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Head Changes Pipe Size Reduction Formula and Calculator

Hydraulics & Pneumatic Engineering & Design
Fluids Engineering and Design
Civil Engineering and Design

Head Changes Caused by Pipe Size Sudden Reduction Formula and Calculator

Sudden Pipe Enlargements Pressure Reduction:

The following equation for the head loss across a sudden contraction of a pipe was determined by the same type of analytic studies as

Formula 1
hL = ( 1 / Cc - 1 )2 V22 / ( 2 g )

This equation gives best results when the head loss is greater than 1 ft (0.3 m).


hL = head loss, ft, m
V1 = velocity in smaller diameter pipe, ft/s (m/s)
V2 = velocity in smaller diameter pipe, ft/s (m/s)
Cc = coefficient of contraction;
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 formula for determining the loss of head caused by a sudden contraction, determined experimentally by Brightmore, is:

Formula 2
hL = 0.7 ( V1 - V2 )2 / ( 2 g )

This equation gives best results if the head loss is less than 1 ft (0.3 m).

A special case of sudden contraction is the entrance loss for pipes. Some typical values of the loss coefficient K in hL = K V2 / ( 2 g ) Equation 3, where V is the velocity in the pipe, are presented in engineering handbooks.



Civil Engineering Formulas SEcond Edition, Tyler G. Hicks, P.E.