Hydraulic Radius

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

hydraulic wettedhydraulic wetted pipeHydraulic radius, abbreviated as \(r_h\), is the area cross-section of water in a pipe or channel divided by the wetting perimeter.

 

Hydraulic Radius formulas

\(\large{ r_h =  \frac  {  A_c }  { P_w }   }\)   
\(\large{ r_h = \left( C \; n \right)^6  }\)  (roughness coefficient)
\(\large{ r_h = \frac{1}{m} \; \left(  \frac{v}{C}  \right)^2  }\)  (Chezy formula
\(\large{ r_h =  \left(   \frac{v\; n}{1.49 \; S^{0.5} }   \right)^{\frac{1}{0.66}}   }\) (Manning equation)

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ A_c }\) = area cross-section of flow

\(\large{ C }\) = Chezy coefficient

\(\large{ n }\) = Manning's roughness coefficient

\(\large{ n }\) = roughness coefficient

\(\large{ m }\) = slope

\(\large{ S }\) = channel slope or energy slope line

\(\large{ k }\) = unit conversion factor (\(k = 1.49\) English units ft/sec) (\(k = 1.0\) SI units m/sec)

\(\large{ v }\) = velocity of flow in a channel, culvert, or pipe

\(\large{ P_w }\) = wetted perimeter

 

Tags: Equations for Pipe Equations for Hydraulic