Tracking Spread of a water jet out of a downward-facing pipe

[Charles Winston]

Hey folks, I'm back with a new question.

If I have a pipe of known diameter, with a known volume of water at a known pressure discharging downwards into atmosphere, how can I calculate the radius of its "spread". That is, how can I find what area beneath the discharging pipe is being covered with water?

A simplified, idealized model, along with a more complicated derivative would be equally appreciated.

Thanks!

 

[Chestermiller]

Hey folks, I'm back with a new question.

If I have a pipe of known diameter, with a known volume of water at a known pressure discharging downwards into atmosphere, how can I calculate the radius of its "spread". That is, how can I find what area beneath the discharging pipe is being covered with water?

A simplified, idealized model, along with a more complicated derivative would be equally appreciated.

Thanks!

What are your thoughts on this so far? Is this a homework problem?

 

[Charles Winston]

So far I've tackled it a few different ways.

First approach is to model it as an expansion into a pipe of diameter equal to the desired coverage, but I'm thinking that methodology is flawed. Essentially, Q1*A1 = Q2*A2.

Second is to examine the system in two dimensions, but I've yet to be able to track down equations or any sources for it. Entirely possible I just don't know what I'm looking for.

I've also tried to treat it as a projectile, but tracking that in two dimensions for a fluid is somewhat tricky.

This part of a company project, but just one step out of a dozen or so.

 

[Chestermiller]

Are you sure that it spreads rather than converging?

 

[Charles Winston]

I can't be sure, but the outlet diameter is 3/4" with a flow rate of 350 gpm. Pressure unknown, but above atmospheric. Would a stream in those conditions behave like, say, a running faucet (i.e. converge) or spread? This I'm not sure of.

On Monday I'm going to have a demonstration of the flow pattern, but it would be difficult from that to determine with any degree of certainty what its spread would be, as the water is at around 180°F.

 

[Chestermiller]

I can't be sure, but the outlet diameter is 3/4" with a flow rate of 350 gpm. Pressure unknown, but above atmospheric. Would a stream in those conditions behave like, say, a running faucet (i.e. converge) or spread? This I'm not sure of.

On Monday I'm going to have a demonstration of the flow pattern, but it would be difficult from that to determine with any degree of certainty what its spread would be, as the water is at around 180°F.

According to this, it's traveling at extremely high speed, 260 ft/sec. Is this about what you were expecting?

 

[jrmichler]

I hope that the audience is well separated / shielded from that water jet. The velocity pressure is over 450 PSI, and if such a jet hit somebody, it would (not could) kill them.

You could try treating it as a projectile. A cylinder of water at a velocity, subject to gravity and air drag along the sides. Ignore air drag on the leading and trailing ends. I expect that gravity force will be small compare to aerodynamic drag, and that the air drag will explain why spray comes off the sides. But that's just a guess. I have not done any calculations. And I'd like to know how it turns out. Can you get us a photo?

 

[Charles Winston]

According to this, it's traveling at extremely high speed, 260 ft/sec. Is this about what you were expecting?

In all honesty, I've got reason to suspect that these stated/given values might not be accurate.

Monday in addition to a physical demonstration, I'll be taking an ultrasonic sensor to the pipe bank to get the flow. There's no infrastructure for that in place currently.

I hope that the audience is well separated / shielded from that water jet. The velocity pressure is over 450 PSI, and if such a jet hit somebody, it would (not could) kill them.

I'll be sure to get pictures, maybe even with a thermographic camera!

Thank you for the drag consideration. That's out of my expertise. I'll be looking into that.