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The application of Appropriate Technology

# Appendix 3. Friction Losses and the Reynolds Number

The frictional head loss for fluids flowing in pipes is calculated by the following equation:

$f_f=f.L.v^2/2.D.g$

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Where:
f is the friction factor (see below for calculation)
L is the pipe length (m)
v is the average fluid velocity (m/s)
D is the pipe diameter (m)
g is the acceleration due to gravity (9.81 m/s/s)

The only variable not available to us immediately is the frictional factor (f). This is dependent on the type of flow occurring in the pipe. There are basically two types of flow (although there is a transition state between them ), these are:

1. Laminar flow. Example: This is similar to the stream of smoke from a cigarette in still air. Close to the cigarette the stream of smoke is very uniform and flowing evenly. This is laminar flow.
2. Turbulent flow. Example: This is when the stream of smoke from the cigarette becomes unstable, with whorls and eddies. This state occurs in the stream of smoke after the laminar flow.

These two states of flow can be described by a dimensionless quantity (just a number) known as the Reynolds Number (NRE). This number is calculated by the following formula:

$N_{RE}=v.D/\mu_k$

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Where:
v is the average fluid velocity (m/s)
D is the pipe diameter (m)
μk is the kinematic viscosity of the fluid (m2/s), which is a measure of how ‘thick’ the fluid is

If the Reynolds Number is less than 2000 then the fluid flow is laminar. In this case the friction factor (f) can be calculated by the following equation:

$f=64/N_{RE}$

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If the Reynolds Number is greater than 2000 then the fluid flow is turbulent. In this case the friction factor (f) can be calculated by use of a Moody Chart.