Hazen-Williams Hydraulic Radius Equation

This hydraulic radius formula is used in Hazen-Williams equations and the coefficient formula.

 

Hazen-Williams Hydraulic Radius Equation formula

\(\large{ r_h = \left(   \frac {v}{ 1.318\;C\;   m^{0.54} } \right)^{\frac {1}{0.63} }  }\)

Where:

Units	English	Metric
\(\large{ r_h }\) = hydraulic radius	\(\large{in}\)	\(\large{mm}\)
\(\large{ C }\) = Hazen-Williams coefficient	\(\large{dimensionless}\)
\(\large{ m }\) = hydraulic grade line slope	\(\large{ft}\)	\(\large{m}\)
\(\large{ v }\) = mean flow velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)

Solve For:

\(\large{ C =  \frac{ v }{ 1.318 \; C \;  r_h^{0.63} \; m^{0.54} }   }\)
\(\large{ m =  \left(  \frac{ v }{ 1.318 \; C \;  r_h^{0.63}  }  \right)^{ \frac{1}{0.54} }  }\)
\(\large{ v = 1.318 \; C \;  r_h^{0.63} \; m^ {0.54}   }\)