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# How to calculate stream flow rate

Updated July 20, 2017

Stream flow rate is the volume of fluid that passes through a given surface per unit of time. Understanding this measurement helps in flood preparation and proper engineering of drainage areas. Stream flow is also a factor in some water quality parameters, including habitat for aquatic species, pollution concentration and land erosion. Flow can be affected by a number of both natural and human factors and can change rapidly.

Write down the following equation for calculating the flow rate F of a stream: F = cross-sectional area (A) of river bed times the corrected velocity (V) of the water in the river.

Measure a 6 m (20-foot) length of the stream along a straight, even section that is at least 15 cm (six inches) deep with a uniform width that is free of debris. Mark the starting point and end point of the measurement with flags.

Determine the width of the stream by using a tape measure to measure several different locations and compute the average of the measurements.

Determine the depth of the stream by taking measurements in 30 cm (one foot) sections straight across from one side of the stream to the other using a metre ruler. When taking the measurement, do not push the ruler into the stream bed sediment and keep it vertical for each measurement. Repeat this in three different sections and calculate the average of the measurements taken.

Place an orange float into the stream at the marked starting point of the 6 m (20-foot) section. Time how long it takes the float to drift from the first flag to the second flag. Repeat this three or four times, and calculate the average time it takes the float to drift downstream. If the float is interrupted during any of the runs, the timing test must be redone.

Calculate the cross-sectional area A of the stream bed using the following equation, A = average depth of the stream (D) times the average width of the stream (W). For example, if the average depth is 0.81 m (2.66 foot) and the average width is 1.66 m (5.46 foot) then the area A = 0.81 m x 1.66 m = 1.345 m squared (or A = 2.66 foot x 5.46 foot = 14.52 square foot).

Calculate the stream’s water velocity (v) using the equation V = [final distance x(f) - initial distance x(i)] ÷ average time (t). If we have a 6 m (20 foot) section of stream where the initial distance is 0, the final distance is 6 m (20 foot) and the average time t was found to be 17 seconds than v = (6 m - 0 m) ÷ 17 s = 0.353 m/s (or v = [20 ft. - 0 ft]. ÷ 17 s = 1.17 ft/s).

Calculate the corrected velocity V for the stream V = v x n which takes into account the roughness of the stream bed. If the stream bed is smooth sand, mud or bedrock than n = .09 and if the bed consists of course rocks, twigs and weeds n = .08.

Plug the values you calculated into the original formula F = A x V. For example if the stream bed is smooth, the water velocity is 0.353 m/s (or 1.17ft/s) and the area is 1.345 m² (14.52 ft²) than the flow rate of the stream is F = 1.345 m² x (0.353 m/s x 0.09) = 0.0427 m³/s (or F = 14.52 ft² x [1.17ft/s x 0.09] = 1.53 ft³/s).

#### Warning

Do not enter fast moving water.

Deep water can have strong under currents, so extreme care should be taken when entering any stream or river.

Always have a second person with you when performing this procedure.

• Tape measure
• Flags
• Metre ruler
• Orange float
• Stopwatch
• Calculator