Project calculations.... might be a difficult question?

[alannap]

Hi,
I am not student but have a mathematical query I have been unable to get answered, even by people in the field.
I have a waterfall above my pond. basically it is a wooden oblong box 252cm long by 24cm wide. On the front of this is a bevelled wooden projection (15cm) to allow the water to flow out and down evenly like a sheet all the way along the 252cm edge.At present this box is filled from the underside by two seperate pipes pumping 2,00 imperial gallons per hour between them. I have bought a new pump and will be increasing this flow to 3,000 imperial gallons per hour as the original flow did not produce the effect I wanted. Now for the problem. I am removing the front projection and replacing this with toughend glass. The glass will cover the whole box section of 252cm X 24cm and project out (15cm) as the original projection did. The glass will need to have holes drilled along its length to allow 2,650 imperial gallons per hour to flow through without creating fountains from each hole, but also keeping the holes as small as possible to avoid weakening the glass too much. What size holes do I need and distance of spaces between them? I would be grateful If anyone has a solution to this. Thanks in advance....Alan.

[tkhunny]

First, you'll have to decide what to do with the extra 350 imp gal - or can you turn down the pumps to less than full capacity?

Second, as defined, your answer does not look unique.

You have 252 cm x 24 cm = 6048 cm^2 to push against. Once you drill holes, you will have less area but the same force against the glass. It's sort of a moving target.

Water coming from holes arranged in a linear fashion may not create the effect you want. I suspect you will create interference patterns. Maybe that's what you want? These patterns MAY be sufficiently flat as you get to the bottom of the glass. Hole size will make a difference.

If it were me, I'd think about other dispersion patterns - maybe a zig-zag (or two lines with alternating spacing). It's possible that slits may be more effective than round holes.

If it were me, I'd think about building a model with some cheap lumber and testing various plans. You may wish to consider adding some randomness to the hole placement and size.

For what it's worth...

[alannap]

First, you'll have to decide what to do with the extra 350 imp gal - or can you turn down the pumps to less than full capacity?

Second, as defined, your answer does not look unique.

You have 252 cm x 24 cm = 6048 cm^2 to push against. Once you drill holes, you will have less area but the same force against the glass. It's sort of a moving target.

Water coming from holes arranged in a linear fashion may not create the effect you want. I suspect you will create interference patterns. Maybe that's what you want? These patterns MAY be sufficiently flat as you get to the bottom of the glass. Hole size will make a difference.

If it were me, I'd think about other dispersion patterns - maybe a zig-zag (or two lines with alternating spacing). It's possible that slits may be more effective than round holes.

If it were me, I'd think about building a model with some cheap lumber and testing various plans. You may wish to consider adding some randomness to the hole placement and size.

For what it's worth...

Thank you for your reply.

Yes the flow will be adjustable. I should actually have stated that in my first submission. I can adjust the flow through the pump quite easily. I agree, for flow factor slits would allow an easier flow but, it would also weaken the glass.
This is what the manufacturer is telling me. They advised me to go to plastic polycarbonate but that also has its problems in relation to sunlight and softness. The system as it was previously also comes though holes in the trough.
It worked very well but I can not use the same amount of holes in the glass. The main reason for this exercise (remember the whole of the existing system is in wood) is that the wood allows algae and slime to accumalite very quickly especially in the summer, it then begins to look unsightly. Even though its oak, each cleaning opens up more grain etc, more bed for the alge. This is why I wanted to move to glass. Easy to clean and less base for the algae to cling and reproduce. I would still like to know if its possible, how to work out mathematically the diameter of the holes needed to allow the flow I require?
Thanks again.

[galactus]

Is the channel sloped at all?. If it is, do you know the grade?. This will be an issue.

I may have to dig out my old hydrology and hydraulics books, for it's been a while since I dealt with this stuff .

We may be able to work something out.

There is a fun little equation that we may use. It's called Manning's equation, and it is used in designing channels, culverts, and what not.

[alannap]

Hello Galactus,
Thank you for finding the time to take an interest in my problem.
No, the channel (within the box section) is perfectly flat.
It's a never before for me with this stuff!!!
I was interested in TK Hunnys suggestion (model) but of course this is very time consuming.
The next problem would then be where to find the extra time!!!