Vertical/horizontal control, stream velocity

Vertical and horizontal control

• Horizontal control: a network of points (stations) whose plan positions, i.e. coordinates, are established accurately by triangulation, traversing or GPS. Details are located from them.
• Vertical control: a set of benchmarks and points whose elevations above a datum (mean sea level) are fixed accurately by levelling. Contours, sections and levels are referred to them.

Measurement of velocity and flow of a stream

1. Select a straight reach of uniform section, and set out a cross-section line across the stream.

2. Cross-sectional area: measure the width with a tape or by ranging, take depths (by sounding rod, echo sounder or levelling) at regular intervals $b$ across the section, and find the area by the trapezoidal rule:

$$A=\sum \frac{(d_i+d_{i+1})}{2}\,b$$

3. Velocity by one of these methods:

• Float method: use a surface float (a bottle or an orange). Mark a length $L$ of the reach (about 30 m) and time $t$ the float takes to cover it. Surface velocity $v_s=L/t$ (mean of several trials). The mean velocity is $v_m=k\,v_s$ with $k\approx0.8$ to $0.9$.
• Current meter: hold the meter at 0.6 of the depth below the surface (which gives the mean velocity), or take readings at 0.2 and 0.8 of the depth and average them. The velocity comes from the meter's rating equation $v=a\,N+b$, where $N$ is the revolutions per second.

4. Discharge: divide the whole section into strips and add up:

$$Q=\sum A_i\,v_i$$

or, for a single section, $Q=A\times v_m$.

Check the work by repeating the observations, and repeat at different times or stages to obtain the stage-discharge relation.