Convection Current Flow Rates

We have all seen those little diagrams of curved pointed lines that indicate convection currents in a grain bin.  How in the winter the air flows up through the middle and down the sides, and then in the summer where it flows down the center of the bin and up along the warm side walls.  We can also get convection currents right through the bin with air flowing through the fan, vents, and center opening.  But just how fast is the air moving with convection currents? Let’s see.

First of all, the only reason we get convection currents is because of the air being at two different temperatures.  Air is heavier if it is colder.  A column of cold air has more weight than a column of warm air, and consequently will push down with a pressure equal to the difference in weight.

According to http://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html , the weight of air is:

ºC         ºF         lbs/ft^3

10        50          7.786

21.1     70          7.492

32.2      90         7.219

If the outside air and the grain are the same temp, the air in the bin and air outside will have the same weight and there will be no pressure difference and therefore no convection current through the bin.   But let’s say that the grain is at room temperature of 21.1ºC , 70ºF, and the outside air is at 10º C.  That is quite a difference in temperature and also a difference in weight, 7.786 – 7.492 = 0.294 pounds per cubic feet.  But the grain in the bin is 20 feet high, so 20 x 0.294 = 5.88.  A column of air, 20 feet tall,  inside the bin weighs 5.88 lbs more than a corresponding 20 foot column of air outside. But 60% of this column is occupied by grain, and only 40% is air; so this column of air is only 2.35 lbs heavier.  But that is the pressure exerted over one square foot, psi or pounds per square inch is a more common unit of measure for pressure. 2.35/144 = .016 psi  This isn’t very much pressure, when you think of our car tires have 30 psi.   Another common pressure unit is inches of water.  How many inches of water would this pressure support? One psi would support a column of water 27.68 inches.  0.016 psi is equivalent to 0.452 “H20.

To determine the flow, one must have some appreciation for the grain resistance. From our past trials we saw that 3000 CFM required a pressure that would support 6 inches of water. Now if we said that pressure and flow were in a linear relationship, (it is not –it is closer to a squared),  the convection current would be about one thirteenth or 226 CFM.  This is a reasonable flow.  The bin we had was about 200 sq feet. so a flow of 226 CFM would be a vertical speed of 1 ft per second or about 1 kmph; but then again one must remember that this is only for a very significant temperature spread; as the temperature of the grain and the outside temperature become less, so too would there be a reduction in the convection current.

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