This would be a tough problem to calculate, because the material that makes up the nozzles is flexible and will expand under pressure. I would advise looking at the models that have been done for blood flow through arteries and veins. There is quite a bit of research available on that subject and it may be possible to adapt those codes for the problem you describe.

I've heard this thesis about the elasticity already. However, these structures do not look like very elastic; they contain much of the collagen fibers which almost not expandable. So, the calculations would make a real revolution in terms of understanding some processes pathogenesis! For example, the lower portion of the common bile duct is referred to as 'a high pressure zone' due to a putative sphincter mechanism. On the other hand, the shape of this portion may contribute much to the local pressure elevation, etc.

Another example of possible hydrodynamics's influence, is various diseases of the gallbladder (Will you see the link below).

One more example is the hernia strangulation mechanism (Another link). The hernial opening profile resembles much that of the Laval nozzle.

At any rate, thank you for the post. Would you kindly give me a hint on the models on blood flow, please?

https://www.researchgate.net/post/What_are_the_current_views_on_Richters_hernia

Article Giant Gallbladder: a Case Report and Review of Literature

The research project I am personally aware of in this field was in the Amsterdam Academic Hospital. See for example:

http://classic.physrev.physiology.org/content/70/2/331.abstract

However, there are similar projects in other institutes. See also the discussion at:

https://www.researchgate.net/post/What_boundary_conditions_should_we_use_when_modeling_blood_flow_in_coronary_arteries

I was only briefly involved, because I studied physics in Amsterdam at the time and had to do some work at the medical physics institute as part of my undergrad studies.

Thank you again! Shall be reading at once!

Studies on the biliary ducts and the gallbladder biomechanics (or, at least, related to) are scarce indeed. What I know of is as follows:

1) Walsh T.H., Akoglu T. The muscle content and contractile capability of the common bile duct .  Ann R Coll Surg Engl. 1979; 61(3):206-209;

2) Die Biokonstruktion der extrahepatische Gallenwege des Menschen / R.Henning, D.Steiner, W.Lierse, G.Weinland, P.Matthaes // Aktuel. Chir. – 1988. - Bd.23. – S.74-8

3) Gallensaure-unabhangige Wirkung von Hymecromon auf die Gallesekretion und die Motilität der Gallenwege / R.M.Hoffmann, G.Schwarz, C.Pohl, D.J.Ziegenhagen, W.Kruis // Dtsch. Med. Wochenschr. – 2005. – Bd.130, H.34-35. – S.1938-43