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

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

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

Symbol 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 $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$