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### Head Changes Caused by Pipe Size Enlargement Formula and Calculator

Head Changes Caused by Pipe Size Enlargement Formula and Calculator

Energy losses occur in pipe contractions, bends, enlargements, and valves and other pipe fittings. These losses can usually be neglected if the length of the pipeline is greater than 1500 times the pipe diameter. However, in short pipelines, because these losses may exceed the friction losses, minor losses must be considered.

Sudden Pipe Enlargements Pressure Change

The following equation for the head loss, ft (m), across a sudden enlargement of pipe diameter has been determined analytically and agrees well with experimental results:

Formula 1
hL = ( V1 - V2 )2 / ( 2 g )

Where:

V1 = velocity before enlargement, ft/s (m/s)
V2 = velocity after enlargement, ft/s (m/s)
g = 32.2 ft/s2 (9.81 m/s2)

It was derived by applying the Bernoulli equation and the momentum equation across an enlargement.

Another equation for the head loss caused by sudden enlargements was determined experimentally by Archer. This equation gives slightly better agreement with experimental results than the preceding formula:

Formula 2
hL = 1.1 ( V1 - V2 )1.92 / ( 2 g )

A special application of these two preceding formulas is the discharge from a pipe into a reservoir. The water in the reservoir has no velocity, so a full velocity head is lost.