Pipe Fitting Losses

Head loss in a pipe is sum of following –

  • Elevation difference, hZ
  • Fitting losses, hL
  • Friction losses, hF

Fitting losses hL is calculated as

hL = K(V²/2g)

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

Friction losses hF is calculated as

hF = 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 –

hTotal = hZ + hL + hF

Pressure drop due to head loss in pipe is calculated as

ΔP = hTotal.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.

Featured Resources :

null Is the voice of the pump and rotating equipment industry. They deliver relevant industry news coverage and powerful technical information to managers, engineers, operators and maintenance professionals around the world.


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/Dn0.3 )

where, K1, K, Kd are constants and Dn 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

Featured Resources :

null Offers drilling contractors and well completion professionals the practical, hands-on knowledge that readers in the oil and gas industry expect from the publishers of Pumps & Systems magazine.


Square Reduction

Square Reduction

For Re1 < 2500

K = (1.2 + 160/Re1)[(D1/D2)4 - 1]

For Re1 > 2500

K = (0.6 + 0.48f1)(D1/D2)²[(D1/D2)² - 1]

Re1 is upstream Reynold’s number at D1 and f1 is friction factor at this Reynold’s number.

Tapered Reduction

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

Rounded Pipe Reduction

K = (0.1 + 50/Re1)[(D1/D2)4 - 1]

Square Expansion

Square Expansion

For Re1 < 4000

K = 2[1 - (D1/D2)4]

For Re1 > 4000

K = (1 + 0.8f1)[1 - (D1/D2)²]²

Re1 is upstream Reynold’s number at D1 and f1 is friction factor at this Reynold’s number.

Tapered Expansion

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

Rounded Pipe Expansion

Use K for square expansion.

Thin Sharp Orifice

Thin Sharp Orifice

For Re1 < 2500
K Value Thin Sharp Orifice Re < 2500

For Re1 > 2500
K Value Thin Sharp Orifice Re > 2500

Thick Orifice

Thick Orifice
For L/D2 > 5, use equations for square reduction and a square expansion.
For L/D2 < 5, multiply K for a thin sharp orifice by

0.584 + (0.0936 / ( (L/D2)1.5 + 0.225))

Pipe Entrances

Flush/ Square Edged

Flush Square Edged

K = 0.5

Rounded

Rounded Pipe Entrances

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)

Inward Projecting (Borda)

K = 0.78

Chamfered

Chamfered Pipe Entrances

K = 0.25

Pipe Exits

K = 1.0 for all geometries

Spreadsheet for Pipe Fitting Losses

References

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

Leave a Reply

Your email address will not be published. Required fields are marked *