At the Class 4 level, slope and velocity aren't just concepts to recognize — you need to be able to design and verify them using the same equation the standards themselves are built on: Manning's equation.
Full Hydraulic Design: Manning's Equation
In U.S. customary units, for a pipe flowing full:
V=n1.49R2/3S1/2 Where:
- V = mean velocity (ft/s)
- n = Manning's roughness coefficient (dimensionless — a property of the pipe's interior surface)
- R = hydraulic radius (ft) = cross-sectional flow area ÷ wetted perimeter
- S = slope of the pipe (ft/ft, i.e., the "grade" expressed as a decimal)
For a circular pipe flowing completely full, the hydraulic radius simplifies to R=D/4, where D is the pipe diameter in feet (since area = πD2/4 and wetted perimeter = πD when full). Regulatory design practice — including the Ten States Standards —