## 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

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

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

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

*C _{0}* and

*C*are assumed to be 1 for class 2 bends.

_{f}*K*is given by the nomograph on page 207 of Miller.

_{b}*For *r/D* > 0.7 or *K _{b}** < 0.4,

*C*is given by Miller Figure 9.3. Otherwise,

_{Re}*C*is given by the equation below.

_{Re}

where the *C _{Re}* for

*r/D*= 1 is also found from Miller Figure 9.3.