Discharge (Stream flow) Measurement Methods: [ Mid-Section and Mean-Section Methods ]

Stream discharge can be measured using (1) volumetric gauging, (2) float gauging, (3) current metering, (4) dilution gauging (constant injection or gulp methods), (5) structural methods, and (6) slope-area methods. The choice of method depends on the characteristics of the stream and on the application.
(1) Volumetric gauging: Stream discharge (in cumecs) at one point in time (i.e., a 'spot discharge') can be measured directly with volumetric gauging, though this is only possible with small river-flows, or indirectly with the velocity-area methods of float gauging and current metering.
(2) Float gauging: involves measuring the velocity of a neutral buoyancy object (e.g., orange or dog biscuit) and multiplying this by the average cross-sectional area (using a tape and rule) of the river. These objects do, however, float close to the river surface, which is faster then the average velocity of the water profile and must, therefore, be reduced by a coefficient (e.g., a river 0.9 m deep has a coefficient of 0.7). Some rivers also have large changes in velocity across the river channel. This cannot be corrected, so the more accurate current metering method is recommended.
(3) Current metering: With current metering the rotation of a current meter's impeller gives the local water velocity following application of a calibration equation (called a rating equation). To cope with the vertical distribution of velocity, measurements should be made at different depths (D) in the water profile. If only two depths are used for measurement, then an average of 0.2D and 0.8D gives a good representation of the profile velocity, or 0.6D if only one depth is used. The transverse (i.e., 'across-river') distribution of velocity can be characterised by first dividing the channel cross-section into a number of 'segments'. The edge of these segments are called 'verticals' and these are the locations at which the measurements to calculated the profile-average velocity should be made (Figure 2). The 'Mean-Section Method' or 'Mid-Section Method' can then be used to calculate the discharge for each segment.
Where the ‘Mean-Section Method’ is used to calculate discharge for each segment using:
Qseg = 0.5(v1+v2) ´ 0.5(d1+d2) ´b
where Qseg is the discharge for each channel segment (cumecs), v1 and v2 are the profile-average water velocities at vertical 1 and 2 respectively (either side of the segment), d1 and d2 are the depths of the flow at verticals 1 and 2 respectively, and b is the chosen width of each channel segment. The average velocity of the water in the two 'end segments' (adjacent to the river banks) are calculated by assuming zero depth and zero velocity at the water's edge. Current metering is an accurate method of river gauging except where the river is very shallow. Under such conditions, an alternative method of dilution gauging can be used.
(4) Dilution gauging: This method is based on 'the two component mixing equation'.
(Q+q)C2 = qC1 + QC0

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When finding the Q-mid why have you multiplied with V-mid instead of the mean of the V-mid

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and what about the average width of the first edge and end edge segment?

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