- #1

Charles Winston

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I'm facing a problem with that rhyming title up there.

The design is thus: a downward-facing, vertical pipe with known constant flow and diameter has water flowing out of it, into a short (15cm-91cm) free fall. At the end of that fall is a bowl of indeterminate depth made of steel with holes punched through it--one larger circular hole in the center, and 8 smaller half-ellipse holes spaced equidistant along the inside curve of the bowl. The area of all the apertures must be sized such that the bowl will reach and maintain steady state with no change in the in-flow. Further, the hole along the curve of the bowl need to spread water horizontally over a specific area (think a similar distribution pattern that you would see with a fire sprinkler).

I understand to find the appropriate answer, I'm going to need to know the exit velocity for the holes (and the required area/flow for that).

I've been looking at this for so long I'm starting to think I'm lost in the weeds, but here are the avenues I've tried to follow to get some sort of answer:

1) Model of a hole in a tank: While this would work great for a static column of x fluid, it doesn't seem to represent what I've got here. I started by assuming the pressure head in the pipe could be added to the height of the column of liquid. The more I thought about that, the less likely that seemed. Eq. used:

2) Bernoulli equation: I next chose to treat the system as a simple contraction, and adjusting later from there. This gave me a wild over-estimate for fluid velocity at the outlet of the holes, so I think I'm either misusing Bernoulli's or making a mistake somewhere. Form used:

3) Force of falling water: A desperate last attempt to figure this out. Good ol' F = ma and P = F/A. Predictably gave me a smaller-than-expected answer, which leads me to think I'm missing something.

If you made it through that, thanks. I would appreciate any help that you can give, and I'll be here to reply to any questions if you've got any.

(Note: Goal is to maximize droplet size, but I'm open to any alternatives to this design)

The design is thus: a downward-facing, vertical pipe with known constant flow and diameter has water flowing out of it, into a short (15cm-91cm) free fall. At the end of that fall is a bowl of indeterminate depth made of steel with holes punched through it--one larger circular hole in the center, and 8 smaller half-ellipse holes spaced equidistant along the inside curve of the bowl. The area of all the apertures must be sized such that the bowl will reach and maintain steady state with no change in the in-flow. Further, the hole along the curve of the bowl need to spread water horizontally over a specific area (think a similar distribution pattern that you would see with a fire sprinkler).

I understand to find the appropriate answer, I'm going to need to know the exit velocity for the holes (and the required area/flow for that).

I've been looking at this for so long I'm starting to think I'm lost in the weeds, but here are the avenues I've tried to follow to get some sort of answer:

1) Model of a hole in a tank: While this would work great for a static column of x fluid, it doesn't seem to represent what I've got here. I started by assuming the pressure head in the pipe could be added to the height of the column of liquid. The more I thought about that, the less likely that seemed. Eq. used:

*v = Cv*(2*g*H )^1/2*

where

v = outlet velocity (m/s)

Cv = velocity coefficient (water 0.97)

g = (9.81 m/s2)

H = height (m)where

v = outlet velocity (m/s)

Cv = velocity coefficient (water 0.97)

g = (9.81 m/s2)

H = height (m)

2) Bernoulli equation: I next chose to treat the system as a simple contraction, and adjusting later from there. This gave me a wild over-estimate for fluid velocity at the outlet of the holes, so I think I'm either misusing Bernoulli's or making a mistake somewhere. Form used:

3) Force of falling water: A desperate last attempt to figure this out. Good ol' F = ma and P = F/A. Predictably gave me a smaller-than-expected answer, which leads me to think I'm missing something.

If you made it through that, thanks. I would appreciate any help that you can give, and I'll be here to reply to any questions if you've got any.

(Note: Goal is to maximize droplet size, but I'm open to any alternatives to this design)

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