Application of ISO4359 for discharge calculation in a narrow flume

Flumes with either width contractions or raised beds to force modular flow conditions (i.e. a transition from sub- to super-critical flow) are a widely used instrument for the measurement of flow rate. The conservation of mass, written as the continuity equation, and the conservation of energy are combined with the existence of a critical depth point to derive a theoretical equation for the discharge as a function of the upstream water depth. This derivation requires a number of assumptions regarding the flow both upstream and in the throat of the contraction. The international standard covering the use of such flumes, ISO4359, places restrictions on the upstream position at which the water depth should be measured, which this work shows to be unnecessary, at least for the small (100mm throat width) flumes examined. The assumption that critical depth occurs at the end of the flume throat is also shown to be incorrect, but has negligible effect on discharge calculation using the ISO4359 method.