Local losses in flumes

Local losses result from changes in cross-section (constriction, sills, flow-measuring flumes), changes in direction and obstacles. Obstacles in flumes include piers for bridges or weirs. Piers constrict the flow cross-section possibly leading to back eddies or backwaters.

From a hydraulic point of view, there are four general cases for piers which class the discharge behaviour as without obstacles, i.e. as normal discharge. The four general cases are:

  • subcritical discharge with little or considerable reduction of cross-section

  • supercritical discharge with little or considerable reduction of cross-section

A non-negligible backwater and possibly a flow transition in front of the pier occurs when the specific energy E of the undisturbed discharge Q is less than the minimum required specific energy Emin that guarantees the complete discharge Q. As the flow width b rest of the flume through the obstacles decreases, Emin increases (see illustrations below). For rectangular flumes with a broad cross-section we get

Discharge at the rounded pier without flow transition

E specific energy with pier, Q discharge, Ed undisturbed specific energy, Emin minimum required specific energy, hd downstream water discharge depth (normal discharge), hu upstream water discharge depth with pier, hc undisturbed critical depth, h‘c critical depth with pier, Δz pier backwater, ΔE loss of specific energy

Discharge at the rounded pier with flow transition