# 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.

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

• 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$$, and relative roughness $$\frac{\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$$. #### Reynolds Number$$ \frac{VD}{v} 

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 $$1.217 * 10^{-5} \frac{ft^2}{s}$$.

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 $$Q = \frac{V}{A}$$ and to keep units in check. 