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### Pipe Enlargement and Reduction Head, Heat and Minor Losses Formula

Pipe Enlargement and Reduction Head, Heat and Minor Losses Formula

Pipe enlargements and reductions contribute to head loss that can be included in minor losses. For sudden enlargement of pipes, head loss equation 1.0 may be used:

hf = ( v1 - v2 )2 / ( 2 g ) - Equation 1.0

Where:

v1 and v2 = velocities of the liquid in the two pipe sizes (m/sec, ft/sec)
D1 and D2 = diameters respectively (m, ft )

Writing Eq. (1.0) in terms of pipe cross-sectional areas A1 and A2,

hf = [ 1 - A1 / A2 )2 ( v2 / ( 2 g ) ] - Equation 1.2

for sudden enlargement

Sudden pipe reduction

 Cc A1 / A2 0 0.2 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00 0.585 0.632 0.624 0.643 0.659 0.681 0.712 0.755 0.813 0.892 1

Figure 1.0 Sudden pipe enlargement and reduction.

For sudden contraction or reduction in pipe size as shown in Fig. 1.0, the head loss is calculated from

hf = ( 1 / Cc -1 ) v22 / ( 2 g ) Equation 1.3

where the coefficient Cc depends on the ratio of the two pipe crosssectional areas A1 and A2 as shown in Fig. 1.2.

Gradual enlargement and reduction of pipe size, as shown in Fig. 1.5, cause less head loss than sudden enlargement and sudden reduction. For gradual expansions, the following equation may be used:

hf = Cc ( v1 - v2 )2 / ( 2 g ) Equation 1.4

Fig 1.5 Gradual pipe enlargement and reduction.