Closed Conduit Hydraulics - Darcy-Weisbach Equation

The Darcy-Weisbach equation is used to determine flow characteristics in closed conduit systems (pipes). It is probably more common than the Hazen-Williams equation due to it being able to solve for systems in both laminar AND turbulent flow.

 h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}

  • headloss h_f (ft)
  • friction factor f, length L
  • length L (ft)
  • diameter D (ft)
  • velocity V \frac{ft}{s}
  • gravity g 32.2 \frac{ft}{s^2}

Friction Factor

The friction factor f is either given or must be calculated using a Moody-Stanton diagram (available in both the AIO and CERM). Getting the friction factor from a Moody-Stanton chart requires the Reynolds Number Re, and relative roughness \dfrac{\epsilon}{D}.

Relative Roughness

The absolute roughness \epsilon is usually given by what material the pipe is made of (e.g. cast iron, concrete, streel) and requires a table look up. The relative roughness is this table value divided by the diamater D.

Reynolds Number


Where V is the velocity of the fluid, D is the diameter, and v is the kinamatic viscosity of the fluid. The standard kinematic viscosity to use is 1.217 * 10^{-5} \dfrac{ft^2}{s}.

Find the line that corresponds to the relative roughness and follow it to where it lines up with the Reynold Number. The friction factor f is directly horizontal from that point. Practice looking these things up the Moody-Stanton graph will become your fast friend!

Remember Q = \dfrac{V}{A} and to keep units in check.


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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