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 formula

\(\large{ r_h =  \frac  {  A_c }  { P_w }   }\) 

Where:

 Units English Metric
\(\large{ r_h }\) = hydraulic radius \(\large{ ft }\) \(\large{ m }\)
\(\large{ A_c }\) = area cross-section of flow \(\large{ ft^2 }\) \(\large{ m^2 }\)
\(\large{ P_w }\) = wetting perimeter \(\large{ ft }\) \(\large{ m }\)

 

Related Hydraulic Radius formulas

\(\large{ r_h = \frac{1}{m} \; \left(  \frac{v}{C}  \right)^2  }\)  (Chezy Formula
\(\large{ r_h = \left(    \frac{ v \; n }{ 1.49 \; S^{\frac{1}{2}} }   \right)^{ \frac{1}{0.66}    }       }\) (Manning's Roughness Coefficient)
\(\large{ r_h = \left( C \; n \right)^6  }\)  (Roughness Coefficient)

Where:

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

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

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

 

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Tags: Pipe Equations Hydraulic Equations