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:

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