# 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

## About Conrad

I am a Civil Engineer. I work in San Diego and am preparing to take the PE Exam. I am interested in surfing, business, travelling, and spending time with my wife. Thanks!

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