

Yes. I get that but the graphs show the performance of two individual pumps and then the combination performance. The OP's data gives H and Q. For each pump, the head is maximum when Q is zero (no?). You will only get flow when operating below that. To get a high enough velocity on exit, you have to operate at below the h max.

But. in any case, that diagram (and the spec of the OPs pump) seems to deal with filling a tank at h. Imparting some 'extra velocity' is another matter, surely. You need Power at the nozzle to accelerate the water as it goes into the narrowing section. Using the nozzle at a lower level can make this power available and will allow a jet to go higher / further but isn't there a limit? How much better than static head can one do?

Operating the nozzle at ground level requires a suitable v to take the trajectory to the required "100ft" theoretically but the jet has to have a certain minimum diameter to keep it intact and laminar. Doesn't that impose a definite maximum range for any given pump characteristic (power and 'effective internal and very non-linear resistance')? Electrical analogy makes the problem more familiar to me.

 

[erobz]

Yes. I get that but the graphs show the performance of two individual pumps and then the combination performance. The OP's data gives H and Q. For each pump, the head is maximum when Q is zero (no?).

I don't see that data, I see a single point on the pump curve.

115 psi(pump + main) - 50 psi ( main ) @ 0 gpm = 65 psi @ 0 gpm

Then I see 30-40 psi loss at the nozzle when the system is open - just a portion of the total system losses. We need the pressure differential across the pump, and we could reverse engineer the flowrate from how far it landed, what angle it was aimed ect... but I would have very low confidence in that. Its would be far better to just acquire the pump curve. Its almost certainly findable online these days, if not the manufacturer has it. It's part of the standard engineering data.

So I don't see the complete performance curve. We have (for all intents and purposes) a single point.

How much better than static head can one do?

None, but that corresponds to no flow ( zero outlet velocity) in the system and consequently zero range. To impart kinetic energy the real pump has to very inefficiently trade potential energy for kinetic energy.

Operating the nozzle at ground level requires a suitable v to take the trajectory to the required "100ft" theoretically but the jet has to have a certain minimum diameter to keep it intact and laminar. Doesn't that impose a definite maximum range for any given pump characteristic (power and 'effective internal and very non-linear resistance')? Electrical analogy makes the problem more familiar to me.

Hello, I am trying to throw water the furthest distance possible from a garden hose and an inline water pump.

I don't understand why the jet must stay intact and laminar (other that maybe precise measurement of range)? That severely limits velocity of the flow at the nozzle.

 

[Baluncore]

I don't understand why the jet must stay intact and laminar (other that maybe precise measurement of range)?

Because individual separated droplets are slowed significantly more than a continuous rod of water.

 

[erobz]

Because individual separated droplets are slowed significantly more than a continuous rod of water.

The OP just wants water to shoot as far away as possible. The limitation on that is going to mainly be pressure and resistance to flow IMO. To have a laminar flow you need low velocity. A fire hose isn't laminar flow, its high pressure and high volume. They have vertical reach of up to 100 ft, the range would be significantly more (theoretically double). While it would be nice to have a smooth beam of water to minimize drag, I don't think it's realistic. The Reynolds number indicates $\frac{VD}{\nu} < 2300$ for laminar flow. For water and a nozzle diameter of 4 mm, that works out to be a velocity of less that 0.6 m/s. What's the range on that fired at 45°? 0.03 meter...

 

[jbriggs444]

The OP just wants water to shoot as far away as possible. The limitation on that is going to mainly be pressure and resistance to flow IMO. To have a laminar flow you need low velocity.

Google delivers tons of hits for laminar flow nozzles, including some DIY. Some designs use an array of soda straws and an initial scouring pad to remove turbulence from the input side.

A high speed stream would seem to be beneficial when it comes to mitigating Plateau Rayleigh instability. If you only have so much time before the stream packetizes due to surface tension, then the more distance you get during that time, the better.

Could a little detergent in the water make the stream go further?

 

[erobz]

Google delivers tons of hits for laminar flow nozzles, including some DIY. Some designs use an array of soda straws and an initial scouring pad to remove turbulence from the input side.

I'm not denying their existence, I'm just saying based on the math they aren't for getting a fluid jet to have the maximum range possible. They are for making clear and cohesive streams which would certainly be desirable, but will not be compatible with high output velocity applications as far as I can tell.

Could a little detergent in the water make the stream go further?

Increasing the viscosity just before the nozzle may be beneficial, to what extent I don't know.

 

[sophiecentaur]

I don't see that data, I see a single point on the pump curve.

HAHA I see a red line and a blue line. Are they not the pump characteristics?

None, but that corresponds to no flow ( zero outlet velocity) in the system and consequently zero range. To impart kinetic energy the real pump has to very inefficiently trade potential energy for kinetic energy.

But hang on. What you say is true for a uniform hose diameter. If that was the only height you could get then why have a tapered nozzle at all? Once the water has emerged from the hose, its trajectory will depend on the actual velocity and not the volume flow rate. The velocity is also a function of the pipe (nozzle) diameter and the KE is proportional to the velocity squared.

 

[erobz]

HAHA I see a red line and a blue line. Are they not the pump characteristics?

No, I just conjured them out of thin air to illustrate adding pumps (curves) in series to show where a problem may occur if the system had the characteristics of "system 2".

But hang on. What you say is true for a uniform hose diameter. If that was the only height you could get then why have a tapered nozzle at all? Once the water has emerged from the hose, its trajectory will depend on the actual velocity and not the volume flow rate. The velocity is also a function of the pipe (nozzle) diameter and the KE is proportional to the velocity squared.

The outlet velocity depends on the flowrate corresponding to the steady state operating point. That is the intersection of what the pump can supply (pressure) as a function of flowrate, and what the system demands at that same flowrate. If you change the nozzle you change the operating point. When you say static head, I assume you mean pump static head, because there is virtually no system static head here. That equates to the no flow condition of the pump. That is the maximum height of a column of water which a particular pump could support. You can't do better than that at any flowrate as far as flow kinetic energy is concerned.

 

[Baluncore]

The OP just wants water to shoot as far away as possible. The limitation on that is going to mainly be pressure and resistance to flow IMO.

This is a dangerous game. We are past the point of subcutaneous injection and entering the realm of traumatic amputation.

Keeping the flow laminar, is a limitation that would make it a safer game for students. What is being indirectly optimised here is the orifice of a water jet cutter.
2005 WJTA American Waterjet Conference. Houston, Texas.
Paper 4A-1. Waterjet Cutting Beyond 400 MPA
https://www.wjta.org/images/wjta/Proceedings/Papers/2005/4A-1 Susuzlu.pdf

The design requirements are quite the opposite of a fuel injection nozzle, as that optimises atomisation and the mixing of the mist with air.

Increasing the viscosity of the water by a factor of two can be achieved simply by using colder water, preferably 0°C. The ridiculous limit would be a super-cooled, ice spaghetti gun.

 

[erobz]

This is a dangerous game. We are past the point of subcutaneous injection and entering the realm of traumatic amputation.

Yeah, pressure is dangerous. Which is why I wanted to analyze the system, instead of what the OP was suggesting "just keep adding pumps" But they are M.I.A. Maybe they are already in the infirmary.

 

[sophiecentaur]

You can't do better than that at any flowrate as far as flow kinetic energy is concerned.

The Power of the jet depends on the velocity (mv²/2 per unit mass) and the velocity is inversely proportional to the cross sectional area (ignoring fluid losses for a given flow rate ). What you are saying seems to imply that there's no point using a nozzle and I'm sure you don't mean that.

 

[erobz]

The Power of the jet depends on the velocity (mv²/2 per unit mass) and the velocity is inversely proportional to the cross sectional area (ignoring fluid losses for a given flow rate ). What you are saying seems to imply that there's no point using a nozzle and I'm sure you don't mean that.

I mean precisely what I said. The point of using the nozzle is to bring the flow to it as slow as possible ( minimizing transmission losses in the conduit, and then rapidly accelerate it through the nozzle. However, there is a balance to that. The resistive energies are proportional to $\frac{Q^2}{A^2}$ ( i.e. $v^2$) too. You will never have a jet at the nozzle with greater kinetic energy per unit volume than the head the pump can supply at no flow. The first of thermodynamics says we aren't getting more out than what we put in and the second law says heat is always generated. period. So, we can't even recover what we put in.

EDIT: I struck through some less than accurate statements I made. I have allowed myself to be seduced by my own pump curves (characteristics typical of a centrifugal pumps). You can get higher kinetic energies than no-flow potential energy, so long as the pump curve has a local maximum at some$Q> 0$. I was too hasty in making the statement above. I apologize.

 

[Lnewqban]

... A quick overview:
My water pressure out of the garden hose is roughly 50psi with the end completely blocked off. Fully open I am getting about 5 gallons per minute of flow.

The pumps I have are 1.6HP, 1300GPH.
...

Please, consider that if your pump is forced to operate far away from that volumetric flow of about 0.36 gallon per second, it can be damaged, as the fluid will heat up rapidly within the casing and the hose.

 

[Cardinal Gramm]

Did anyone in chemistry class shoot water out of a pipette? It would shoot a needle of water great distance (>10') with no turbulence. We would prank each other because you could wet someone's shirt down and they would never notice the momentum of the flow. The throw distance given the discharge diameter was insanely high.

My guess is the surface velocity is the limiting factor for laminar flow. That means there is no way to shoot farther.

Rather than focusing on the system upstream of the orifice, I'd focus on what is required downstream to achieve the desired distance. The fire hose (especially the fire tugs) is probably the best example.

When you deal with turbulence, I'm guessing it is striping away layers of the stream so to get great distance, you have to have more layers, i.e. a larger stream diameter.

There is probably a tradeoff between increased turbulence from increased velocity and flow diameter, so there is a peak efficiency to achieve the distance objective.

This is beyond my pay grade.