Help with entrance effects for fluid please

Entrance effects are very important.
http://en.wikipedia.org/wiki/Vena_contracta
google images 'vena contracta'

 

The fluid moves as a radial flow towards the pipe entrance. As it enters the pipe it is still accelerating and still has radial velocity. That causes the entrance separation and the vena contracta which together represent a pressure loss and an obstruction to flow like an orifice. If a tapered horn like a trumpet is mounted at the pipe entrance then the flow can be better regulated and the vena contracta avoided.