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

h_f = \dfrac{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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