A weir is basically an obstruction in the flow path in an open channel. The weir will cause an increase in the water depth as the water flows over the weir. In general, the greater the flow rate, the greater will be the increase in depth of flow, The height of water above the top of the weir is the measurement usually used to correlate with flow rate.

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The two major types of weir are sharp crested weir and broad crested weir. The crest is the term used for the top of the weir, where the water flows over it. The two diagrams here show a sharp crested weir and a broad crested weir. As you can see by the diagrams, the names are very descriptive. The sharp crested weir has a sharp surface at the crest or top, where the water flows over it, and the broad crested weir has a broad flat surface at the top.
The height of the water above the crest of the weir is called the head over the weir and is shown as H in both of the diagrams. It is the parameter that is measured and used to determine the flowrate. There are equations available to calculate flow rate, Q, over the weir for given head over the weir, H. Also for a given weir, Q can be experimentally correlated with H. See the article, The Broad Crested Weir for Open Channel Flow Measurement for more detailed information on the broad crested weir.