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Effect of short constriction on air flow?

Tanner C | Posted in General Questions on

I’ve arrived at this question in designing my roof venting system (explanation in comments), but the heart of it is a physics problem which I have not been able to answer. I’m guessing someone who does HVAC calculations may know.

How is total airflow (in CFM or comparable) in a system affected by a short constriction? 
Example: air in a 2 inch square duct passes through a short 1 inch square coupler before returning to 2 inch. Say the length of the coupling Is small relative to the length of the run (1/100th or smaller)

For a given inlet pressure (same fan?) Is the total airflow in the system the same as if it were all 1 inch square? Alternatively, is it just that the 1in coupling adds some resistance to the system and the size of the duct on either side is still relevant? How might I calculate this? I have read through the energy vanguard duct sizing articles but maybe I missed something.

Thanks!

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Replies

  1. Expert Member
    Dana Dorsett | | #1

    This problem isn't well suited to napkin-math calculations. Are you up for taking a fluid dynamic course? :-)

    The velocity of the short stub is higher, resulting on more duct impedance, that could be represented as an "equivalent length" of larger duct. If the size transition is abrupt rather than conical the "equivalent length". Whether anybody has an easy to use table or online calculator for estimating this stuff is unknown to me.

  2. Tanner C | | #2

    So the origin of the question: I was initially planning on having a 1 in roof vent channel (vaulted ceiling) fed directly by a 3/8" rainscreen gap. For my tiny house's tiny roof that 3/8 in gap is actually more than sufficient by the 1:150 rule. Then recently I found the Lstiburek roof venting rule suggesting that ridge vent area be greater than eave vent area to avoid depressurizing the attic/vent channel and encouraging ceiling air leaks. As my ridge vent sheathing gap is about 1 1/4in I thought I could add an additional 3/8 in of air intake at the eaves for a total of 3/4 in each side. Then I realized my framers only left about 3/8 in between the rafter blocking and roof sheathing at the eaves. If I add additional venting will it have any effect or will that 3/8 in gap above the blocking dictate total airflow. I could always stop down the ridge vent to 3/4in so that it is at least balanced with the eave vents. Struggling to upload my drawing...

  3. Tanner C | | #3

    Thanks Dana, It is more complex than expected haha but very interesting. I have an undergrad level math and engineering background so was hoping if someone didn't have the answer they could point me to the right equations. I suspect Bernoulli's and Darcy Weisbach are involved. Or maybe an HVAC design software?

  4. Tanner C | | #4

    Drawing of proposed additional eave venting

  5. Expert Member
    Zephyr7 | | #5

    To “really” solve this problem is complex. Shape, temperature, length — all play a roll. You end up with an unsolveable differential equation because of viscosity, so you only ever get a very close approximation anyway since you have to drop one term.

    Most of the time, tables of “equivalent pipe” are used, so regular transition fittings are rated for their equivalent amount of extra feet of pipe. In your case, it looks like you’re trying to add enough extra vent area to compensate for the flow restriction of your assembly. It will be exceedingly difficult to do that with any accuracy.

    I’d allow maybe an extra 10% by area and call it good. It’s not a particularly critical application. Code for roof venting is by area and not pressure drop or flow rate so no one is going to check with a meter like they would on something like a natural gas pipe.

    Bill

  6. Tanner C | | #6

    Thanks Bill, so your feeling or past calculations suggest that to have a short restriction ( following the simplified example) of 1/2 the cross sectional area of the rest of the conduit would not halve the total flow but rather reduce it some smallish percentage?

    1. Expert Member
      Zephyr7 | | #7

      It will act like an orifice and limit maximum flow. There are similar “devices” (it seems odd to call a disc with a hole in it a “device”) in natural gas appliances to limit the max flow on purpose.

      Velocity will increase in the constricted area, and turbulence, among other things, will limit the the maximum flow at any given pressure. In water systems, I’d be worried about that high velocity flow eroding the pipe, but in passive systems like attic vents that’s not a concern.

      Is there any way to reduce the constriction though? 50% reduction in area is pretty severe. It won’t halve your flow, but it will most likely reduce it more than just a “tiny” percentage.

      Bill

  7. Expert Member
    Akos | | #8

    Tanner,

    One way to ballpark it is to convert the vent space cross section to equivalent round duct and use an HVAC enquivlent length table to compare (https://i1.wp.com/hvacrschool.com/wp-content/uploads/2017/05/img_7320.jpg?ssl=1) .

    Because of the low flow velocity, it won't be accurate, but you can get a feel of some of the effects.

    For a tiny house, I would focus more on getting an airtight ceiling than worrying about vent gaps. If your ceiling doesn't leak, even an "undervented" roof will work. No amount of venting can fix a leaky ceiling.

  8. Expert Member
    Malcolm Taylor | | #9

    Tanner,

    What stops you using a reciprocating saw to cut down the blocking and increase the size of the 3/8" gap?

  9. Tanner C | | #10

    Thanks again all!
    Akos, I will be spending lots of time trying to ensure an airtight ceiling and should be able to get away with only one penetration for the wood stove flue pipe.

    To clarify, even with just 3/8" at the eaves I'll have 3x the 1:150 vent area to roof deck "standard". My concern is more that as it stands I have nearly twice the open area at the ridge. I figure I could somehow stop down the opening at the ridge, or increase vent area at the eaves. If I stop down the ridge opening to 3/4in I will still have about 2:150 vent: roof deck area. On the other hand, adding an air inlet just below the fascia may have the added benefit of allowing some fresh air mixing in with that from the rain screen, a debated merit about which I don't have much of an opinion.

    Malcolm: My "fascia" board is on the wall sheathing and primarily fastened to the top plates, making it more of a "frieze" board I suppose. I have been considering your method but would have to remove my fascia or make the cuts from the inside. This is definitely doable but just a bit higher on the PITA scale.

    Photos attached for reference. Again, very grateful for all of your insights, this community has been invaluable for me throughout this build!

    1. Expert Member
      Malcolm Taylor | | #11

      Tanner,

      I didn't know you were that far along. I'd leave all enough alone. I wouldn't worry about the proportion of eave to ridge ventilation either. The situation isn't really analogous to the situation of most houses. The area of the roof, the distance from eave to ridge, and the volume of air we are talking about are all so much smaller. An imbalance in the two vents won't make any appreciable difference.

      Edit: Hey - your Tyvek is upside down!

  10. Tanner C | | #12

    Malcolm,

    Fair enough!

    The WRB has a higher coefficient of bipolarity in an anisotropic orientation, allowing for better attenuation of radiolarian radiation. But mostly it confuses the hell out of bugs that make it into my rainscreen.

  11. GBA Editor
    Martin Holladay | | #13

    Tanner,
    Akos had the best answer: "I would focus more on getting an airtight ceiling than worrying about vent gaps. If your ceiling doesn't leak, even an 'undervented' roof will work. No amount of venting can fix a leaky ceiling."

  12. Expert Member
    Zephyr7 | | #14

    If you’re not really worried about having so much extra ridge vent area, you could staple up some fiberglass window screen before installing the ridge vent. They window screen material will serve to partially reduce the area due to the extra material (the mesh) that will be “in the way” of the airflow.

    I agree with Martin though, your efforts are better spent making sure your ceiling is airtight and not worrying so much about the vent area in the attic.

    Bill

  13. Tom May | | #15

    Yes the airflow will be the same. Volume flow rate (CFM) Q = velocity x area. So if the opening gets smaller, the velocity will increase. You can't have a volume of air entering a location without the same volume of air exiting, otherwise you will build up pressure. But in an open system that can't happen. Look up venturi. And yes Bernoulli's principle also applies. But since the pressures are basically the same, atmospheric, and the height is basically negligible, you end up with pgh1 + 1/2 p v1^2 = pgh2 +1/2 p v2^2 which should result in a slight change in velocity.

  14. Jon R | | #16

    Resistance in series is additive.

    For more low intake area, you could use under shingle vents.

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