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Inlet velocity and flow from approach piping to the stilling well

Please see the attached file for the fully formatted problem(s).

Please see the attached file for the fully formatted problem(s).

> 1200 gallons/min of water flows into approach piping that is tapered in design ----- 1000 gallons/min enters a stilling well while 200 gallons per minute recirculates back to a tank:

Question: How do you determine the inlet velocity and flow from the approach piping to the stilling well?

> The stilling well has a weir so that the water enters the first chamber of the stilling well, then overflows the weir to the 2nd chamber

>Then the water enters the inlet to a diffuser tube bank which consists of 36 4" round diffuser tubes that are 18" long ---- there are 3 rows stacked on top of each other (12 diffuser tubes per row)

Question:

How do you determine what the inlet and outlet velocity and flow is at each of the 36 diffuser tubes?

> Then from the diffuser tube bank, the water flows into a semi-enclosed channel with progressively smaller and smaller dimension until the water exits the small opening of this "sheet flow" channel and fills a 4 ft. x 4 ft x 2 ft high tank below it

Question:

How would you determine the velocity and flow at the discharge slice or opening of this channel??

How long will it take to fill the 4ft x 4 ft x 2 ft high tank below this opening once you know the velocity and flow from the channel opening??

I have provided a fairly detailed sketch of the problem on the attached Excel file --- there are 2 x-section views of the theoretical equipment and a plan view.

Please explain the flow and velocity calculations as clearly as possible at all stages to this problem!

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Solution Preview

Please see attached file, thanks.

How do you determine the inlet velocity and flow from the approach piping to the stilling well?
The design of the approach piping is similar to that of the tapered header in the headbox of papermachine. The cross-sectional area of the approach piping decreases with the direction of the flow, allowing a uniform pressure profile along the flowpath. This ensures that even flows are distributed in each of the channel entering the stilling well (otherwise you will end up with a non-uniform paper sheet like in your previous question.)
It is therefore reasonable to assume that there will be even flow in each of the entering channel to the stilling well. And there are five of them, so in each channel, the flow rate will be 1000/5 = 200 gpm.
Now convert this to SI unit
1 US gallon = 0.00378 ...

Solution Summary

Advanced fluid mecahnics: The inlet velocity and flow from approach piping to the stilling well is calculated

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