Moody's chart basis and uses

Description

Moody's chart is a graph of the Darcy-Weisbach friction factor $f$ against the Reynolds number $Re$ for flow in circular pipes, with a family of curves for different relative roughness $k/D$ (equivalent sand roughness / diameter). Both axes are logarithmic: $Re$ (from about $10^3$ to $10^8$) on the horizontal axis, $f$ (about 0.008 to 0.1) on the vertical axis, and the relative roughness is marked on the right-hand scale.

 f
 0.1 |\ laminar     critical     k/D curves
     | \  f=64/Re   zone    _________ 0.05
 0.05|  \          |      __/   ______ 0.01
     |   \_        |  ___/ ___/ ______ 0.001
 0.02|     \______ |_/ ___/   _______  0.0001
     |  smooth pipe curve ___/  (rough: flat lines)
 0.01|                   transition|  fully rough
     +--------------------------------- Re (log)
     10^3   10^4    10^5   10^6    10^7

Regions of the chart:

Basis of the chart

1. Laminar flow: Hagen-Poiseuille law gives $f = 64/Re$.
2. Smooth pipes: Blasius ($f = 0.316/Re^{0.25}$, $Re < 10^5$) and Prandtl's universal law $\dfrac{1}{\sqrt f} = 2\log_{10}(Re\sqrt f) - 0.8$.
3. Rough pipes: von Karman-Prandtl law from Nikuradse's sand-roughened pipe experiments, $\dfrac{1}{\sqrt f} = 2\log_{10}\dfrac{D}{k} + 1.14$.
4. Transition region: the Colebrook-White equation, which joins the smooth and rough laws:

$$\frac{1}{\sqrt f} = -2\log_{10}\left(\frac{k/D}{3.7} + \frac{2.51}{Re\sqrt f}\right)$$

Moody plotted this equation using the equivalent roughness of commercial pipes (Nikuradse's artificial roughness corrected to commercial pipe behaviour).

Uses

• To find $f$ for a given $Re$ and $k/D$, then the head loss $h_f = \dfrac{fLV^2}{2gD}$.
• To identify the flow regime (laminar, smooth, transition, rough) of a pipe.
• To solve the three types of pipe problems (find $h_f$, find $Q$, find $D$), by iteration.
• To get the equivalent roughness $k$ of an old or commercial pipe from test data.
• To compare materials and judge how much capacity is lost as a pipe ages and becomes rough.