The loss coefficient during sudden expansion can be obtained by writing control volume continuity and momentum equation as shown in Fig. 5.6.3. Further the energy equation is applied between the sections (2) and (3). The resulting governing equations are written as follows;

(5.6.7)

The terms in the above equation can be rearranged to obtain the loss coefficient as given below;

(5.6.8)

Here, are the cross-sectional areas of small pipe and larger pipe, respectively. Similarly, d and D are the diameters of small and larger pipe, respectively.

For the case of sudden contraction, the flow initiates from a larger pipe and enters into the smaller pipe (Fig. 5.6.4). The flow separation in the downstream pipe causes the main stream to contract through minimum diameter , called as vena-contracta . This is similar to the case as shown in Fig. 5.6.2. The value of minor loss coefficient changes gradually (Fig. 5.6.5) from one extreme with to the other extreme of . Another empirical relation for minor loss coefficient during sudden contraction is obtained through experimental evidence (Eq. 5.6.9) and it holds good with reasonable accuracy in many practical situations.

(5.6.9)

 

Fig. 5.6.4: Flow pattern during sudden contraction.

Fig. 5.6.5: Variation of loss coefficient with area ratio in a pipe.