Bend Loss Model

90 degree bends

The three Bend loss correlations are all for turbulent Reynolds numbers (Crane 1988Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Co., Joliet, IL, 1988., A-29).

The K-factors for a smooth flanged bend with r/D ≥ 1 are provided in Table 1.

Table 1: K-factors for 90 degree smooth flanged bends

A table of K-factors for the Bend junction with based on the r/d ratio. A diagram indicating what the radius and diamter of a pipe in K factor calculation for a bend correlate to.

The standard threaded elbow is given by:

where f_T is the turbulent friction factor given in Table 2.

Table 2: Pipe friction factors used for Crane formulas

A table of pipe Frictrion Factors used for Crane calculations.

The Mitre bend is given by:

Non-90 degree bends

The two non-90 degree bend loss correlations are for turbulent Reynolds numbers (Crane 1988, A-29).

A smooth flanged bend with r/D ≥ 1 is given by:

where n is the number of 90 degree bends, K is the loss factor for one 90 degree bend (Table 1), and f_T is given by Table 2.

The Mitre bend is given by Table 3.

Table 3: K values for Mitre bends

A table showing the K factor values of Mitre bends for various values of mu. A diagram of a Mitre bend indicating what the value of mu indicates.

Smooth Flanged Bends, r/D < 1

The smooth, flanged bend with r/D < 1 loss factor uses a correlation applicable for turbulent Reynolds numbers (Miller 1990Miller, D. S., Internal Flow Systems, 2nd edition, Gulf Publishing Company, Houston, TX, 1990., 209)

The loss coefficient is calculated based on Miller's class 2 bend model, which is sufficient for general design purposes, and is given by

C₀ and C_f are assumed to be 1 for class 2 bends. K_b* is given by the nomograph on page 207 of Miller.

For r/D > 0.7 or K_b* < 0.4, C_Re is given by Miller Figure 9.3. Otherwise, C_Re is given by the equation below.

where the C_Re for r/D = 1 is also found from Miller Figure 9.3.