# 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-sectionsupercritical 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