The original answer is incorrect (at least in the North American meaning of the term 'Hydraulically smooth'. Hydraulically smooth mean that the roughness on the wall of the pipe is less than 1/2 of the thickness of the viscous sublayer of the turbulent flow. The viscous sublayer is (well) less than 1% of the pipe diameter. The viscous sublayer thickness is calculated as:
t=5D*(8^0.5)/((f^0/5)*Re
where t is the thickness, D is the Diameter, f is the Darcy Friction Factor (found from the Moody Diagram or the Colebrook Equation, and Re is the Reynolds number, based upon pipe diameter and the average flow velocity in the pipe.
Re = u*D/v
u is average velocity
v is kinematic viscosity
As a last comment on the old response, it is in fact describing the critical flow rate for transition to turbulence (i.e. the flow rate for Re ~= 2300). The exact value for transition to turbulence is dicey to determine, and does, as the answer says, depend on the roughness and disturbances. Further, as the equation for Reynolds number shows, the transition to turbulence also depends on diameter. Laminar (not turbulent) flow is often called 'smooth', and the study of fluid motion is hydraulics, so it's easy to get the meaning of 'hydraulically smooth', mixed up with 'smooth (laminar) flow'
*****Old (incorrect) response*****
The flow rate inside a pipe that will produce laminar(No turbulence) flow. The physical smoothness plays a part but need not be as smooth as glass. A concrete, cast iron , copper and glass pipe can all produce laminar flow. The flow rate at which turbulence begins (no longer hydraulically smooth) will depend upon the surface texture where rougher surfaces will cause turbulence to occur at lower flow rates compared to a smoother material. Raise the flow rate enough and your will eventually get turbulence.
So to have hydraulically smooth pipes you would need to spec no only the material but diameter as well to ensure laminar flow up to the max expected flow rate. Also any turbulence inducing fittings would also be included. For example a bar grate in a storm water system could be installed such that hydraulically smooth flow is maintained for low flow rates. (The water ca easily pass around the bars). During the high flows a storm would produce the bar grate would cause a restriction and you would no longer have smooth flow.
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