Free jet decay

It is not clear to me why you would "hestitate to use the available models ... because of the large dimensions (of this particular item)". In fact, with relatively large dimensions, you will have a relatively high Reynolds number, and the notion of a "core" velocity should be most accurate.

If you can determine (from a fluid textbook) the velocity profile for pipe flow for the Reynolds number at the venturi exit, it will be a very good approximation to assume that the velocity profile remains "intact" for the range of 1 - 1.67 diameters downstream.

If it is very important to know this velocity, you could make a few measurements (or hire someone to do so).

The "near field" analytical solutions of free shear flows are difficult in general. Be mindful that the assertion of a "core where the velocity does not decrease" is a convenient way to skip the near field considerations, and begin the "far field" analysis with a known momentum flux, and a "plug type" velocity profile. This permits a closed-form solution which will be sufficiently accurate for the far field (> 10 diameters downstream). This expedient works even for rather low Reynolds number flows, where there would be some dissipation - even in the near field.