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

Fluids Engineering

Hydraulic and Pneumatic Knowledge

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:

*h _{f} = ( v_{1} - v_{2} )^{2} / ( 2 g )* - Equation 1.0

Where:

*v _{1}* and

*v*= velocities of the liquid in the two pipe sizes (m/sec, ft/sec)

_{2}D

_{1}and D

_{2}= diameters respectively (m, ft )

Writing Eq. (1.0) in terms of pipe cross-sectional
areas A_{1} and A_{2},

*h _{f} = *[

*1 - A*] - Equation 1.2

_{1}/ A_{2})^{2}( v^{2}/ ( 2 g )for sudden enlargement

Sudden pipe reduction

A _{1} / A_{2} |
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 ) v_{2}^{2} / ( 2 g ) Equation 1.3*

where the coefficient *C _{c}* depends on the ratio of the two pipe crosssectional
areas

*A*and

_{1}*A*as shown in Fig. 1.2.

_{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} ( v_{1} - v_{2} )^{2} / ( 2 g ) Equation 1.4*

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 D

_{2}/D

_{1}and the cone angle β in the gradual expansion. A graph showing the variation of

*C*with β and the diameter ratio is shown in Fig. 1.6.

_{c}Related:

- Pipe Flow Gradual Size Enlargement Formula and Calculator
- Pex (Cross-Linked Polyethylene) Specifications
- Pressure Drop Equivalent Length of Pipes and Fittings HVAC
- Loss of Air Pressure Due To Pipe Friction Table 1
- Loss of Pressure Through Screw Pipe Fittings
- Pressure Drop Along Pipe Length
- Pipe Friction Equations Within Pipe For Fluid Flow
- Xtra Strong (XS) Size Steel Pipe Weights TAble Calculator

Reference:

Piping Calculations Manual,

E. Shashi Menon, P.E.

2005