Air flow through small rectangular opening

[marcske]

Hello,
I have to calculate the air flow through a small rectangular opening with following data:
- temperature at one side: 1200°C
- temperature at other side: 20°C
- pressure at hotter side is 3 mm WC lower than the colder side
- the length of the opening is 240 mm
- the width of the opening is 1 mm

Does anyone know how to calculate this?
Thanks in advance for your appreciated help.

Marcske

 

[Nidum]

Need more complete description of problem . Could you provide a clear diagram and some explanation of what is actually happening ?

 

[russ_watters]

I'd use Bernoulli's equation to calculate the velocity based on the pressure difference. The answer is going to be very low though.

 

[256bits]

I'd use Bernoulli's equation to calculate the velocity based on the pressure difference. The answer is going to be very low though.

And even lower than that, I think, as due to the increase in temperature, the air will expand going from the cool side to the hot.

 

[marcske]

The actual problem is small openings in a furnace that is under a slight vacuum. There are several openings of an average of 1 mm by 240 mm (appx. 100 - 150 openings). I would like to calculate the losses related to the excess oxygen that you need for complete combustion and the extra air that you need to heat from ambient to 1200°C in the furnace. I know that the air flow through 1 opening will be very low, but the total may be sufficient to do something about these losses. My first thought was to use an equation for rectangular orifices, but the flow is not only driven by the pressure difference, but also the difference in temperature (air density). I do not know how to combine both effects.

 

[Nidum]

I've met this problem before in furnaces made from loose blocks with many very small gaps between blocks . Ingress of air caused localised chilling and oxidation of furnace charge . In the end we identified some areas of blocks as causing problems and some not . Problem areas were just sealed with cement and no further difficulties were experienced .

Before doing any more complicated analysis try doing an order of magnitude calculation - assume maximum density air everywhere along flow path . If mass flow calculated is very small then no further work is needed .

To work this problem out in detail the length of the flow path would be needed and some estimate would have to be made of the temperature profile along the flow path .

Bear in mind though that with such a small pressure difference convection currents inside furnace and draughts in ambient air might affect flow rates significantly .

 

[Nidum]

Incidentally we did our first assessment of where the larger air leaks were by going around all the joints with a lighted candle - you don't always need high tech methods !

 

[marcske]

Thank you for your reply. The openings here are around peep doors and cannot just be covered but need a new concept of sealing. As this implies a serious cost, I would like to perform a benefit calculation based on the losses by air ingress.

 

[Nidum]

Try doing a bag test . Large plastic bag blown up but not pressurised with mouth of bag held around closed peep door and sealed with Duck tape . Known volume of air in bag . Time to collapse .

 

[russ_watters]

My first thought was to use an equation for rectangular orifices, but the flow is not only driven by the pressure difference, but also the difference in temperature (air density). I do not know how to combine both effects.

Could you provide the equation you are using and source so we can evaluate it?