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

[fonz]

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

Thanks
Dan

 

[MrRobotoToo]

If the viscosity is negligible, then yes.

 

[cjl]

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.

 

[rcgldr]

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.

 

[pmacias]

According to the Venturi Principle, the pressure and velocity at points 1 and 3 are not necessarily equal. The principle states that as the velocity of a fluid increases, the pressure decreases. Therefore, at point 1 where the fluid is moving faster, the pressure will be lower compared to point 3 where the fluid is moving slower. Similarly, the volumes at points 1 and 3 may also not be equal, as the volume of a fluid can change with changes in pressure. However, the principle does state that the total energy at both points should be equal, meaning that the sum of the kinetic and potential energies should be the same.