I understand that the volumetric flow either side of a venturi tube is the same - that makes total sense to me. However, what I'm interested in finding out is how to calculate the difference in flow rate vs the total potential flow without said tube section. Here's a rough diagram explaining things:

enter image description here

So, in the bottom system the venturi effect tells us that v2 equals v3. However, assuming all other variables are the same between the two systems, my assumption is that v1 does not equal v2/v3 - the constriction of the pipe will cause some loss of volumetric flow vs the larger one. Firstly, is this assumption correct?

Secondly, is there a formula or theory for calculating/explaining this? Of course the exact dimensions will mean the flow loss will vary - in particular the throat diameter and length, as well as the angles of the converging and diverging cones. But it doesn't seem to be covered by the venturi effect per se.


1 Answer 1


Assuming the fluid is viscous (which is a very reasonable assumption), then you are correct in your assumption that the restriction will reduce the overall flow rate the tube can accommodate (all else equal).

The typical explanation of the Venturi effect is a simplified analysis that only applies to incompressible, inviscid fluids along a streamline.

When you include viscosity, the restriction of the pipe would create friction loss, where the fluid loses energy due to interactions between the fluid and the walls. There are many empirical ways to approximate how much friction loss is expected based on pipe roughness, flow velocities, pipe sizes, fluid, and any flow restrictions such as orifices or elbows.

The one I can recall using is the Darcy–Weisbach equation which would allow you to determine the expected head loss (and therefore affect on flow rate) that would be introduced by adding a Venturi tube compared to not having one.

  • $\begingroup$ Another possible effect is losing a 1D flow caracter (= turbulence) that serves as an "obstacle" to a laminar flow. $\endgroup$ Commented Sep 17, 2019 at 17:35
  • $\begingroup$ Thank you for the answer, this is exactly what I was looking for. $\endgroup$
    – stooshie45
    Commented Sep 18, 2019 at 7:40

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