# Loss coefficient

Minor losses in pipe flow occur due to changes in geometry and can be a significant part in calculating the velocity, pressure, or head in piping systems. Minor losses are generally expressed in terms of a **loss coefficient** defined as

where is the additional irreversible head loss in a piping system caused by the insertion of the component.

## Typical loss coefficients for turbulent flow

#### Bends and Branches

- smooth bend: (flanged); (threaded)
- miter bend: (without vanes); (with vanes)
- threaded elbow:
- return bend: (flanged); (threaded)
- Tee (branch flow): (flanged); (threaded)
- Tee (line flow): (flanged); (threaded)
- Threaded union:

#### Valves

- Globe valve (fully open):
- Angle valve (fully open):
- Ball valve (fully open):
- Swing check valve:
- Gate valve (fully open):
- Gate valve (1/4 closed):
- Gate valve (1/2 closed):
- Gate valve (3/4 closed):

*These are representative values for loss coefficients. Actual values depend on the design and manufacture of the components and may differ from the the representative values. Actual manufacturer's data should always be used in the final design. *

#### Sudden expansion of a pipe

At cross section 1, the average flow velocity is equal to , the pressure is and the cross-sectional area is . The corresponding flow quantities at cross section 2 – well behind the expansion (and regions of separated flow) – are , and , respectively. At the expansion, the flow separates and there are turbulent recirculating flow zones with mechanical energy losses. The loss coefficient for this sudden expansion is expressed as

and is based on the , or the upstream velocity in the pipe with the smaller cross-sectional area . If the flow is laminar in both sections, the loss coefficient becomes

### Sudden contraction of a pipe

In case of a sudden reduction of pipe diameter, without streamlining, the flow is not able to follow the sharp bend into the narrower pipe. As a result, there is flow separation, creating recirculating separation zones at the entrance of the narrower pipe. The main flow is contracted between the separated flow areas, and later on expands again to cover the full pipe area. The loss coefficient for this flow contraction is expressed as

and is based on the , or the downstream velocity in the pipe with smaller cross-sectional area .If the flow is laminar, the loss coefficient becomes