# Is it possible to fire a ball of water that holds its shape?

## Background

I participate every year in a huge water balloon battle. The clash happens between two universities so you can imagine that the commitment, at least for some people, is quite high. To give you an idea last year some 40000 (thats 40e3) water baloons were thrown, plus there were some home made war machines, namely a catapult, a trebuchet, some arquebuses running on compressed air and such. Safety is of course the primary concern and nothing more than water/water balloons has ever been thrown.

## Actual Question

I want to build a water cannon and I would love some advice/ideas. What do I mean by water cannon? I mean a machine capable of throwing a lot of water, from 1 to 3 litres, at some 20 metres at least, in a shape like a cannonball rather than a stream.

Is it possible for a "blob" of water to maintain its shape after being shot in the air at some speed, at least for a limited range? I see two challenges: accelerating the water and "keeping it together" while in the air. The latter can be achieved with a plastic container (such as a balloon), while the first part may be trickier. Balloons tend to rip and explode if accelerated too much, while leaving the balloon out may make the second challenge impossible.

The design I am considering could have a huge tank connected to a smaller one that serves as the "firing chamber." You fill the firing chamber, then close the line between the tank and the firing chamber, then you open another line that launches the water out through a barrel. The idea is to use compressed air but my main concern is that the water will not maintain a "ball" form while in the air.

## Constraints

The best solution for me would be one that works within the constraints for the water balloon battle.

• About 100 € material cost.
• No fire is allowed in the propulsion system, compressed air is fine but no electric compressor is allowed so efficiency is a must. Our arquebus could fire a lemon sized balloon some 50 m away on about 2 atm.
• Safety is absolutely the primary concern. For no reason at all there can be risks for the operators or the opponents. We experimented with a firing shell with our arquebus because friction with the barrel would destroy the balloon, and the shell was secured to the barrel with many redundant wires to be sure not to fire it too.

Workforce and time are pretty unlimited if the project is cool. We have some very high manual skills and quite a lot of common and not so common tools.

This precise question has been researched in detail. As Olin Lathrop suggested, there is a maximum drop size. So, "balls" of water will tend to break up into smaller droplets. How big will the largest stable droplet be? The answer is that it depends on the surface tension of the water, how fast the droplet is launched, the drag coefficient, and atmospheric air density. Most of these you have little control of, though you can get a modest increase (~6%) in surface tension by using nearly freezing water (which may be advantageous in this situation for other reasons too). Just don't use actually frozen water, as while that would solve the breakup problem, it would be extremely dangerous.

Here's an equation that gives you an idea of how things vary (from the book Atomization and Sprays by A. Lefebvre):

$$D_\text{max} = \frac{8 \sigma}{C_\text{D} \rho_\text{a} U^2}$$

where $D_\text{max}$ is the maximum diameter, $\sigma$ is the surface tension of the water, $C_\text{D}$ is the drag coefficient of the droplet, $\rho_\text{a}$ is the atmospheric air density, and $U$ is how fast the droplet is launched.

From this equation, you can see that higher surface tension is better, and faster launches hurt the drop size. Plugging in some plausible numbers, I get a maximum droplet size on the order of a centimeter assuming the launch velocity is 10 m/s. These droplets are not very big but may be okay for your application.

On a related point, as you can see in the book I linked to, no, the "ball" won't maintain its shape. The book gives a series of illustrations to show possible distortions the drop will go through prior to breaking up (e.g.).

The water balloon acts similarly to a fluid with extremely (impossibly) high surface tension. The tension in the balloon itself is pretty similar to surface tension. So, I think it is in your best interest to keep using balloons. You can avoid popping for a compressed air cannon with a sabot.

You don't need anything that elaborate to launch water balloons quite nicely. I was actually kicked out of a dorm in college due to a "water balloon incident".

It turns out that surgical tubing makes a great rubber band. It can stretch to about 4x its rest length, and is pretty efficient at releasing the stored energy back. We used about 2.5 feet of doubled-up tubing on each side of a basket. That means when stretched all the way back, the tubing was 10 feet long on each side. That's quite a few pounds of pull.

For the basket we used the largest plastic funnel available in the local grocery store. Cut holes on opposite sides of the wide part for each of the surgical tubing strings. The funnel forms a nice shape for holding the water balloon, and the hole in the small end lets air in so that the balloon can exit the basket without getting stuck by air suction.

This simple and cheap device worked very well. We were shooting about 1 pound water balloons, which is about as massive as you should get with something going that fast. We could easily shoot up and over a wing of the dorm that was 4 stories above where we were shooting from. We had the two people holding the loose ends of the surgical tubing sitting on a concrete wall, with the third person below on the ground. The launch angle was fairly close to optimal, and I'd say we could shoot about 75 meters, maybe even a bit more.

Another time we were shooting from the balcony of a dorm on a hill, probably about 20 m from the street. Even though the launch angle was only moderately up, we could shoot into the courtyard behind a building across and down the street a bit, probably about 100 m total horizontal distance.

With two people holding the ends on level ground, you won't achieve launch angle for maximum distance, but you probably don't actually want to optimize for that anyway. You could always make some rig to hold the ends of the tubing and allow rotation of the whole mechanism for aiming and the like. It depends on how fancy you want to get. Three people is very cheap, mobile, sets up easily, and can do fire-and-run easily.

• Thanks for your input Olin, we usually have two or three groups of people firing with similar devices. What you suggest is comparable to a mortar, I wanna build a tank. – Vladimir Cravero Mar 23 '15 at 14:22

You totally changed the question by editing it, so now I'm giving a different answer from before. I'll let the original answer stay because what it says is still valid, although no longer as relevant.

No, you can't fire "balls" of water. Liquid moving through air doesn't work that way. Any ball more than drop size would break up, and drops have too little mass for their air resistance to be shootable the distance you want.

A ball of water is held together by its surface tension. In a weightless environment, you can have balls of water that stay together. However, this doesn't work anymore as the ball moves through the air. As the size of a ball increases, the air pressure forces on it also increase, but the surface tension force stays the same. Then there is also the speed of the ball. As the ball size gets bigger, the terminal velocity also gets bigger, and the air forces on the ball go with the square of the velocity.

All this means that balls of liquid moving through air are inherently limited in size. That's what a "drop" is. There is a reason that raindrops only get to a certain size. A maximum size raindrop in a cloud will grow as it hits other micro drops of cloud on the way down. If it grows too big, the air forces on it get larger due to its size alone. At the same time the speed goes up and the air force goes up with the square of that speed. All these factor together limit water at 1 atm of air to about 50 µl in size.

• related: what-if.xkcd.com/12 – mart Mar 24 '15 at 6:31
• So if I can make a big enough ball it won't have time to disperse... It would be nice to be able to work out some numbers on how big the ball should be to see if it's feasible (probably not). – Vladimir Cravero Mar 24 '15 at 8:10
• @Vlad: Even if you could launch a perfectly formed ball of water out of your device, it would break up very quickly. For a ballistic flight of 20 m distant, the minimum speed is 10 m/s. – Olin Lathrop Mar 24 '15 at 13:37
• yeah that's what I am suspecting. I was thinking on asking a question about how to launch a ballon without breaking it, that might help me with my project and be answerable on a SE site. – Vladimir Cravero Mar 24 '15 at 13:39
• @Vlad: I'd stick to 500 ml (about 1 pound) or less. Anything more and people could get hurt. – Olin Lathrop Mar 24 '15 at 13:54

# Options

It is probably possible to do something similar to what you want. It really depends on the range that you are looking for and how concerned you are about it being a "ball".

## Fire Hose

If a fire hose can shoot a stream of water, then all you need is a really short stream of water. It might not be a "ball" like you are wanting, but it would get water across the field. To get the range, you might need to have it be more of a stream than a short burst.

## Laminar Fountain

To have a compact "package" of water stay together, you will need a special nozzle and water system. Something similar to this is used in fountains. It looks like the phrase is jumping jets or laminar fountain. These are fountains that keep their shape and have a very abrupt start and end.

There are two controlling factors for these types of fountains:

1. Sharp start and stop mechanism.
2. Laminar flowing water.

Start and stop

A rotating disk with a hole in it could create a repetitive on/off pattern. This could be powered by a cordless drill or something similar. The rate could be adjusted spacing the holes.

Laminar water

Keeping the flowing water laminar is going to be the biggest problem. Laminar flow is defined by the Reynolds Number being below 2100. For the situation of water flowing in a tube: $$R_e = (2.475×10^6)*v*D < 2100 \\ where: \\ v = velocity (m/s)\\ D = diameter (m)$$

The requirement for the flow to be laminar is going to restrict the speed of the water leaving the tube. This is going to directly affect the range that water will shoot. It may be in the end that there just isn't as much range as you want.

Check out some DIY laminar fountain tutorials for various ways that these streams have been created. A couple that I found via a web search are, Laminar Fountains for the math and The Laminar Project Forum for other ideas.

Water Pressure

You seem to have limits on how you can create the water pressure. You mention that compressed air is an option, so moving forward with a pressure tank for the water seems like the most reasonable way to go.

• While you literally answered my question you don't really provide any insights on how and why, that's the whole point actually. Thanks for your input too. – Vladimir Cravero Mar 23 '15 at 17:35
• Fire hoses don't shoot streams of water. The stream starts breaking up shortly past the nozzle, and will be a large number of individual drops by the time it hits something. – Olin Lathrop Mar 23 '15 at 20:33
• The Reynolds number criteria you give does not apply to the laminar fountain case. Laminar pipe flows have been observed up to Reynolds numbers of 100,000! (See here.) The laminar fountains use turbulence reduction techniques such that the flow is stable at higher Reynolds numbers. I have looked into such techniques for fire protection applications, and the pressure drop required to reduce the turbulence to the level in the laminar fountains is likely too much to be practical for fire protection, unfortunately. – Ben Trettel Mar 30 '15 at 19:48