Hydraulics & Pneumatic Engineering & Design
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Civil Engineering and Design

Head Changes Caused by Pipe Size Sudden Reduction Formula and Calculator

Preview Head Changes Caused by Pipe Size Sudden Reduction 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
h_L = ( 1 / C_c - 1 )² V₂² / ( 2 g )

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

Where:

h_L = head loss, ft, m
V₁ = velocity in smaller diameter pipe, ft/s (m/s)
V₂ = velocity in smaller diameter pipe, ft/s (m/s)
C_c = 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
h_L = 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 h_L = K V² / ( 2 g ) Equation 3, where V is the velocity in the pipe, are presented in engineering handbooks.

Related:

• Head Changes Caused by Pipe Size Enlargement Formula and Calculator
• Hydraulic Head Pressure
• Head Loss Darcy - Weisback Equation - Fluid Flow Hydraulic and Pneumatic
• Forced and Natural Fluid Circulation - Fluid Flow Hydraulic and Pneumatic
• Pipe Friction Equations Within Pipe For Fluid Flow

Reference:

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