Pipe Enlargement and Reduction Head, Heat and Minor Losses Formula

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Pipe Enlargement and Reduction Head, Heat and Minor Losses Formula

Fluids Engineering
Hydraulic and Pneumatic Knowledge

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:

h_f = ( 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,

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

for sudden enlargement

Sudden pipe reduction

A₁ / A₂	0.00	0.20	0.10	0.30	0.40	0.50	0.60	0.70	0.80	0.90	1.00
Cc	0.585	0.632	0.624	0.643	0.659	0.681	0.712	0.755	0.813	0.892	1.000

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

h_f = ( 1 / C_c -1 ) v₂² / ( 2 g ) Equation 1.3

where the coefficient C_c 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:

h_f = C_c ( v₁ - v₂ )² / ( 2 g ) Equation 1.4

Gradual pipe enlargement and reduction.

Fig 1.5 Gradual pipe enlargement and reduction.

Figure 1.6 Gradual pipe expansion head loss coefficient.

where C_c depends on the diameter ratio D₂/D₁ and the cone angle β in the gradual expansion. A graph showing the variation of C_c with β and the diameter ratio is shown in Fig. 1.6.

Reference:
Piping Calculations Manual,
E. Shashi Menon, P.E.
2005