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

Hydraulics & Pneumatic Engineering & Design

Fluids Engineering and Design

Civil Engineering and Design

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.

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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

h_{L} = ( V_{1} - V_{2} )^{2} / ( 2 g )

Where:

V_{1} = velocity before enlargement, ft/s (m/s)

V_{2} = velocity after enlargement, ft/s (m/s)

g = 32.2 ft/s^{2} (9.81 m/s^{2})

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

h_{L} = 1.1 ( V_{1} - V_{2} )^{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.

Gradual Enlargements Pressure Change

Formula 3

h_{L} = K ( V_{1} - V_{2} )^{2} / ( 2 g )

where K = loss coefficient, as given in engineering handbooks.

Related:

- 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.