Area-velocity method and mid-section method

Area-velocity method: procedure

The discharge at a river section is $Q = \int v\,dA$, found by measuring velocity at many points of the cross-section.

1. Select a site on a straight reach with stable bed, parallel flow and a gauge nearby.
2. Mark the section with a tagged cable, rope or bridge markings. Record the stage.
3. Divide the width into 15 to 30 verticals so that no strip carries more than 10 % of the flow (closer verticals where depth varies strongly).
4. At each vertical, measure the depth (sounding rod or weight) and the velocity with a current meter held at 0.6 d (shallow) or at 0.2 d and 0.8 d (deeper) for 40 to 60 s. The velocity $v = aN + b$ from the revolutions $N$ per second.
5. Compute the mean velocity of each vertical, the area of each strip, and sum the partial discharges.

Mid-section method

Each measured vertical is assumed to represent a strip extending half-way to the verticals on either side.

   water surface
 ___|_____|_____|_____|___
 \  |  d1 |  d2 |  d3 | /
  \ |     |     |     |/
   b(i-1)  b(i)  b(i+1)
        <--w_i-->

Width of strip $i$:

$$w_i = \frac{b_{i+1}-b_{i-1}}{2}$$

Partial discharge:

$$q_i = v_i\,d_i\,w_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2}$$

Total discharge:

$$Q = \sum_{i=1}^{n} q_i$$

where $v_i$ is the mean velocity in the vertical and $d_i$ the depth at that vertical. The end verticals at the banks have zero depth. This is the method normally used because it is simple and does not need a separate area calculation.