Dear Y. Choi, I fully agree ...
Published by Bruno Peeters, managing director at Model Engineering
Dear Y. Choi,
I fully agree with the reply of Katalin Kiss and Peter Styles. We successfully apply Coolebrook-White in our hydraulic designs and simulations since almost 30 years now. When a sewer would be full of water with submerged in- and outlets then the slope of the sewer does not matter but only the difference in static head (in/out) and of course the sewer size, wall roughness and discrete losses at junctions, traps, ... In such cases gravity flow velocities in straight new HDPE or PP pipes may well exceed 3 m/s.
When a sewer or channel is not full and its outlet is free, then the flow is largely driven by the bottom slope (assuming no discontinuities). When this slope would be too steep, then the top layers of the water will "shoot" over the lower layers resulting in friction and turbulence with additional losses limiting the bulk liquid velocity. Using normal slopes we size for 1 - 2 m/s velocity at 100% design flow.
By the way, there is no 9.8 m/s or other velocity limit if there would be no friction (vacuum, zero wall losses). The velocity of a rain droplet is only limited by its friction in the air.