Closed Conduit Hydraulics – Hazen Williams Equation

Hazen-Williams can be used to determine the flow characteristics in closed conduits (pipe systems).

For Velocity

$$ V = 1.318CR^{0.63}S^{0.54} \text{    (US)}$$

$$ V = 0.849CR^{0.63}S^{0.54} \text{   (SI)}$$

S = slope, in decimal form. This is equivalent to \( h_f/L\)

R = hydraulic radius, \(\text{(Area of flow)}/\text{(wetted perimeter)}\)

C = Roughness Coefficient, get this from a table (available in both the AIO and CERM)

For Head Loss

To derive these \( h_f/L\) has been substituted for S.

$$ h_f = \frac{0.6V^{1.85}L}{C^{1.85}R^{1.165}} \text{     (US, ft and ft/s)}$$

$$  h_f = \frac{1.35V^{1.85}L}{C^{1.85}R^{1.165}} \text{     (SI, m and m/s)}$$

The Hazen-Williams equation is similar to the Darcy-Weisbach equation, but it is only used for turbulent flow.

When to use Hazen-Williams

1. You are only given C
2. You prefer it and are sure the flow is turbulent (Reynolds number (Re) > 4000)
3. You are directly told to (from the examples it looks like several problem prompts do this)

When to NOT use Hazen-Williams

1. The flow is NOT turbulent (Re < 2100)
2. You are given \(f\). If you are given a friction factor use Darcy-Weisbach