Bernoulli Principle Question

Bernoulli Principle Question

As I am sure most of my readers know, the Bernoulli Principle explains that if you constrict the flow of a fluid or gas, the speed of fluid or gas increases. There's a mass of equations here that explains how to apply it to incompressible and compressible masses. What I am trying to figure out--and I suspect one of my readers knows the answer--is what formula determines the velocity increase of air at low speeds (5-20 mph) as you constrict the input. For example, if you had a pipe that was one meter wide at the opening, and .5 meters wide at the exit, what happens to the speed of air as it goes through the pipe? It goes up, but how much?

Obviously, a rough inner surface will introduce turbulence, reducing velocity compared to a smooth inner surface. A pipe that shrinks down rapidly, I'm guessing, will introduce more turbulence than a pipe with a more gradual reduction.