Minor Losses

What are Minor Losses?

Although the greatest cause of head loss (pressure drop) of fluid flow in a pipe is friction, there are other losses that result from abrupt changes to the flow at entrances, valves, fitting, bends, and exits. These losses are are minor if the length of pipe is long (and therefore hf is high) but they must be considered especially when the length of the pipe is short. There are two primary methods of calculation these minor losses: velocity head and equivalent length.

Velocity Head, Circular Pipes

The velocity head method adds a term for minor losses in h_L

where

• k = Loss coefficient (See Table 1)
• V = velocity of flow (ft/sec)
• g = gravity (ft/sec²)

Equivalent Length, Circular Pipes

The equivalent length adds an appropriate distance (L_eq) to the actual length of pipe to account for the minor losses.

where

• k = Loss coefficient (See Table 1)
• D = diameter of pipe (ft)
• f = friction factor

Notes: (x to 1) is the area ratio, sudden enlargement is based on V1, and well-rounded entrance and sudden contractions are based on V2.

The equivalent length can also be read directly from a table such as CERM Appendix 17.D

Equivalent Length, Non-Circular Pipes

In the case of con-circular pipes, the equivalent length equation requires the use of equivalent diameter in the place of diameter

where

• k = Loss coefficient (See Table 1)
• Deq = equivalent diameter of pipe (ft). See equation below
• f = friction factor

where

• Hydraulic Radius

Relationship between Velocity Head and Equivalent Length

The velocity head and equivalent length methods are related by the equation

where

• f = friction factor
• L_eq = Equivalent Length
• D = Diameter
• V = velocity of flow (ft/sec)
• g = gravity (ft/sec²)
• k = Loss coefficient (See Table 1)

References:

1. Larock, Jeppson, & Watters, "Hydraulics of Pipeline Systems", 2000