Minor Losses in Pipe Systems

The fluid in a typical piping system consists of inlets, exits, enlargements, contractions, various fittings, bends and elbows etc. These components interrupt the smooth flow of fluid and cause additional losses because of mixing and flow separation. So in typical systems with long pipes, the total losses involve the major losses (head loss contribution) and the minor losses (any other losses except head loss). The major head losses for laminar and turbulent pipe flows have already been discussed while the cause of additional minor losses may be due to the followings;

•  Pipe entrance or exit

•  Sudden expansion or contraction

•  Gradual expansion or contraction

•  Losses due to pipe fittings (valves, bends, elbows etc.)

A desirable method to express minor losses is to introduce an equivalent length of a straight pipe that satisfies Darcy friction-factor relation in the following form;

(5.6.5)

where, is the minor loss coefficient resulting from any of the above sources. So the total loss coefficient for a constant diameter pipe is given by the following expression;

(5.6.6)

It should be noted from Eq. (5.6.6) that the losses must be added separately if the pipe size and the average velocity for each component change. The total length is considered along the pipe axis including any bends.

Entrance and Exit Losses : Any fluid from a reservoir may enter into the pipe through variety of shaped region such as re-entrant, square-edged inlet and rounded inlet. Each of the geometries shown in Fig. 5.6.1 is associated with a minor head loss coefficient . A typical flow pattern (Fig. 5.6.2) of a square-edged entrance region has a vena-contracta because the fluid cannot turn at right angle and it must separate from the sharp corner. The maximum velocity at the section (2) is greater than that of section (3) while the pressure is lower. Had the flow been slowed down efficiently, the kinetic energy could have converted into pressure and an ideal pressure distribution would result as shown through dotted line (Fig. 5.6.2). An obvious way to reduce the entrance loss is to rounded entrance region and thereby reducing the vena-contracta effect.

 

Fig. 5.6.1: Typical inlets for entrance loss in a pipe: (a) Reentrant ; (b) Sharp-edged inlet ; (c) Rounded inlet .