water running over a border

[milena02]

Maybe a wrong forum to post it.
If so please redirect me.
A swimming pool will have all around it a leveled border.
Width 4.4 meter , length 13 meter
The pump can deliver 35 m3/hour.
The water will overflow all around the border.
Now the one million dollar question.
HOW MUCH WILL THE WATER RISE FROM THE BORDER??

 

[msquared48]

Q = VA
A = Perimeter P X Depth D
D = Q / (V X P)

Mike McCann
MMC Engineering

 

[msquared48]

Just to note further, that is the simplistic solution, disregarding the surface roughness and wier configuration. It will give you a rough answer, but not the "exact" solution.

Mike McCann
MMC Engineering

 

[itsmoked]

A weir with a length of 34.8m and a flow of 35m³.

You left out what the edge is like. How wide is the edge?

If it's like a tile width you're supposed to bring the velocity across the weir to this party too.

Keith Cress
kcress -

http://www.flaminsystems.com

 

[msquared48]

I took the border width to be 4.4 meters which would make this a very wide broad-crested wier. May be less than that, but certainly still a broad crested wier analysis.

Mike McCann
MMC Engineering

 

[cvg]

the problem is that you cannot guarantee the entire border is level. there will be low and high points no matter how good your pool contractor is. the water will concentrate at the lowest points.

 

[msquared48]

True...

Mike McCann
MMC Engineering

 

[milena02]

Cvg , and Msquared48, guess it is a perfect or theoric border ,and the length is 13+13+4.4+4.4 REAL

 

[msquared48]

So then, how wide is the border then, in meters, or to put it another way, what is the length of the spillway?

Mike McCann
MMC Engineering

 

[milena02]

See attached a sketch , angle 45 ° material is 304AISI.
Bending I do not know yet , it is at the shop.

 

[milena02]

at my original post
A swimming pool will have all around it a leveled border.
Width 4.4 meter , length 13 meter.

 

[cvg]

looks more like a sharp crested weir. use the weir equation and the appropriate weir coefficient

http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/chap07_03.html

http://www.engineeringcivil.com/weirs.html

 

[itsmoked]

Ah yes a sharp weir - not at all what I was picturing.

Well, over 34.8m weir, a measly 35m³/hr translates to only:
35/3600m³/s or
0.01m³/s

About 2mm of flow over the edge.



Keith Cress
kcress -

http://www.flaminsystems.com

 

[milena02]

Hi all you , thanks for your help.
I want to ask a further more.

How I can made a small scale prototype.
I was thinking on a a small tank , but I guess I need to keep the area perimeter ratio.

1st case, and not a prototype ,
If for the same perimeter say 36 m ,to work with round numbers,I have 13m length and 5m wide= 65 m2 area, and for 35 m3/hour the water speed is 0.000270062 m/seg , but If I keep the perimeter changing the side sizes, speed will increase , thus the over flow will be great.
m3/h m3/seg
flow 35 0.009722222
meter meter m2 meter m/seg
lenght wide area perimeter speed
13 5 65 36 0.000149573
17 1 17 36 0.000571895
17.9 0.1 1.79 36 0.005431409
17.95 0.05 0.8975 36 0.01083256

Attached is the xls

Then the given formula seem to be not the best suited.
Hydraulics was and, seem to be,a empirical solution science, despite the modern software, as if I'm not wrong , they use the same Darcy-Weisbach formula, and others.

So how can I design a prototype?

My intention, is to build small pool and start pumping up water until I get the desired overflow, the scale the flow to meet the new poll overflow.

My final purpose is to calculate the flow need for any overflow at any pool I have to build.

Thanks again.

 

[cvg]

as long as you keep the length of the weir constant, speed and depth of flow over it are constant. Speed of the overflow has no relation to the area of the pool.

 

[milena02]

Hi CVG , please check my point of view , meanwhile I keep the weir length constant , and reduce area , speed increase.
So it is like when you let flow water in a round hose, it reach a overflow , but if you squeeze it , for the same flow , the overflow will increase.

As far as I see on text books , weir formula are for open channel , and in this case I consider the pool as a big pipe.

Of course I can be wrong.


How can I build a scaled prototype?

Shall I consider the prototype to have the same HYDRAULIC RATIO??

If so , when I know the flow at the model , how I rescale it to get the real pump flow value ?

 

[cvg]

I don't know what calculation you are doing, but I don't see a weir equation on your spreadsheet, nor do I see the continuity equation (Q=VA). You need to check your calculations. Area has nothing to do with the flow velocity over the weir. Weir equation has nothing to do with an open channel and can be used in pipes, tanks, pools also. Really not sure what your hydraulic ratio is or how that applies to a weir. As far a building a scale model, that is a subject for another book and I really can't do it justice on the web site.

http://www.usbr.gov/pmts/hydraulics_lab/history/75th/Tours/Station1.pdf

 

[milena02]

Ok , guess I made a scaled pool wit a 0.348 weir lenght , no matter what area , assume 0.087 m square.
Then I fit a pump and increase flow to have the same overflow I want to have at the 34.8 m weir.
I scale by 0.01 or 100 ,
So what will be the flow for the real pool's pump?

 

[msquared48]

As cvg said, this gets into hydraulic modeling, and is really more than we can solve here in the forum.

Another thought here is that the 45 degree backslope at the interior of the pool rim will have an impact on the flow and depth, and that the "sharp crested" condition is only an approximation since, realistically, there is a small radius to the bend thast will increase the flow.

If you need an exact solution, then a livfesize model would be appropriate here, with, say a 3 foot weir width for the flow. You should be able to back in the Q and depth at the weir you will get with this setup. I do not think that a reduced model will give you the accurate depth measurement that you seek.

Mike McCann
MMC Engineering

 

[itsmoked]

I would make a 1 meter model and then do as Mike sez and work the sharp weir equations backward to give the right constants to then calculate your depth for any length or flow.

Keith Cress
kcress -

http://www.flaminsystems.com