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

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 h_F 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 D_n is nominal pipe diameter in inches.

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

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

Inward Projecting (Borda)

K = 0.78

Chamfered

K = 0.25

Pipe Exits

K = 1.0 for all geometries

Resources

1. Web based calculation available at checalc.com
2. Spreadsheet for Pipe Fitting Losses

References

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