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

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SUMMARY

The discussion centers on the Venturi Principle, specifically addressing whether p1 equals p3 and v1 equals v3 in an inviscid flow scenario. It is established that if viscosity is negligible and the cross-sectional areas A1 and A3 are equal, then p1 equals p3 and v1 equals v3. However, if the cross-sectional areas differ, the flow characteristics at section 3 cannot be determined solely based on the information provided. The conclusion emphasizes that mass flow remains constant, leading to v3 being equal to v1 under specific conditions.

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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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