Equalizing airflow through multi-hole orifices

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Discussion Overview

The discussion revolves around the behavior of airflow through multi-hole orifices compared to a single orifice with the same total area, particularly in the context of a 3D printed siren whistle designed to produce different tones based on airflow dynamics. The focus includes theoretical considerations, practical observations, and the influence of design factors such as the number of blades on the turbine.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes the application of the Bernoulli equation but questions whether multiple holes with the same total area behave the same as a single hole of that area.
  • Another participant argues that flow should not be the same due to friction, highlighting that a higher perimeter-to-area ratio in multiple holes could increase friction, affecting flow rates.
  • A participant observes that the actual performance contradicts expectations, suggesting that the number of blades on the turbine may have a more significant impact on airflow than the surface area of the holes.
  • One reply proposes that a constant flow may lead to a greater pressure drop on the side with more holes, potentially explaining the observed higher velocity on that side.

Areas of Agreement / Disagreement

Participants express differing views on the airflow behavior through multiple versus single holes, with no consensus reached on the primary factors influencing the observed performance differences.

Contextual Notes

Participants note the potential influence of friction and pressure drop, but the specific impact of these factors remains unresolved and dependent on the particular design and operating conditions of the turbine.

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TL;DR
One pressure vessel has 6 holes from which air escapes, another has 8 holes, total open area of the holes is same on each vessel. Should the volume flow be the same?
I know the Bernoulli equation for calculating the air velocity through a pressurized hole, but I am wondering if one hole of a given area behaves the same as multiple holes with the same total area. The Bernoulli equation doesn't make a distinction.

Background: As a personal 3D design and printing project I designed a siren whistle patterned after a Francis turbine, in which a dual runner (two runners back to back) chops the air coming out of exit holes on each side. The number of blades on each side of the runner is different (6 and 8) with a corresponding number of exit holes. As the runner rotates, the turbine produces two tones, with the airflow interrupted 6 times per rotation on one side, and 8 times per rotation on the other. The holes on each side have the same total open area.

The device works pretty well, but if I cover the holes on one side or the other, to allow only one side of the runner to drive its rotation, the rotation speed is clearly different for the same input pressure (by my best guess by breathing into it). It's slower when air exits only the 6-hole side.

That made me wonder if several small holes behave differently than fewer holes with the same open area.

Hmm, as I write this, I realize the difference could also be due to the different number of blades. The side with the higher number has a higher surface area on which the air can impart force.
 
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To your summary question:

No - the flow shouldn't be the same. One of the factors controlling the flow is friction. The implementation with more holes has a higher 'perimeter/area' ratio. More 'perimeter' results in more friction. How much actual difference that makes depends on how large a factor friction is in your specific case - higher velocities result in more significant friction terms.
 
That's what I thought. However, the effect I observe is the opposite of what would be expected (higher rotation when exhausting through the 8 hole side instead of the 6 hole side) so maybe the runner blade area is having a greater effect, which may be mitigated only slightly by the greater surface area of the holes.
 
If you drive the turbine with a constant flow, then it may have greater pressure drop with the 8 hole side, which may explain the higher velocity.
 

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