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.