# 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.

• 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.