Stream gauging with calibration equation

The data table was not printed in the paper, so the full method is shown; the student puts in the given values.

Principle

Discharge is found by the velocity–area method: the cross-section is divided into vertical segments, the velocity in each is measured by a current meter, and

$$Q = \sum \Delta Q_i = \sum w_i\,y_i\,\bar{V}_i$$

Steps

1. Revolutions per second at each vertical: $N_i = \dfrac{\text{revolutions}}{\text{time (s)}}$.
2. Velocity at 0.6 depth from the calibration equation:

$$V_i = 0.55N_i + 0.04\ \text{m/s}$$

The velocity at 0.6y below the surface is taken as the mean velocity of that vertical. 3. Width of each segment (mid-section method):

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

where $x$ is the distance of the vertical from the bank. 4. Segment discharge: $\Delta Q_i = w_i\,y_i\,V_i$. 5. Total discharge: $Q = \sum \Delta Q_i$. The edge verticals (depth 0) give zero flow.

Table layout

Illustration

For a vertical at 4 m (neighbours at 1 m and 7 m) with depth 2.5 m and 60 revolutions in 100 s: $N = 0.6$ rev/s, $V = 0.55 \times 0.6 + 0.04 = 0.37$ m/s, $w = (7 - 1)/2 = 3$ m, $\Delta Q = 3 \times 2.5 \times 0.37 = 2.775$ m³/s.

Repeating for every vertical and adding gives the stream discharge. (For the similar question with verticals at 1, 4, 7 and 10 m from the left edge, this method gives Q ≈ 10.99 m³/s.)