Fluid Flow

## 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.

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
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
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 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 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/Re1)[(D1/D2)4 - 1]

Square Expansion For Re1 < 4000

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

For Re1 > 4000

K = (1 + 0.8f1)[1 - (D1/D2)²]²

Re>Re1 is upstream Reynold's number at D1 and f1 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 Re1 > 2500 For Re1 > 2500 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 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

Resources

References

1. Chemical Engineering Fluid Mechanics, Ron Darby, 2nd Edition