### 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.

 Minor Hydraulic Losses Explained

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

h_L = \frac{kV^2}{2g}

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 (Leq) to the actual length of pipe to account for the minor losses.

L_{eq} = \frac{kD}{f}

where

• k = Loss coefficient (See Table 1)
• D = diameter of pipe (ft)
• f = friction factor
 Table 1: Loss Coefficient (k)[1] Type of pipe fixture Loss Coefficient Globe valve (fully open) 6.4 Globe valve (half open) 9.5 Angle valve (fully open) 5.0 Swing check valve (fully open) 2.5 Butterfly valve (fully open) 0.4 Gate valve (fully open) 0.2 Gate valve (3/4 open) 1.0 Gate valve (half open) 5.6 Gate valve (one-quarter open) 24.0 Check valve, swing type (fully open) 2.3 Check valve, lift type (fully open) 12.0 Check valve, ball type (fully open) 70.0 Foot Valve (fully open) 15.0 Close return bend (180º) 2.2 Standard tee 1.8 Standard (short radius) elbow (90º) 0.9 Medium radius elbow (90º) 0.7 Long sweep elbow (90º) 0.6 45 degree elbow 0.4 Pipe entrance (Square-edged) 0.5 Pipe entrance (Re-entrant) 0.8 Pipe entrance (Rounded, r/D < 0.16) 0.1 Pipe exit 1.0 Sudden contraction (2 to 1) 0.25 Sudden contraction (5 to 1) 0.41 Sudden contraction (10 to 1) 0.46 Orifice plate (1.5 to 1) 0.85 Orifice plate (2 to 1) 3.4 Orifice plate (4 to 1) 29.0 Sudden enlargement (1-A1/A2)2 90 degree miter bend (without vanes) 1.1 90 degree miter bend (with vanes) 0.2 General contraction (30 degree included angle) 0.02 General contraction (70 degree included angle) 0.07

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

L_{eq} = \frac{kD_{eq}}{f}

where

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

D_{eq} = 4 * \text{hydraulic radius} = 4* \frac{\text{cross sectional area}}{\text{wetted perimeter}}

where

## Relationship between Velocity Head and Equivalent Length

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

\frac{fL_{eq}}{D} \frac{V^2}{2g} = k\frac{V^2}{2g}

where

• f = friction factor
• Leq = 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

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