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water running over a border

water running over a border

water running over a border

(OP)
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??


  

RE: water running over a border

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

Mike McCann
MMC Engineering

RE: water running over a border

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

RE: water running over a border

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

RE: water running over a border

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

RE: water running over a border

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.

RE: water running over a border

True...

Mike McCann
MMC Engineering

RE: water running over a border

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

RE: water running over a border

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

RE: water running over a border

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

  

RE: water running over a border

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

RE: water running over a border

(OP)
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.

 




 

  

RE: water running over a border

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.

RE: water running over a border

(OP)
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 ?



 

RE: water running over a border

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.

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

 

RE: water running over a border

(OP)
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?
  

RE: water running over a border

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

RE: water running over a border

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

RE: water running over a border

I'm not expert in weirs, but the relationship for Q in point 1) of the 2nd reference given by cvg seems to be completely out concerning dimensions. However that relationship reduces to Q=bh3/2/3 for the simple case under examination.
Another reference gives me the following equation:
q=Kh3/2
where K is a dimensional constant depending only on fluid density (and the gravitational constant) and q is q=Q/b (b=width of weir or pool perimeter in the present case). So the formula above is confirmed.
In conclusion, if the goal is to keep the same crest height in the model as in the actual pool, then simply Q/b must be kept constant.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: water running over a border

(OP)
Hi all, thanks again for your post.
I have to ask you ,  please understand my point of view.

1._ It is not a open channel weir.
     In a open channel, weir it is only one side , 2 sides  are the channel border , and the 4th is the water upward the channel, so the the water is constrain in 3 sides.

2._ The pool area is the same as a BIG HUGE pipe end standing vertical, so its border is horizontal, and water overflow all over the border, there is no constrain.
Some where I see the way to size flow by the height the water rise in a open vertical end pipe.

3._ guess it is a circle pipe  , it will have the hydraulic radius as Hr = pi*r*r/2*pi*r or Hr= r/2
, for a 1.0 meter diameter Hr = 0.25 m , and perimeter = 3.14 m , and area 0.785 m2, for a flow  of 35 m3/h the speed is 0.012 ms
4._ Now for a rectangle with the same wet  perimeter as the pipe, but with a 1.5 m side by 0.07 m have the same perimeter 3.14 m but the area is 0.105 m2 so the Hr = 0.0334 m . and for the same flow 35m3/h the speed is 138.88m/s, it is only a sample calculation,  maybe it can not be a real case , as speed is 500 km/hr.  
5.- So it can not behave the same way for a given flow,
it is evident that in the rectangular shape the water will rise upper than in the round pipe.


 

RE: water running over a border

You've already been warned above by someone else: you are on the wrong path. The pool has nothing to do with a BIG HUGE pipe.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: water running over a border

(OP)
Hi Prex , if not so , can you tell me , not talking about a pool.

What is a circular vertical thank ,15 m diameter , when it is fill by the botton end.
The same used at oil industrie to hold fluids.

Is or is not a pipe?

Will fluid overflow by its border or not, when the fluid reach the border.

 

RE: water running over a border

You can call it as you like, and OK, you can view it as a pipe, if this suits you.
The point is that this is not the correct model to calculate the height of the crest going beyond the border, as the velocity in your BIG HUGE pipe is negligible with respect to the velocity of the overflowing water and has no influence on crest height.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: water running over a border

(OP)
I agree with you, thing are going clear, now.
Thanks    

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