# Is there a calculation for flow loss through a venturi tube vs a full bore?

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: 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.