I know you said “ignoring friction”. But that’s ignoring about 90% of the phenomenon the OP is interested in. Andy L was the first to point this out.
They *will *have the same trajectory in a vacuum. Because, as you say, there will be no friction to consider.
But the difference between a parcel of rock and a parcel of water in an atmosphere at the speeds we’re discussing is that one is absolutely rigid and the other is, well, liquid. Very quickly the parcel of water will break up into small drops and the drag explodes. Plus kinetic energy that was inside the parcel is consumed in breaking it up, further slowing the constituent sub-chunks.
Compare using a catapult to launch a brick with the same catapult launching a brick-shaped open container of dry (or damp) sand. Once the “sabot” comes off the sand quickly spreads and falls.
As another, more fun, example consider the many videos of punkin’ chunkin’. If the pumpkin holds together it can fly many hundreds or even a thousand yards. If instead it “pies” the furthest chips land a couple hundred feet downrange.
I don’t want to seem like I’m nitpicking your nitpicking, because your nitpick is actually an important nitpick to be nitpicking about … God above only knows how often I’ve nitpicked about friction in regards to nitpicking some people’s ideas about when to nitpick some fluid mechanicking nitpick …
Let’s start with boundary layer friction in the piping … the water molecules that touch the inside of the hose are going to be all but completely stationary, then as we move towards the center of the pipe the water velocity will steadily increase until we reach maximum velocity at the center … so even in a vacuum, the water is exiting the pipe at all different speeds … thus we’ll see a fan-like formation where the slower water falls closer to the exit and faster water falls further away … if the water doesn’t completely boil away beforenithandpick … so let’s use an ionic liquid instead of water, something with an exceptionally low vapor pressure, this will still boil away in our vacuum but the rate of boiling away will be slower …
Are we conducting this experiment at a non-equatorial position on a rotating ellipsoid? … now we have opposite sides of the piping under different amounts of acceleration … a recipe for vortex formation and her associated angular momentum … once we exit the pipe this quickly (instantly) becomes linear momentum dispersed radially given out hereto-beforehand mentioned fan effect more of a three dimensional formation … our exit velocity vector will have both right-left and up-down components that gives us more of a spray effect … even using ionic liquids in a vacuum …
All the above assumes as perfectly smooth a finish on these pipes as possible … which isn’t very smooth under actual friction-bearing conditions … all these irregularities are going to introduce the fluid mechanic’s worst nightmares … turbulence … it’s enough to make an anchor weep … however we are to measure the chaos we’re going to be measuring tons and bunches (roughly a tablespoon and a half) of the nasty stuff and God alone knows what that does to our exit formations … only that we know it will vary over time in profound and … chaotic … ways …
If we were nitpicking in truth, this poor child is going to be bald by this time …
… and our water or ionic liquid hasn’t even exited the pipe !!! … yet …
At 25 KSI, the exit velocity will be high enough so that aerodynamically-induced breakup results in the pencil stream being rapidly turned into a fine mist. Those tiny droplets start out with plenty of velocity, but their small size means they are way above their terminal velocity, so they are then quickly decelerated by the atmosphere. It’s a bit like hitting a badminton shuttlecock as hard as you can: it quickly traverses about 20 feet horizontal, and then falls pretty much straight down.
Your garden hose nozzle, operating at 100 psi, has a much lower exit velocity. The droplets that form will be bigger, with a higher terminal velocity. They start out with lower velocity, but don’t experience such violent deceleration. Their flight path will be something closer to a parabola.
Note that if you have a really massive jet of water, it generates its own local airflow, reducing the aerodynamic drag/breakup of the entire jet. At that point you can get a flight path even closer to parabolic. Dams generally produce pressures of only a few hundred psi, but their bypass pipes can put on a spectacular show, launching water a few hundred feet horizontally.
For a tank in which all the pressure is supplied by gravity, I was curious about the tradeoffs between having a hole high above the ground (so the stream will have more time to travel before hitting the ground) and having a hole low to the ground (so the stream will have higher velocity (due to the higher pressure at lower depths).
It turns out that if you want the stream of water to travel the furthest horizontally, the proper position for the hole is halfway between the top of the (full) tank and its base. If the base of the tank is above the ground, then the proper position of the hole is halfway between the top of the full tank and the ground, if possible, or (if the tank is well above the ground), at the base of the tank. All this depends on the usual simplifying assumptions - the hole is large enough that the water can form a stream instead of a spray of droplets, the wind is low enough to allow the stream to persist, etc., etc.
Per AndyL’s video: I used the concept, modified to simulate a situation closer to my criteria. I formed four horizontally aligned holes ranging in size from 1/16" thru 3/8" into a rectangular milk jug about 2" from the base. This gave me a consistent “launch point” reference for measuring flight distance as opposed to a cylindrical jug. Being horizontally aligned assured that pressure would be consistent at all four orifices.
Probably to no one’s surprise… The largest hole produced the longest trajectory, the second largest hole produced the second longest distance, and so forth, and so forth. Actually, it was quite linear!
Sometimes, it doesn’t take much to amuse me.:rolleyes:
Well yeah, I did think but wasn’t sure of the totality of it. Pardon my ignorance, it must be great to be you.
Otherwise, good points.
I would add however, I’m not referring to fluid streams exiting a hose in spray form, but rather, as a solid column of liquid. Your terminal velocity? concept would still come into play, but not until the solid stream began to break apart. Perhaps the earlier mentioned mass/volume factor comes into play here, and would shoehorn nicely into your point about large flows creating their own (protective) airflows?
Anybody willing to perform homebrew physics experiments is somebody with an actively curious mind not yet overcome by laziness or cynicism. Which is a marvelous thing and deserves celebration.
Yep, I was too. Generally speaking, a single, collimated jet of liquid in air will break up in fairly short order under most circumstances. At low velocities, turbulence within the jet itself will generate irregularities in the free surface; surface tension will then act on those irregularities, pinching the jet into large droplets (those nifty public water fountains that produce glass-like “rods” of water require very finely polished nozzles to produce laminar flow in the exiting jet of water, providing maximum lifetime for the whole jet before breakup begins). As the exit velocity goes up, increasing turbulence within the jet helps induce breakup earlier and earlier, and into smaller and smaller droplets. As exit velocity increases further, aerodynamic effects come into play, producing yet smaller droplets.
Which gogogophers I think you implicitly appreciated when you described how the high pressure stream through the pencil tip “dissipates and falls to the ground” (emphasis mine).
LSLGuy: Thanks for the kind words, sorry for the delayed reply.
I’m still unclear after re-reading this thread…
Does flow velocity increase (at a given supply pressure) as pipe diameter increases, with an open-ended discharge to atmospheric pressure? As best I can tell, some here say yes, some say no.
***Think: A large horizontal manifold @ 100psi that has nipples of various diameters welded on, say 1" through 6". *** …Open all the block valves (that I neglected to mention). Would the 6" nipple have a higher exit velocity than the 1" nipple?
You are getting two answers because you are asking two different questions …
“Does flow velocity increase (at a given supply pressure) as pipe diameter increases” — No, velocity decreases (at a given supply pressure) as pipe diameter increases …
“with an open-ended discharge to atmospheric pressure?” — Here, we don’t have “pipe diameter” or “supply pressure” … this is water in free-fall doing what water does when in free-fall … it will do many weird and pretty things while it’s falling … but on average it’s just falling to the ground … it’s not really useful treating this in a fluid mechanical way, just apply Newton’s gravity and air resistance …
concept would still come into play, but not until the solid stream began to break apart. Perhaps the earlier mentioned mass/volume factor comes into play here, and would shoehorn nicely into your point about large flows creating their own (protective) airflows?