Flow through a vertical slot 1

[yank38]

Can someone help with an equation to determine the expected gravity flow through a vertical slot (Height/width ratio >30).

 

[mjpetrag]

That's a pretty vague question, but you might be able to use the Manning formula for that....

http://www.engineeringtoolbox.com/mannings-formula-gravity-flow-d_800.html

 

[yank38]

I actually tried that already and it doesn't pass a reality check. I have a plating tank that has wire running through it stacked in a vertical fashion through slots in each end. This tank will have solution pumped into it and I'm trying to determine how much solution will flow through the slots at each end to properly size a pump.

 

[dvd]

Sounds like worst case will be with no wire running. It might be more accurate to experiment than to calculate. The flow will be dependent on the fluid column so you should be able to make a simple test set-up and time the flow.

 

[katmar]

As a first attempt I would calculate the flow or pressure drop through a circular orifice with the same area as the slot. If your flow is turbulent I would expect this to give an accuracy of 40% or better (just my gut feel) which may be enough for a design.

If the downstream side of the slot is filling up your pressure drop across the slot will change as the tank fills, so you may have to calculate the flow in incremental steps.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BarryEng]

I'm not sure that I have the correct idea of your problem - however, let's give it a go. When I design flows from a clarifier to a filter (both structures attached) thru a vertical slot, I use the classic (Francis) weir formula.

Q = 1.84(L-0.1nH)H^^1.5

Remember that this formula assumes a sharp edged weir, so there will be viscous effects if you are flowing over a concrete (effective thickness is large) wall.

Q = flow (m^^3/s)
L = width of slot (m)
n = number of end contractions (for a slot, this = 2).
Head over weir (m)

The reason for the (L-0.1nH), is that the effective width is reduced by 10% of the head for every end contraction.

For a slot 0.5 m wide & 2 m high.
Putting L = 0.5m, H = 2m, n = 2

Q = 1.84(0.5 - 0.1 x 2 x 2)(2)^^1.5
= 0.52 m^^3/s

This formula assumes a free top water level (top water level below the top of the slot).

If the slot is submerged, I'm with dvd (It might be more accurate to experiment than to calculate).

If the slot is completely submerged, there are solutions in fluid mechanics books like 'Douglas', 'Schaum' etc etc.

If I am on the right track, indicate in this thread & I will find the actual formulae from various books that I have.

Have I assessed your problem correctly?

 

[siretb]

I do not like much the formula proposed by BarryEng, because it yields a zero flow if one extends H to 2.5. (you mention H= 30L)
I'd rather used an unmodified Francis Formula.
This should be enough for a rough estimate.

Be careful that if the width gets very small, you flow might not be turbulent, but get laminar. What is the actual slit dimension?

 

[yank38]

The dimensions of the slot are 3/8" wide by 13" high.
L-.1nH yields a negative number with these dimensions.

Thanks to everyone for your help. I'll continue to search.To manually measure it, which is a great suggestion, is currently practical.

 

[stanier]

Try to get hold of any book by Idelchik. They are out of print but an engineering library may well have one. The books are translated from the Russian experiments on fluid losses through all manner of fittings. I am sure you will find what you want.

 

[katmar]

See thread378-156536 . A slot is not very different from a rectangular orifice.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BRIS]

A vertical slot with a free surface is a weir - not an orifice.

The main controlling feature of a weir is that critical depth (minimum energy of flow) occurs slightly upstream.

Unless the shape will fit a standard weir formulae (see BarryEng) you will need to try and calculate the critical depth based on flow area and end contractions. Easier to make a model and measure it.

 

[katmar]

I agree that a vertical slot with a free surface is not an orifice, but it is most certainly not a weir either. The typical limitations on weir models is that the weir crest should not exceed 0.5 of the weir width. In this case the crest is 35x the width and as Yank38 has noted, application of the Francis formula resulted in negative flows being predicted.

If I had to choose either the orifice formula or the weir formula as an approximation for a vertical slot I would definitely choose the orifice route.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BRIS]

A slot is a weir regardless of whether it fits into any standard model of a weir. The important characteristic of a weir that it is free surface flow and at some point the flow is at minimum energy (at transition from sub critical to super critical critical depth if you like). You can calculate the flow through a weir/slot from this principle

If you assume an orifice you are stuck with trying to decide what is the top level of the orifice. It is certainly not the liquid level in the tank because there is an acceleration of flow and a draw down through the slot. If you assume your slot is an orifice with the the top of the orifice set at 2/3 of depth of liqued in the tank above the cill of the slot then you will get a near approximation. But in this case you have actually assumed a weir not an orifice.

The slot is hydraulically a weir but even if you consider it as an orifice the problem remains to estimate the area of flow at the vena contracta. The end contractions and the lifting of the nappe.

If you use an orifice formulae you will have an error because there is no contraction of the top surface. If you use a weir formula that is outside of its modelled range you will also have an error in the estimate of the contracted area but less so than assuming an orifice.

Make a model