Fluid dynamics: Water flow in free air quandry.

Straight to the question: What determines the horizontal distance a stream of fluid (water) will travel, when discharged from a system into the atmosphere?

The water pressure at my house is appx. 100# (high, I know, but it is what it is) and my 5/8" garden hose will shoot a stream about 35-40’… The hose inlet pressure on our fire suppression system at work is also about 100#; but when hooked up to a 4" hose, it is capable of launching water (a guess) 150’… The hydro blast units at work pump out about 25,000# pressure through a 1/4" hose with a pencil tip, and when the operator sprays into open air the entire water stream dissipates and falls to the ground in about 35-40’.


Could it be velocity at play here? Whereas: The velocity in a 4" pipe is greater than that of a 5/8" pipe, at a given (same) pressure, when opened to the atmosphere? Just a wild guess.

It seems that pressure is irrelevant in this situation, and volume is the key… But that just “feels” counter-intuitive. For example: If one designed a system with only 5# pressure and opened it to the atmosphere via a 12" outlet, I’m sure (?) the resulting stream would fall to the ground within a couple of feet of horizontal travel. So what gives? There is some fundamental concept at work here concerning pressure/volume that I am too ignorant to grasp, so please enlighten me.

I think the velocity is the key. The water will reach the ground after square root (2*height/(32)) seconds (where height is measured in feet), just due to gravity (assuming you’re aiming the hose horizontally), and the distance the stream reaches will be the exhaust velocity times that time. The atmosphere won’t make much difference (the amount of time the water spends in the air is too short for friction to play much of a part in the problem).

The “external ballistics” you allude to makes perfect sense, I never thought to consider it from that perspective. Of course… similar to firearms, the higher the velocity, the greater the range.

Yep. See this video by the way for an easy experiment on the subject Liquid Pressure - YouTube - the streams from the lower holes go farther because the pressure at the lower holes causes higher exit velocity.

Pressure and pipe diameter have everything to do with exit velocity … but once exited, the stream is ballistic as Andy L says …

Andy L are you sure that drags on the different streams of water of different mass and diameter, one through a “pencil tip”, is not a factor?

I think as long as the flow remains a stream that drag is a small factor; if the stream breaks up into droplets, then drag will become the major factor, but I could be wrong. If the stream breaks up into droplets partway through flight, you might end up with a stream that looks like a parabola (in which gravity and the initial velocity dominate the motion) up until the point where stream breaks up, at which point, the droplets fall more or less straight down (since the initial horizontal velocity gets dissipated by drag).

Just a quick safety tip … don’t watch Andy L’s video if you’ve drank a couple cups of coffee … at least go pee first before you watch …

I think we’re trying to answer the question using ideal conditions … air resistance, turbulence and evaporation are all factors that determine the exact shape and trajectory of the water stream … but all these frictional elements are proportional to velocity … the important point here is that once the fluid exits the pressure immediately drops to standard atmospheric pressure … whatever pressures and forces acting on the water inside the pipe come to an abrupt end once the water exits the pipe … then it’s just Sir Issac Newton and gravity at play …

A parcel of water and a rock at the exact same velocity will have the same trajectory … ignoring friction …

One factor is how laminar the water flow is. Commercial laminar flow nozzles are in those neat fountains where each stream of water leaps through the air without degenerating into droplets, then disappears down a matching hole where it hits.

It’s true that the ***maximum ***horizontal distance is limited by pressure, but the stream shape has a big influence while it is moving through the air. The OP’s 4" hose probably does a reasonable job of providing laminar flow. And laminar flow allows the central part of the stream to be at the highest possible velocity.

There are lot of YouTube videos on home made laminar flow systems, they are simple to make and fun to watch.


I may be misunderstanding the op but that seems to be what is being described. The stream is coming out from a pencil tip opening at 25,000 psi pressure and thus I am sure at very high initial velocity, yet it all “dissipates and falls to the ground in about 35-40’” same as water leaving his home hose at 100 psi pressure. That would not be the case in a vacuum.

I am also not believing that water at the same pressure exits a 4 inch pipe with greater velocity than when it exits a 1/4 inch pipe.

Again, I may be misunderstanding the question and the answer both …

This was the question I attempted to illustrate in the OP: That the ballistic distance didn’t appear to be (strictly) a factor of pressure, as in the example of a garden hose vs a fire hose. Both essentially the same pressure, but one in flight goes much further than the other.

So, it seems the pipe diameter affects the flow velocity at a given pressure, with all other things being equal?

If so, is this due to the lower surface area of pipe per volume of fluid flowing through it… In other words, less drag (per unit volume) as size increases, or is it more complex than that?

Is there a reference someone could point out related to this?

Yeah, talking about how the maximum distance is constrained by the initial water velocity produced by pressure is a good way to talk about this. Thanks.

Laminar flow characteristics no doubt play some roll… But to the extent that I describe? After all, the fire hose and the garden hose each have an adjustable nozzle that focus their discharge down to a concentrated, single stream. To clarify: all examples assume a straight run of hose, with no kinks, bends, reducers, etc. All things being equal except pipe (hose) diameter. Let’s forget about the hydro blaster I mentioned in the OP, it seems to muddy the water.

Perhaps it doesn’t, I don’t know, hence all my questions.
Perhaps a larger volume discharge thru a 4" hose vs a 5/8" hose exit at the same velocity, but the larger mass from the larger hose tends to “hold together” and not atomize (increase drag) as soon, hence… Travel further.

I don’t know, just spitballin’ here!.. Ya’ll tell me.

To simplify even further: Let’s take the laminar variable of the nozzle out of the equation. Chop them off. Now there is merely a open-ended pipe.

The same effect as described in the OP will be observed, albeit all at a shorter distance. But the noticeable differences are still there.

The question of mass kept coming up in my thinking as I read the thread. :smack:

The gopher beat me to it. :stuck_out_tongue:

Wellll… Kinda-sorta. Actually, the video is lame. Overall, I get the picture, but if you notice, the bottom orifice displays the least linear projection, probably due to a lack of consistency in control methodology.
My question however, relates to orifice **size ** at the same pressure as related to it’s distance of projecture… Not merely a pressure drop in a column of water.

However, a like experiment could be conducted in the same fashion by making holes of varying diameters at the same elevation in the bottle, and comparing the distance of their projection.

**Thanks! **

I think what you’re looking for is Bernoulli’s principle … if the fluid in a single fluid flow has an increase in speed, then the pressure will drop … that all works while the fluid is contained within a pipe or hose and thus forms a single fluid flow … this means that pressure has everything to do with speed … including exit speed …

However, once we exit the single fluid flow, Bernoulli’s principle no longer holds … here we effectively have zero net pressure (water pressure = air pressure) and the only forces acting on the water is gravity and friction …

Bernoulli’s principle is used to compare two different points in the same fluid flow … it cannot be used to compare two points in two different flows …


I agree with that.

The lowest orifice seems to have the smallest downward curvature (indicating the largest velocity), except for times when the flow is getting entrained onto the surface of the bottle.

Anyway, if I’ve got the right equations, the water velocity is equal to the square root of (2*Pressure/density), so (as DSeid suggested), the area of the hole drops out of the equation. I was initially surprised by this, because when I put my thumb on the end of the hose, the exit velocity definitely gets higher - but by putting my thumb on the end of the hose, I’m definitely increasing the pressure in the hose (I can feel it in my thumb!).

You’ve slowed down the velocity, so pressure goes up … just past your thumb, pressure drops to normal, so velocity increases … but gravity takes hold instantly …