Water gun efficiency

Threads about how water guns work and other miscellaneous water gun technology threads.
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SSCBen
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Water gun efficiency

Post by SSCBen » Wed Oct 15, 2008 9:43 pm

Recently I thought of a simple way to measure water gun efficiency. Thermodynamic efficiency of a system is based on what you put in and what you get out. Water guns can have similar formulas.

One simple measure of efficiency is range/flow which is quite meaningful as is. Water guns with high range and low water output generally are desirable. So this would be the best but I have another idea too. My other idea is based on the range of a water gun. Edit: After some thought, a graph of range vs. output would probably be the best way to look at efficiency.

efficiency = (Maximum true water gun range)/(Theoretical maximum range)

While I haven't worked the exact formula out something like that is what we're looking for. The theoretical maximum range would be based on the velocity of a point particle at a starting velocity based on the flow and nozzle diameter (V = Q/A is the equation), at a height, neglecting drag, at the optimal angle (which is not 45 degrees at a height). Basically, it's the theoretical maximum range.

The good thing about this formula is that there is a maximum efficiency. Obviously we can't expect any efficiency close to 1, in fact, I bet efficiencies of 0.25 are really high.

The main problem with this efficiency is that the equation would be complicated. Another problem is that efficiency could vary wildly for different nozzle diameters, but that can be expected I suppose. The most efficient nozzle would likely be the one that gets best range, which minimizes velocity so that drag is reduced but still is wide enough to handle a good amount of drag.

One last somewhat on-topic thing: I'm going to use SI units for the most part from now on because they're so much easier to work with (especially with water).
Last edited by SSCBen on Wed Oct 15, 2008 10:11 pm, edited 1 time in total.

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cantab
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Re: Water gun efficiency

Post by cantab » Wed Oct 15, 2008 10:39 pm

Given the measured range, calculate the theoretical minimum velocity to attain that range, Vt.

Either by video, or using the output and nozzle diameter method I described in the physics thread, find the actual initial velocity, Va.

Then, the efficiency is the theoretical minimum power divided by the actual power (using my definition of power)

Most of the terms will cancel, leaving the efficiency

n = Vt^2/Va^2
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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Fri Oct 17, 2008 3:21 am

I've started replies to this thread maybe 3 times now... maybe this one will actually get posted!

Your method is an interesting one cantab that makes a lot of sense. Now I need to get some time to put some actual values into these equations to see what sort of results we get and if any of them make any sense...

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cantab
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Re: Water gun efficiency

Post by cantab » Sun Oct 26, 2008 10:30 am

Now that I think about it, the 'theoretical minimum power', based on range and output (but not in a trivial way) would actually be a better measure of water gun performance than the initial stream power. I might call this 'effective power'.

Also, we can come up with multiple measures of efficiency. My idea measures losses due to drag in the air, after the stream has left the gun. But if one instead uses a definition of power like Ben's latest, then one gets at losses within the gun.
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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Wed Dec 24, 2008 3:11 pm

I was thinking again about efficiency when something that seems more "correct" came to mind.

Measuring the total kinetic energy of a stream would require figuring out how much water is shot, and the energy would vary greatly depending on how much is shot. So any measure of efficiency of that alone would not make sense. However, specific energy, that is, energy per unit volume, makes perfect sense. Therefore, finding the specific kinetic energy of the stream and dividing that by the specific potential energy of the pressure chamber should result in a meaningful measure of the energy efficiency of the gun.

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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Tue Jan 20, 2009 2:53 pm

After some thought, the approach I detailed above would vary at every instant, not giving a very meaningful measure of efficiency.

Therefore the sum of the total kinetic energy of the stream divided by the total energy required to pressurize the water is the most meaningful. To find the total kinetic energy you'd have to integrate the kinetic energy of infinitesimally small slices of the stream over the entire stream. A reasonable approximation of that would be 1/2*v^2*V*rho, where v is the average velocity of the entire stream, V is the total water volume, and rho is the density of water.

I'll keep an eye on this as I design my next water gun. If I can maximize efficiency of a pump gun, you'd get more power for the same amount of energy input, which can be very advantageous.

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Re: Water gun efficiency

Post by cantab » Tue Jan 20, 2009 7:01 pm

I think your physics is a bit better than mine...I ran away from the subject in my first year at uni.

As I tried (and failed) to address before, efficiency within the gun is only one part of the issue. Two guns could require equal energy to pressurise and give equal kinetic energy in their streams, but if one produces a nice laminated stream while the other gives a messy spray, there's a clear difference there. Figuring out how to quantify that is the tricky bit.
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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Tue Jan 20, 2009 7:26 pm

Yeah, energy efficiency wouldn't take that into account. The range energy efficiency we discussed earlier would take that into account. A combined efficiency (the two multiplied together) would be most useful but more specific efficiencies allow you to pinpoint the problem.

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adronl
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Re: Water gun efficiency

Post by adronl » Tue May 12, 2009 7:44 am

Pretty much on everything that I have though of and built is all based on air pressure or the measurable amount of pressure on the water. For maximum efficiency and power air pressure seems the way to go a high pressure tire valve is cheap like 2.50 to 5.00 they screw together form the inside out which is convenient the good ones can hold ridiculous amounts of pressure I found some for about 2.50 that have a safe operating level of 150psi. air is the best way to go it seems with something you can actually shoot people with it is easy and cheap to do safely. For the extra money you would spend building a wicked gun you could buy a very small AC air compressor that will power up your gun in seconds and keep it going to the last drop. I call that efficiency pneumatic guns are awesome but you get into serious cost. To truly beat a well designed APH you really would have to go almost weapons grade with high pressure parts you can make a gun at the right diameter that will hold over 200psi. The problem water at a great velocity particulates faster because water just does not have the properties to be a good projectile. Which leads to Nozzles and Angles The best nozzles we have are fire nozzles and police and military grade water cannons there are already engineers that have devoted their careers to fluid dynamics & as it seems some here may follow. There are already good formulas for determining flow and max efficiency but what is the best nozzle you have found you can buy for a good deal on the consumer market is the question I have. With greater distance there is a demand for volume when power increases or you have a really big mist gun or crappy pressure washer I personally want the max distance. On the angle It depends on the gun that's the way I see it on that, somewhere between like 38-22 degrees
Last edited by adronl on Tue May 12, 2009 7:54 am, edited 1 time in total.

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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Tue May 12, 2009 5:06 pm

I don't think you understand what efficiency in this context is. Efficiency is how much of the input energy is used to propel a water stream. After a great deal more thought, not much can be done to improve the energy efficiency of water guns as the most prevalent wasted energy is that of pressurized air which does not expand fully.

Maximizing range (in metric m) over specific power (i.e. W/kg) or what cantab mentioned are the most reasonable options.

The best nozzle is some sort of conical nozzle like the fire hose one used on Supercannon II. These nozzles are typically hard to come by and compared against an endcap nozzle on a well designed water gun, they really do not make too much of a difference.

The angle issue is difficult. Something around 35 degrees likely is optimal for most guns. It is worth noting that this angle depends greatly on the water gun and current atmospheric conditions.
Last edited by SSCBen on Tue May 12, 2009 8:05 pm, edited 1 time in total.

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adronl
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Re: Water gun efficiency

Post by adronl » Tue May 12, 2009 7:17 pm

If that is what you are getting at then a good pre-charge with a bladder would take it I would think. You never loose you air pressure in great amounts because the bladder prevents it and all you really need for a charge is a male to male 3/4" you can probably get 60-80psi and if you want more you can raise the air pressure surrounding the bladder to get 100-120. I am wandering how that 2 1/2 inch nozzle from McMaster Carr would perform but you know that thing doesn't really get peak efficiency I noticed that 70-100 with a 1/8" in sweeper nozzle was short only 2' of a 3/8" nozzle. The 1/8 saves a lot of pressure but and water but still delivers but I think just a tad bit larger would get the peak. Like with all the store bought piston guns they get up to 70 ft and almost all of them have a nozzle just about that size. You can find a brass sweeper nozzle at Home Depot. It seems you pretty much have to loose efficiency after 70'. If you figure out the sweet perfect #'s do tell there isn't some kind of chart out there for this kind of thing I mean hydrodynamic water efficiency follows a curve of increasing size to volume and pressure
Last edited by adronl on Tue May 12, 2009 7:24 pm, edited 1 time in total.

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Silence
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Re: Water gun efficiency

Post by Silence » Tue May 12, 2009 7:50 pm

Bladders are usually used to generate pressure of their own. Unfortunately you sacrifice either pressure (there's pretty much an upper end), flow (large-diameter rubber doesn't generate as much pressure), or both. For separating air and water, pistons are infinitely more durable and easier to mount. Ben used one in Supercannon II; take a look at the pictures and you'll see what I mean.

If your 3/8" nozzle was drilled then that's probably why its range was unimpressive.

There really are diminishing returns for water gun range, but all this analysis still matters. Take the nozzles as an example: if you design a good nozzle, then you can scale it down and save water.

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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Tue May 12, 2009 8:18 pm

adronl, could you please divide your posts into paragraphs? Reading a block of text is difficult.

As for pressurized gas around a bladder, it's bad idea that's difficult to implement and maintain and has no benefit over a piston water gun with a good air-water ratio. Use a piston.

Anyway, it'd be worth noting that bladders are probably bad for efficiency due to hysteresis. With that being said, I would not be surprised if the energy losses are small.

The store bought piston guns also do not get 70 feet. They claim to, but I've never seen anyone get that. I suppose if you're particularly strong it's possible, but most people won't get over 45 feet.

I've not quite sure what you mean by "hydrodynamic water efficiency curve". Again, let me reiterate that water gun efficiency is for the most part near 100% except in bad designs like pressurized reservoir water guns.

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adronl
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Re: Water gun efficiency

Post by adronl » Tue May 12, 2009 8:23 pm

At a low 60psi the 3/8 that is not drilled got 52' and the 1/8 got 50' I haven't gotten the chance to really measure a high pressure test yet. I am going to be building a 6", 3", and a 2" piston gun parts are in the mail. As far as efficiency yes it is great no air bubbles to ruin your distance. I am thinking there may be issues with if it can be a pre-charge is where I am going with my idea. Yeah normally you would have air or a bladder but why not both it is science it might produce great results. Have you tried it before or are you trying to steer me away from the idea for a reason? ;)

Also would not the air pressure help cancel out the hysteresis

Oh yeah Sorry about the block text I just get going
Last edited by adronl on Tue May 12, 2009 8:30 pm, edited 1 time in total.

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SSCBen
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Re: Water gun efficiency

Post by SSCBen » Tue May 12, 2009 8:34 pm

Yeah normally you would have air or a bladder but why not both it is science it might produce great results. Have you tried it before or are you trying to stear me away from the idea for a reason?
Why not both? Such a system would be hard to build in a way that would allow for maintenance (replacement of the bladder if it pops, etc.). It also has no advantages over the greatly simpler piston design. In engineering there's a rule called KISS which means "Keep it simple stupid". If another design does the same thing with less complications, use that one.

Science doesn't mean try everything until you find the best thing. Theory and practical limits will give you an idea of how well something will work before making it.

I get asked about this idea all of the time and I am yet to see anyone implement it. If you think it'll work well, go prove me wrong. I know I've said that a number of times about this idea and so far I've never seen anyone even make it, probably because they realized there's no reason to make it.

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