# Moody Diagram

## moody_diagram.jpg

The Moody diagram enables the pressure loss in straight sections of pipe to be determined.  Pressure losses associated with elbows, tees, valves, etc. are determined using methods discussed on the following pages.

By Traroth (Own work) [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

The Moody diagram is a plot of the Darcy friction factor as a function of Reynolds number and relative roughness. The Moody diagram shows both the laminar and turbulent regimes as well as a transition zone between laminar and turbulent flow. The turbulent flow region of the plot is based on the Colebrook equation discussed on the previous page.

The determination of the Darcy friction factor using the Moody diagram requires several pieces of information.  First, the Reynolds number based on the diameter of the pipe, kinematic viscosity, and average velocity must be known.

Second, the relative roughness must be determined.  The relative roughness is the ratio of the asperities height on the pipe wall to the diameter of the pipe.  The asperities could be measured, but generally aren’t.  Handbook values for specific types of pipe are used.

The horizontal axis of a Moody diagram contains the Reynolds number and the vertical axis is a plot of the friction factor.  The Reynolds number is first located on the horizontal axis.  Next, the Reynolds number is followed vertically to the desired relative roughness value.  The friction factor is then read off of the vertical axis.  Note that the pressure drop in can be computed once the friction factor is known.  If the flow is laminar, the friction factor does not depend on the relative roughness and a single straight line is used to determine the friction factor.

## Example

Determine the friction factor for a 50 mm inside diameter drawn tube having a Reynolds number of 100,000.  The asperities determined to have a height of 0.0025mm.  The relative roughness (ε/d) is computed to be 5x10-5.  A friction factor of 0.018 is read from the Moody diagram.  Now that the relative roughness is known, the pressure drop can be computed.

## Learning Objectives

Learn how the Darcy friction factor is determined using the Moody Diagram.