Hazen-Williams Hydraulic Grade Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

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

 

Hazen-Williams Hydraulic Grade Equation formulas

\(\large{ m =   \left(     \frac {v} { 1.318\;C \;  r_h^{0.63} } \right)   ^{\frac {1}{0.54} }  }\)   
\(\large{ m =   \left(     \frac {Q} { 0.285\;C  \;   d^{2.63} } \right)   ^{\frac {1}{0.54} }  }\)   

Where:

 Units English Metric
\(\large{ m }\) = hydraulic grade line slope \(\large{ft}\)  \(\large{m}\) 
\(\large{ Q }\) = flow rate \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\)
\(\large{ C }\) = Hazen-Williams coefficient \(\large{dimensionless}\)
\(\large{ r_h }\) = hydraulic radius \(\large{in}\) \(\large{mm}\)
\(\large{ d }\) = inside diameter of pipe \(\large{in}\) \(\large{mm}\)
\(\large{ v }\) = mean flow velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)

Solve For:

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

 

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Tags: Equations for Hydraulic Equations for Open Channel Equations for Hazen-Williams