Loss Coefficient (k)

The loss coefficient (k) is the number of velocity heads that would be equivalent to the head loss across the fitting:

F i t t i n g space h e a d space l o s s space left parenthesis m right parenthesis equals k cross times v e l o c i t y space h e a d equals k fraction numerator u to the power of ² over denominator 2 g end fraction

Consider the figure below which shows two horizontal lengths of pipe connected by a 90° horizontal bend.

Figure: Two horizontal lengths of pipe connected by a 90° bend

Figure: Two horizontal lengths of pipe connected by a 90° bend

The head loss across the bend – between sections A and B – would be given by:

F i t t i n g space h e a d space l o s s subscript A minus B end subscript space left parenthesis m right parenthesis equals k fraction numerator u to the power of ² over denominator 2 g end fraction

So, if we wanted to express the fitting head loss as a fitting pressure loss in N/m², we would convert using the density of the fluid and acceleration due to gravity g, as we have done previously by:

F i t t i n g space p r e s s u r e space l o s s space left parenthesis N divided by m to the power of ² right parenthesis equals left parenthesis k fraction numerator u to the power of ² over denominator 2 g end fraction right parenthesis rho g

F i t t i n g space p r e s s u r e space l o s s space left parenthesis N divided by m to the power of ² right parenthesis equals left parenthesis k u to the power of ² over 2 right parenthesis rho

Let us look at a worked example to determine the fitting loss as a head and as a pressure.

A pipeline carries water of density 1,000 kg/m³ at an average flow velocity of 1 m/s.

A fitting in the line has a loss coefficient k of 1. Determine the head loss (m water) across the fitting and the equivalent pressure loss of the fitting.

F i t t i n g space h e a d space l o s s space left parenthesis m space w a t e r right parenthesis equals k fraction numerator u to the power of ² over denominator 2 g end fraction equals 1 cross times fraction numerator 1 to the power of ² over denominator 2 cross times 9.81 end fraction equals 0.051 m

And converting this to a pressure:

P r e s s u r e space l o s s space left parenthesis P a right parenthesis equals rho g h equals 1 comma 000 cross times 9.81 cross times 0.051 equals 500.3 space P a

Some typical fitting loss coefficients for pipeline and ductwork fittings are shown in the tables below.

Table: Loss coefficient k for various pipe fittings

Table: Loss coefficient k for various pipe fittings

Table: Loss coefficient k for various duct fittings

Table: Loss coefficient k for various duct fittings

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