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References and Resources for Mid-Section Method Discharge Measurements


The AquaCalc stream flow computers were designed to use the United States Geological Survey’s (USGS) Mid-Section Method for the calculation of discharge (Q) in open-channel streams.


A discussion of the Mid-Section method can be found in theAquaCalc Pro Plus Instruction Manual, which can be downloaded here.


Additional resources are available from the USGS itself.


USGS Mid-Section Method Resources

The USGS has an educational site that discusses discharge measurement in broad terms here:


The USGS has more detailed training materials and a report on Discharge Measurements here:


The whole report can be downloaded here:

https://pubs.usgs.gov/twri/twri3a8/pdf/TWRI_3-A8.pdf )

And finally the old “bible” of the USGS Water Supply Division: “Water Supply Papers 2175 - Measurement and Computation of Streamflow”. This has a lot of information and theory:



The following is taken from the AquaCalc Pro Plus Instruction Manual:

A Little Theory – The USGS Midsection Method

It is important to understand how a section discharge is calculated in the AquaCalc. The AquaCalc uses the Midsection method that is used by the United States Geological Survey and is well documented in the now out of print Geological Survey Water-Supply Paper 2175 by S. E. Rantz and others titled “Measurement and Computation of Streamflow: Volume 1. Measurement of Stage and Discharge”. This document is published on the Internet and can be reviewed at: http://water.usgs.gov/pubs/wsp/wsp2175/

Using this method, a cross-section at the stream is selected at which to measure. A tag-line (basically a tape measure) is stretched perpendicularly across the water from one edge of water to the opposite side. The stream is broken into “sub-sections” by taking velocity measurements at selected “verticals” in the stream. Several velocity measurements may be taken at different depths in each vertical. Based on USGS standards, no more than five percent (5%) of the total discharge should occur in any sub-section. This is designed to increase the accuracy of the total discharge. Please see the following diagram.


Calculating Discharge

A section discharge is the sum of the discharge in each of the individual subsections associated with each vertical. The sub -section discharge is calculated by multiplying the mean velocity for the vertical times the area of the subsection. The area is determined as the depth of the subsection times its width. The width for a subsection is determined for a given vertical by taking the distance half-way from the previous vertical to the distance halfway to the next vertical as shown by the below by the bold rectangle indicating the subsection area for vertical number 4.

The following is the sub-section discharge equation for vertical number four:



q = subsection discharge

v = mean velocity of vertical

b = distance from initial bank point

d = depth at the vertical.

It is important to note that each subsection assumes an equal depth across the sub-section. Good in-stream practices will place the locations of verticals at locations that minimize either the loss or gain of area: at breaks in the slope of a stream -bed. Also note that there is a “lost triangle” of area at the left of the drawing, just to the right of vertical number 1. It is important when selecting bank side verticals that the discharge in these “lost triangles” be insignificant.

The total discharge for the stream is the sum of the sub-section discharge values.

Calculating the Mean Velocity of a Vertical

The AquaCalc defaults to taking measurements at the six-tenths, two-tenths, and eight-tenths of stream depth locations in a vertical. A measurement taken at the 6-tenths (.6) depth is considered to approximate the mean velocity in the vertical. When a two point measurement is taken at the 2-tenths (.2) and 8-tenths (.8) position, the average of the measured velocities is used as the mean velocity of the vertical:


When velocity measurements are taken at the .2 and .6 and .8 positions, the .2 and .8 velocities are averaged, and that velocity is then averaged with the .6 velocity:


Adjusting Observed Velocity with Method and Horizontal Angle Coefficients

The Horizontal Angle and Method Coefficients can be used to adjust the velocity in each observation. They are simple multipliers to the measured observation velocity.

The horizontal angle entry is used to correct for flow conditions that are not perpendicular to the tag line, such as at bridge that angles across a stream. It is entered as a coefficient that corresponds to the angle from perpendicular; The decimal point must be entered.


Angle in degrees

















An Angle Coefficient Protractor that can be used in the stream is available from JBS, and is reprinted in the back of this manual.

The Method Coefficient is used at the discretion of the hydrographer to adjust the velocity of an observation. An example of its use might be at a vertical where it is not possible to place the current meter at the 6 tenths depth due to weed growth. A coefficient might be used to adjust the velocity measured at a point closer to the surface.

To enter a Method coefficient, press the 1 / Method Coeff key while in the Measure screen and enter a coefficient. When completed press the Enter key.


Discharge Measurement Resources

AquaCalc LLC. telephone +1.916.372.0534 e-mail: sales@aquacalc.com

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