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The Colebrook equation was developed in 1939 by C.F. Colebrook and C.M. White. The equation is implicit and very difficult to factor for () - the friction factor. In most cases engineers will use the chart developed by L.F. Moody to find the friction factor.

(Colebrook Equation)

Where:


= Reynold's Number (Must be above 2000)

= Friction Factor

= Absolute Roughness (ft)

= Inside Pipe Diameter (ft)

Table 1: Absolute Roughness for various types of pipe

The Reynold's Number can be determined with the following equation:

Where:


V = Average Pipe Velocity ()

D = Inside Diameter of Pipe ()

ν = Kinematic Viscosity ()

For the people that are brave enough to solve the colebrook equation to find head loss, below is a spreadsheet that I put together to make the calculation as simple as possible:

The solver function in Microsoft Excel is used to solve for values of "" that satisfy the equation. The example above has numbers for a chilled water piping system. Notice the calculated head loss per 100 Feet is approximately the same as the numbers calculated by others such as "Cameron Hydraulic." This is pretty cool when you consider you don't have to look up every single value when you are sizing a system and trying to find the total head loss.


You can even set up a table such as the one below to automatically calculated the inside diameter of a given pipe:

Table 2: Inside Diameters of Various Pipe Sizes

And if you want to continue a step further you can set up a table that proves that both sides of the equation are equal. This may allow you to sleep easier.

Table 3: Data tabulated to show "f" factor is correct

Picture 1: Chilled Water Pump