Venturi Principle: Is p1=p3 and v1=v3?

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    Principle Venturi
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Discussion Overview

The discussion revolves around the Venturi Principle, specifically questioning whether the pressures (p1 and p3) and velocities (v1 and v3) at two points in a fluid flow are equal under certain conditions. The scope includes theoretical considerations related to fluid dynamics and the implications of viscosity and cross-sectional area on flow characteristics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that if viscosity is negligible, then p1 equals p3 and v1 equals v3.
  • Another participant agrees that if the cross-sectional areas are the same and the flow is inviscid, then p1 equals p3 and v1 equals v3, but notes uncertainty regarding whether A1 equals A3.
  • A further contribution reiterates that under the same conditions (inviscid flow and equal cross-sectional areas), the flow characteristics at section 3 cannot be definitively determined, suggesting that the flow could behave differently if the diameter at section 3 is not the same as at section 1.
  • This participant emphasizes that the average net flow velocity at section 3 should match v1 if mass flow is constant, assuming equal diameters.

Areas of Agreement / Disagreement

Participants express varying views on the conditions under which p1 equals p3 and v1 equals v3, with some agreeing on specific conditions while others highlight uncertainties and alternative scenarios. The discussion remains unresolved regarding the implications of cross-sectional area and flow behavior.

Contextual Notes

There are limitations regarding assumptions about viscosity, cross-sectional areas, and the nature of the flow (inviscid vs. viscous) that are not fully explored or defined in the discussion.

fonz
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venturi3.gif


Just simply, from the diagram above is p1=p3 and v1=v3?

Thanks
Dan
 
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If the viscosity is negligible, then yes.
 
If the cross sectional areas are the same and the flow is inviscid, then yes. From the diagram, it isn't certain that A1 = A3 though.
 
cjl said:
If the cross sectional areas are the same and the flow is inviscid, then yes.
If the flow is inviscid, then the inner flow at section 3 can't be determined. With zero viscosity, there's no reason that the flow from section 2 couldn't simply continue with the same diameter as the tube in section 2, flowing at v2 while the surrounding fluid in section 3 isn't moving at all, since there's no interaction between shear boundaries with an inviscid flow. The "average" net flow v3 should be the same as v1 since mass flow is constant, assuming section 3 diameter is the same as section 1 diameter.
 

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