# Hazen-Williams Equation

on . Posted in Fluid Dynamics

Hazen-Williams equation is an empirical formula used in civil engineering and fluid dynamics to calculate the flow rate of water in a pressurized pipe or conduit.  It is commonly employed to estimate the flow of water through pipes for various applications, such as water distribution systems, municipal water supply, and plumbing design.  It's important to note that the Hazen-Williams equation is primarily used for water flow calculations in relatively simple systems where the flow is pressurized and steady.  It is less accurate for situations with turbulent flow or non-water fluids.  For such cases, more complex equations like the Darcy-Weisbach equation or computational fluid dynamics simulations are often used.

### Hazen-Williams Equation

$$v = k \; C \; r_h^{0.63} \; S^ {0.54}$$     (Hazen-Williams Equation)

$$C = v \;/\; k \; r_h^{0.63} \; S^ {0.54}$$

$$r_h = \left( v \;/\; k \; C \; S^{0.54} \right)^{ \frac{1}{0.63} }$$

$$S = \left( v\;/\; k \; C \; r_h^{0.63} \right)^{ \frac{1}{0.54} }$$

### Solve for v

 conversion factor, k roughness coefficient, C hydraulic radius, rh slope of energy grade line, S

### Solve for C

 flow velocity, v conversion factor, k hydraulic radius, rh slope of energy grade line, S

### Solve for rh

 flow velocity, v conversion factor, k roughness coefficient, C slope of energy grade line, S

### Solve for S

 flow velocity, v conversion factor, k roughness coefficient, C hydraulic radius, rh

Symbol English Metric
$$v$$ = mean flow velocity (flow rate) $$ft\;/\;sec$$ $$m\;/\;s$$
$$k$$ = conversion factor (1.318 English units) (0.849 Metric units) $$dimensionless$$ $$dimensionless$$
$$C$$ = Hazen-Williams roughness coefficient $$dimensionless$$ $$dimensionless$$
$$r_h$$ = hydraulic radius $$in$$ $$mm$$
$$S$$ = slope of energy grade line (head loss per unit of pipe $$\frac{h_l}{l}$$) $$ft$$ $$m$$