Hydrostatic bellmouth

[mac114]

Hi there,
Does anyone have a formula for calculating the flow discharging from a hydrostatic bellmouth (for a given difference between the TWL in the adjacent tank and the bellmouth level, including the losses through the connecting pipework)?

The specific application that I am concerned about at the moment is desludging a humus tank in a wastewater treatment works. I am concerned that the system might be too sensitive (when adjusting the height of the bellmouth in relation to the TWL in the humus tank). I.E. When the bellmouth is lowered 1mm the flow might increase 10L/s.
Many thanks.

 

[BigInch]

Not totally sure by what you mean with "hydrostatic bellmouth". If you want to post a sketch, see the paperclip below?

http://virtualpipeline.spaces.msn.com

 

[mac114]

Sorry, I have attached a sketch of my specific arrangement and a another drawing of an example of the hydrostatic bellmouth I am talking about.

http://files.engineering.com/getfil...a-80d1-62922ce0ee71&file=Humus_Desludging.pdf

http://files.engineering.com/getfil...9e7b-741d85e5e672&file=Hydrostatic_valves.pdf

 

[BigInch]

The sensitivity of flowrate to small variations as would usually be an adjustment like that, will tend to be in the same proportion as is the amount of the adjustment to the total height H. Here,

http://www.lmnoeng.com/TankDischarge.htm

you can find the following equation. We'll make a "differential" out of it for small changes,

Q = Co * A * (2gH)^0.5

Q1 = Co * A * (2gH1)^0.5
Q2 = Co * A * (2gH2)^0.5

Co * A * (2g)^0.5 is a constant, so that will = K

Q1 = K * H1^0.5
Q2 = K * H2^0.5

Q2 = Q1 +K * (H2^0.5 - H1^0.5)

So if flowrate was 100 l/s and the height was 3m
and you changed it to 2.8 m, the new flow would be
Q2 = 100 + K * (1.67 - 1.73)
Q2 = 100 - 0.06 * K

What you may have to be careful with is that, depending on the size of the reservoir, it may take some time for its level to drop to the new adjusted level of the bellmouth height, so plan to make a small adjustment, wait for the reservoir to get to the new level, then adjust again if needed. Record how long it takes for the reservoir to reach a new level each time you make a 10mm adjustment and you will learn to time your lunch break....

http://virtualpipeline.spaces.msn.com

 

[rcooper]

For the actual bellmouth, I have modelled these as sharp weirs with the weir length equal to the bellmouth diameter.