How do speed and density change in a turbulent flow?

Velocity;
In the case of pipe flow, the velocity remains constant simply through continuity, and the losses are influencing only to pressure. In the open channel flow the velocity depends on up- and downstream conditions, and can therefore even be higher after the object, but also lower if the object causes a hydraulic jump.

Density;
In the pipe flow the density is influenced only through the thermal expansion caused by the pressure turning to heat. In the open channel flow the density can change quite a lot if air entrainment occurs. The Turbulence has only indirect influence to density.