# Pipe Fitting Losses

Head loss in a pipe is sum of following –

- Elevation difference, h
_{Z} - Fitting losses, h
_{L} - Friction losses, h
_{F}

Fitting losses h_{L} is calculated as

`h`_{L} = K(V²/2g)

where, K is resistance coefficient due to fittings, V is fluid velocity and g is acceleration due to gravity.

Friction losses h_{F} is calculated as

`h`_{F} = f(L/D)(V²/2g)

where, f is Darcy’s pipe friction factor, L is pipe length and D is pipe inside diameter.

Total head loss in a pipe –

`h`_{Total} = h_{Z} + h_{L} + h_{F}

Pressure drop due to head loss in pipe is calculated as

`ΔP = h`_{Total}.ρ.g

where, ρ is fluid density.

There are several methods for estimating pipe fitting losses like equivalent length method, K method, 2-K (Hooper) method and 3-K (Darby) method. 3-K method is most accurate followed by 2-K method.

### 2-K (Hooper) Method

`K = K1/Re + K`_{∞} (1 + 1/ID )

where, Re is Reynold’s number, K1, K_{∞} are constants and ID is inside diameter in inches.

### 3-K (Darby) Method

`K = K1/Re + K`_{∞} (1 + Kd/D_{n}^{0.3} )

where, K1, K_{∞}, Kd are constants and D_{n} is nominal pipe diameter in inches.

Constants for 3K and 2K method for some common fittings.

90° Elbow | K1 | K_{∞} |
Kd |
---|---|---|---|

Threaded, r/D = 1 | 800 | 0.14 | 4.0 |

Threaded, Long Radius, r/D = 1.5 | 800 | 0.071 | 4.2 |

Flanged, Welded, Bend, r/D = 1 | 800 | 0.091 | 4.0 |

Flanged, Welded, Bend, r/D = 2 | 800 | 0.056 | 3.9 |

Flanged, Welded, Bend, r/D = 4 | 800 | 0.066 | 3.9 |

Flanged, Welded, Bend, r/D = 6 | 800 | 0.075 | 4.2 |

Mitered, 1 Weld, 90° | 1000 | 0.270 | 4.0 |

Mitered, 2 Weld, 45° | 800 | 0.068 | 4.1 |

Mitered, 3 Weld, 30° | 800 | 0.035 | 4.2 |

2K Method | |||

Mitered, 4 Weld, 22.5° | 800 | 0.27 | |

Mitered, 5 Weld, 18° | 800 | 0.25 |

45° Elbow | K1 | K_{∞} |
Kd |
---|---|---|---|

Standard, r/D = 1 | 500 | 0.071 | 4.2 |

Long Radius, r/D = 1.5 | 500 | 0.052 | 4.0 |

Mitered, 1 Weld, 45° | 500 | 0.086 | 4.0 |

Mitered, 2 Weld, 22.5° | 500 | 0.052 | 4.0 |

180° Bend | K1 | K_{∞} |
Kd |
---|---|---|---|

Threaded, r/D = 1 | 1000 | 0.230 | 4.0 |

Flanged/ Welded, r/D = 1 | 1000 | 0.120 | 4.0 |

Long Radius, r/D = 1.5 | 1000 | 0.100 | 4.0 |

Tees | K1 | K_{∞} |
Kd |
---|---|---|---|

Standard, Threaded, r/D = 1 | 500 | 0.274 | 4.0 |

Long Radius, Threaded, r/D = 1.5 | 800 | 0.140 | 4.0 |

Standard, Flanged/ Welded, r/D = 1 | 800 | 0.280 | 4.0 |

Stub-in Branch | 1000 | 0.340 | 4.0 |

Run Through, Threaded, r/D = 1 | 200 | 0.091 | 4.0 |

Run Through, Flanged/ Welded, r/D = 1 | 150 | 0.050 | 4.0 |

Run Through Stub in Branch | 100 | 0 | 0 |

Valves | K1 | K_{∞} |
Kd |
---|---|---|---|

Angle Valve = 45°, β = 1 | 950 | 0.250 | 4.0 |

Angle Valve = 90°, β = 1 | 1000 | 0.690 | 4.0 |

Globe Valve, β = 1 | 1500 | 1.700 | 3.6 |

Plug Valve, Branch Flow | 500 | 0.410 | 4.0 |

Plug Valve, Straight Through | 300 | 0.084 | 3.9 |

Plug Valve, 3-way, Flow Through | 300 | 0.140 | 4.0 |

Gate Valve, β = 1 | 300 | 0.037 | 3.9 |

Ball Valve, β = 1 | 300 | 0.017 | 3.5 |

Butterfly Valve | 1000 | 0.690 | 4.9 |

Swing Check Valve | 1500 | 0.460 | 4.0 |

Lift Check Valve | 2000 | 2.850 | 3.8 |

2K Method | |||

Diaphragm Valve, Dam Type | 1000 | 2.0 | |

Tilting Disk Check Valve | 1000 | 0.5 |

### Square Reduction

For Re_{1} < 2500

`K = (1.2 + 160/Re`_{1})[(D_{1}/D_{2})^{4} - 1]

For Re_{1} > 2500

`K = (0.6 + 0.48f`_{1})(D_{1}/D_{2})²[(D_{1}/D_{2})² - 1]

Re_{1} is upstream Reynold’s number at D_{1} and f_{1} is friction factor at this Reynold’s number.

### Tapered Reduction

For θ < 45°, multiply K from square reduction by 1.6 sin(θ/2).

For θ > 45°, multiply K from square reduction by sin(θ/2)^{0.5}.

### Rounded Pipe Reduction

`K = (0.1 + 50/Re`_{1})[(D_{1}/D_{2})^{4} - 1]

### Square Expansion

For Re_{1} < 4000

`K = 2[1 - (D`_{1}/D_{2})^{4}]

For Re_{1} > 4000

`K = (1 + 0.8f`_{1})[1 - (D_{1}/D_{2})²]²

Re_{1} is upstream Reynold’s number at D_{1} and f_{1} is friction factor at this Reynold’s number.

### Tapered Expansion

For θ < 45° multiply K for square expansion by 2.6 sin(θ/2).

For θ > 45° use K for square expansion.

### Rounded Pipe Expansion

Use K for square expansion.

### Thin Sharp Orifice

For Re_{1} < 2500

For Re_{1} > 2500

### Thick Orifice

For L/D_{2} > 5, use equations for square reduction and a square expansion.

For L/D_{2} < 5, multiply K for a thin sharp orifice by

`0.584 + (0.0936 / ( (L/D`_{2})^{1.5} + 0.225))

#### Pipe Entrances

### Flush/ Square Edged

K = 0.5

### Rounded

r/D | K |
---|---|

0.02 | 0.28 |

0.04 | 0.24 |

0.06 | 0.15 |

0.10 | 0.09 |

0.15+ | 0.04 |

### Inward Projecting (Borda)

K = 0.78

### Chamfered

K = 0.25

### Pipe Exits

K = 1.0 for all geometries

Spreadsheet for Pipe Fitting Losses

### References

- Pressure Loss from fittings 3K method at Neutrium.net
- Pressure Loss Expansion & Reduction at Neutrium.net
- Chemical Engineering Fluid Mechanics, Ron Darby, 2
^{nd}Edition