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Engineering: CSA vs. Equivalent Diameter

Posts: 112
Location: Groton, CT
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After reading through a lot of material on Rocket stoves and RMH's, I have seen a common problem with the engineering of these devices: Using Cross-sectional area as the only factor in flow calculations. I hope that this quick explanation can shed some light on why, sometimes, RMH's don't draft as well as you think they should.

Cross sectional area (CSA): The assumption is that any channel, round, oval or rectangular, with the same CSA will flow the same. This is simply not true. If the channel is square it is close, but imagine if you will an extremely pinched rectangular channel, say 100" by 0.28". This channel will have a CSA of 28 square inches, the same as a 6" round duct. But will it flow the same? Not even close. Here is the appropriate formula:

From Engineering Toolbox (http://www.engineeringtoolbox.com/equivalent-diameter-d_205.html):

de = 1.30 x ((a x b)^0.625 / (a + b)^0.25) (1)


de = equivalent diameter (mm, inches)

a = length of major or minor side (mm, inches)

b = length of minor or major side (mm, inches)

Example 1: You want to join a square riser to a round chimney. The chimney is 6" diameter, or 28.27 square inches. An equivalent CSA square channel has sides at 5.32 inches. From the formula above:
de = 1.30 x ((5.32 x 5.32)^0.625 / (5.32 + 5.32)^0.25) = 1.30 x 8.08 / 1.80 = 5.84.

So, for this example, something with an equivilant CSA to a tube has an Equivilant diameter of 5.84", and an equivalent CSA of 26.80 square inches, more than a 5% reduction in flow.

Example 2 (more common): You want to join a rectangular riser to a round exhaust tube. The exhaust is 6" diameter, again 28.27 square inches. Using firebrick for your riser, you decide to go with a rectagle 7.1 x 4", which has a CSA slightly more than the exhaust at 28.4 square inches. By the formula again:
de = 1.30 x ((7.1 x 4)^0.625 / (7.1 + 4)^0.25) = 1.30 x 8.10 / 1.83 = 5.75.

So, even though you thought you were being conservative by using a slightly larger CSA, your Equivalent Diameter is a quarter inch less, and equivilant CSA is 26", a full 8% drop in flow.

Run the numbers for my initial sort-of-rediculous 100 x .28" channel and you get a de of 3.32", equivalent CSA of 8.66", a massive 70% drop in flow.

So what does this mean for my RMH design? Simply enough, if you are going to use a rectagular section, which most people do:

1) Select your exhaust diameter
2) Select the height of your feed tube based on the height of your brick. (common brick is 3" tall, so 2 stacked with mortar is going to be about 6")
3) Don't try to use the fomula to solve for b... It is difficult. Instead use the tables or provided calculator on the above website.
4) In this case, the number is fairly easy. A 6" x 5" chamber will give you an Equivalent Diameter of 6".
5) Do your best to eliminate restrictions elsewhere in the system.

Other parts of the RMH system could also use some hard engineering, but I will leave that for a later topic. Things to keep in mind for the future:
1) Calculate the pressure drop across the RMH system (pretty tough to accomplish)
2) Calculate the Equivalent Diameter of a tube bend (formulas exist for this also, although it is generally difficult to find odd-sized tubing or even join said tubing to your standard ductwork, so it is probably pointless)
3) Calculate the ideal flow rate through the system to maximize heat transfer (a very tough problem, but it happens to be my specialty)

For now, however, I would recommend building the RMH with the J-tube sections sized to maintain continuous Equivalent Diameter vice CSA, I would also recommend using a slightly oversized exhaust (say, 7" instead of 6", to minimize pressure drop over the exhaust), and I would recommend building a little bit of adjustability into the height of the barrel.

Hope this information helps!
Posts: 69
Location: Susquehanna, PA
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Wow Dave if you only knew how I could have used that knowledge 2-3 months ago. lol
I digress. These calculations should be of some good use in the future though. I must admit, I prefer the sound of maintaining CSA as opposed to having steady ED.
lol Lord, forgive me for that there, Im sorry.
Good stuff. I look forward to seeing who chooses to discuss this thoroughly instead of humorously.
Posts: 57
Location: Eastern edge of the Blue Ridge Mnts. Virginia
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Thanks for the great information Dave! I think they should Pin this thread to the top though. Reading through post after post and thread after thread I see the same problem... lack of exhaust area and too much resistance in the initial exhaust and piping in the mass area. You have saved me a ton of work! Chris
Posts: 91
Location: Spokane, Washington
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I agree with Martin and Chris... pin this thread at the top.

Dave: I too think that any ED past the burn point should be larger than all previous comparable critical dimensions in the system. This is going to help ensure proper draft and promote flow through the mass. --if I am accurately grokking your jist

As far as hacking at certain design improvement possibilities... wouldn't the elimination of many of the right angles and 90 degree flow collisions help promote proper draft? What about air induction at the burn point (similar to a p-channel) to induce a cyclonic flow up a tapered heat riser? Reduction angles? 30 degrees in, 5 degrees out? Hemispherical bottoms on the feed and the riser? Offset riser in the barrel to help collect gases rather than collide?

There are so many points of interest... it's hard to know which to tackle first.
Posts: 51
Location: Middle of Germany
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Hi Dave,

thanks a lot. But what about thermal expansion and other factors of the air changing temperature on the way through the RMH?
Just have a look at: http://www.engineeringtoolbox.com/air-properties-d_156.html
And than remember that in the RMH's the temperature is much more higher than only 400°C.

Posts: 4154
Location: Northern New York Zone4-5 the OUTER 'RONDACs percip 36''
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Bump ! big AL
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