Loss of Energy due to Sudden Contraction

Consider a pipe carrying certain liquid of specific weight whose cross-sectional area at a certain section reduces abruptly from A₁ to A₂ as shown in Fig. 2. Although, a sudden contraction is reverse of sudden enlargement geometrically, the Bernoulli's equation cannot be applied because the streamlines between section ‘1' and ‘2' are curved. So, the liquid is accelerated due to which the pressure at the annular face varies in an unknown manner, which cannot be determined easily. However, no major loss of energy occurs in the region between the upstream (section 1) and the accelerating flow in the converging portion. As the liquid flows from the wider pipe to narrower pipe, a vena-contracta is formed, after which the stream of liquid widens again to fill up completely the narrower pipe. In between the vena-contracta and the wall of the pipe, lot of eddies are formed that accounts for considerable dissipation of energy. In this region, the flow pattern is almost similar to that of sudden enlargement. So, the head loss can be expressed as,

                                                                                 (5)