Flow of Water into a Bowl with Holes

[Charles Winston]

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:

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)

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)

 

[jrmichler]

I think I understand what you are asking, but to make sure, please add a diagram. Is the purpose of the side holes to make jets of water? If so, indicate on the diagram how far the jets are supposed to jet. Indicate any constraints (15 to 91 cm is a constraint).

 

[Charles Winston]

Of course!

Top-down view of the bowl I know the original post specifies 8 holes, but this is a stand-in I have on hand.

Side view of the assembly (note: the two vertical pieces that extend from the pipe to the bowl itself are supports attaching it to the ceiling, welded on either side of the center hole, 1.27 cm in diameter).

Constraints:

The fluid is water at 82.2 C, density 0.97056 g/cm³.
The inner diameter of the pipe is 19mm, and the outlet flow is 1.324 m³/min.
The diameter of the bowl from edge to edge is 20.32 cm, and the depth is 2.54 cm, though I'm looking to change that, eventually.
Each hole around the circumference needs to shoot a jet out ~2.4 m horizontally. The distance from the holes to the bottom of the chamber is ~6.86 m.
The center hole is 1.27 cm in diameter (though I'll be looking to vary this eventually), and there are no specifications for the diameter of the side holes.

Apologies if I've over- or underspecified any part of this. I'll be available to answer any questions as they pop up. Please let me know if any further clarification on the design of the system is needed.

I appreciate any help you can provide in regards to modeling the system.

 

[gmax137]

what is the purpose of the bowl? why don't you put an end cap on the pipe, and drill holes (radially) in the pipe wall?

 

[Charles Winston]

what is the purpose of the bowl? why don't you put an end cap on the pipe, and drill holes (radially) in the pipe wall?

The purpose of the bowl is to distribute hot water evenly over a material being heat conditioned. It's to be used in conditioning blocks of wood for production of veneer and plywood. If my explanation doesn't make sense, which is more than likely, https://www.academia.edu/14920541/Veneer_block_conditioning_manual_for_veneer_and_plywood_production, provides an overview. The specific conditioning system is (b).

While I haven't found literature that deals with this exact process, my understanding of heat transfer is that I would prefer to maximize droplet size to maximize heat flux per volume of fluid. This may be flawed or incomplete, so feel free to correct me here.

There are a couple things I've considered from the point of putting radial holes along a capped-off pipe, though that has been an idea on the table from the start. The pump/valve system itself is not designed for any backflow, the piping itself cannot be replaced currently, and there are material problems with the flow area needed for the radial holes and the area of the pipe available for those holes. Of course, this is still under advisement.

 

[ChemAir]

This is what I would call a distributor plate design. Usually they are designed for uniform distribution over a range of flows. They are very common in absorption and distillation columns

Some links that may help:
http://ssu.ac.ir/cms/fileadmin/user...varihaye_zist_mohiti/e_book/air/pached/10.pdf
http://www.koch-glitsch.com/Document%20Library/Plastic_Packing_Liquid_Distributors.pdf
http://www.traysrus.co.uk/liquid-distributors.php

Perry's Chemical Engineering Handbook discusses these, pipe spray headers, and spargers, I believe, as well, but I'm not sure it addresses some specifics in this question.

 

[jrmichler]

Two things:
1) If your plate needs to shoot streams of water a specified distance both horizontally and vertically, you need to do some calculations. A jet of water will exit the plate perpendicular to the plate at the hole. You calculate the velocity necessary to hit the target point. This is just the cannon ball calculation found in every physics book. Then you calculate the head of water needed to get that velocity from Bernoulli's equation. The flow rate through that hole is velocity times area times the orifice coefficient. Then iterate the plate design as indicated, and repeat the calculations until you have a finished design.

2) An alternative is to buy a nozzle with all the engineering done for you. Spraying Systems Company is a good source: www.spray.com. One of their Fulljet nozzles may meet your needs: https://www.spray.com/Assets/SPRAY/Cat75HYD_US_B.pdf. I have used their nozzles, and they perform as advertised. If droplet size is a concern, call their tech support.