Moody Chart Calculator

What is a Moody Chart

moody chart

A Moody Chart (or Moody Diagram) is a diagram used in the calculation of pressure drop or head loss due to friction in pipe flow. More specifically, a Moody diagram is used to find the friction factor for flow in a pipe.

Friction factor is plotted vs. Reynolds number and relative roughness on a Moody chart. Relative roughness is defined as the pipe roughness height, ε, divided by the inside diameter, D. Reynolds number, Re, is the ratio of inertial fluid flow effects to viscous flow effects. Reynolds number greater than 4000 indicates turbulent flow, while Reynolds number less than approximately 2000 indicates laminar flow.

Once the Reynolds number and relative roughness are known, the friction factor can be found from the chart and used in the Darcy Weisbach equation for calculating the pressures loss due to friction.

The Darcy Weisbach equation is shown below:

darcy weisbach equation

where:

  • Δp = pressure loss [Pa]
  • L = the length of the pipe [m]
  • fD = Darcy friction factor (or Darcy Weisbach friction factor) [unitless]
  • ρ = fluid density [kg/m3]
  • v = mean fluid velocity [m/s]
  • D = pipe inside diameter (or hydraulic diameter for non-circular ducts) [m]

Moody Chart Calculator: How Does It Work?

The underlying equation that was used to create the Moody chart can be solved to obtain a numerical result for the Darcy friction factor.

Each of the curves on a Moody diagram represent the result of an equation that describes the Darcy friction factor as a function of the relative roughness and Reynolds number. This equation is called the Colebrook Equation. It was solved by Lewis Moody in the 1940’s and displayed graphically in what came to be known as the or Moody diagram.

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The Colebrook White equation is an equation that was created by fitting a function to experimental data. It is also an implicit equation that cannot be solved directly for the friction factor. The Moody diagram was a necessary tool for finding the friction factor at a time when there was not widespread use of graphing calculators or spreadsheets to solve the Colebrook equation.

In recent years, several alternative equations have been proposed that relate friction factor to relative roughness and diameter, such as the Haaland Equation and Swamee-Jain equation. These explicit approximations can be used to solve directly for f. The Moody chart calculator above uses the Haaland Equation.

How to Read a Moody Chart

The first step in reading a Moody diagram is to calculate the relative roughness of the pipe wall. Relative roughness is the dimensionless ratio of roughness height, ε, to internal pipe diameter, D.

The approximate roughness height, or surface roughness, of some common pipe materials can be found in the table below:

roughness height table

Once, the relative roughness has been calculated, find the closest curve of constant relatively roughness from the right axis of the Moody diagram. If the relative roughness falls between two curves, interpolation may be required.

Next, calculate the Reynolds number for the flow. Reynolds number is calculated from the following equation:

reynolds number

where

  • ρ = the fluid density
  • v = the fluid mean velocity
  • D = pipe internal diameter
  • µ = the fluid dynamic viscosity

Next, find the point where the curve of relative roughness intersects the calculated Reynolds number.

Finally, determine the friction factor by tracing horizontally from the intersection between the curve and Reynolds number to the left axis. You may need to estimate the value of the friction factor if the intersection falls between two friction factors on the right axis.

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The accuracy of estimating a friction factor from a Moody chart is dependent on two things:

  1. The ability to interpolate for values between the curves of relative roughness.
  2. The accuracy of the roughness height value.

With careful usage of the Moody chart, or by using a Moody chart calculator, you can eliminate the error due to number 1 above. However, an incorrect roughness height will yield inaccurate results with both the numerical and graphical approaches to finding the friction factor.

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