Basically the cross section of an unobstructed area of the stream is measured and a weighted float such as a bottle weighted with pebbles is timed as it floats down a 100 foot course.
The weir method is more time consuming but may be the most satisfactory test if the stream is very small, shallow, rocky, obstructed, or if there is an existing dam. A weir is a dam with an opening or notch through which the entire stream flows. The flow may be calculated by precisely measuring the depth of water flowing over the crest of the weir. Tongue and groove planking makes a good temporary weir for streams not more than one or two feet deep and six to ten feet wide.
Stream flow varies greatly from season to season; thus field data must be gathered many times throughout the year.
The selected references give more detail on how to measure stream flow by the weir or float method. No matter what method of flow measurement is used, it is very important to measure stream flow many times over a year or more.
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