D.3.2 Mean Section Method

Prior to 1974 the Water Investigations Branch used another form of computation of discharge. This involved doubling the values of depth and velocity taken at the vertical and adding the value of depths and velocities of the preceding and following verticals. Twenty-five per cent of the sum of both depth and velocity was then used to calculate the mean discharge using a width for this partial section of one half the distance from the preceding vertical to one half the distance to the following vertical.

After a period in which check computations were carried out by computer programs and the results of both mid-section and mean section were produced, it was determined that a comparison of the results using both methods produced differences of less than 1% in most instances. The province adopted the mid-section method for all subsequent discharge calculation.

D.3.3 Mid-Section Method

The mid-section method of computing discharge measurements is carried out as follows:

1. Observed depth at the vertical is considered to be the mean depth for the section or panel.
2. It is assumed that the mean velocity at the observation vertical represents the mean velocity for the section.
3. Width for each section is computed as one-half the distance from the preceding vertical plus one-half the distance to the following vertical.
   In Figure D-18, the discharge for the heavily outlined section at distance b6 from the initial point is computed as:

The calculations for the first and last sections of a discharge measurement are handled in much the same manner as just described. The main difference is in the determination of the widths. Because at the beginning and the end of a measuring section there is no preceding or following vertical, the width becomes one-half the distance from the edge to the first vertical or from the last vertical from the edge. Figure D-19 shows typical edge sections. As a result of the computational procedures, in these instances the area and discharge are not derived for the edge sections. Therefore, when making a discharge measurement, the first and last verticals should be taken as close to the edge as possible. The two edge sections will then be very small in proportion to the total measurement and an estimated discharge for these sections will introduce very little if any appreciable error.

An edge section will also occur where there is a vertical drop at the water's edge, such as at a pier, a bridge abutment, or a wingwall. Again, the width calculation is one-half the distance from the previous or to the following vertical as shown in Figure D-19. Here, however, an area and discharge can be computed. Once again, soundings should be arranged so that edge sections are made as small as possible.

Keep in mind that caution must be exercised when observing depths and velocities close to piers and abutments. At times, it may be necessary to estimate these values to avoid the possibility of the meter and weight assembly being damaged against the pier or abutment. In some instances, debris will have lodged on or against the pier and this further complicates matters. Where these situations are encountered, it becomes necessary to estimate the depth from the previous vertical and the velocity which is expressed as a percentage of that observed at the previous vertical.

Figure D-18. Typical stream cross-section with numbered verticals, Panel 6 is highlighted.

Figure D-19. Method for selection of edge verticals.