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.
|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|
|Mitered, 4 Weld, 22.5°||800||0.27|
|Mitered, 5 Weld, 18°||800||0.25|
|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|
|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|
|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|
|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|
|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|
|Swing Check Valve||1500||0.460||4.0|
|Lift Check Valve||2000||2.850||3.8|
|Diaphragm Valve, Dam Type||1000||2.0|
|Tilting Disk Check Valve||1000||0.5|
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.
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]
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.
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
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))
Flush/ Square Edged
K = 0.5
Inward Projecting (Borda)
K = 0.78
K = 0.25
K = 1.0 for all geometries
- Chemical Engineering Fluid Mechanics, Ron Darby, 2nd Edition