Determination of water discharge

Base equation

The discharge Q is the volume of water V flowing through a cross Section of a river per time unit t. Therefore the dimension is m³/s, l/s, ft³/s or m³/day.

By applying the continuity equation the expression above can be transformed into the base equation of the discharge measurement:

where A is the wetted cross-Sectional area and vm the mean flow velocity.

The integrated velocity radar sensor measures the local velocity vl at the water surface and not the mean velocity vm. Therefore, a dimensionless correction factor k has to be implemented to calculate the mean velocity from the local velocity:

The k-factor depends on the flow conditions and consequently on the water level W. Its usual range is 60 to 90 % of vl. In combination with the base equation the discharge is calculated:

For the SQ a discharge table is generated from the cross-Sectional areas A(W) and the k-factors k(W) for different water levels. This table is stored in the SQ sensor and is the basis for the discharge calculation. It is essential that the water levels of the discharge table correspond to the same reference as the water level measurement of the SQ sensor.

k-Factors

The k-factors are determined by numerical hydraulic modelling. The k-factors mainly depend on the water level, the shape of the channel/river cross-Section, the turbulence of the flowing water and the mounting position of the SQ sensor. By applying a hydraulic model the total water level range can be determined and the discharge calculated from the time of installation. As the k-factors are site-specific they have to be determined for each measurement site.

The PC software SQ-Commander by Sommer Messtechnik can be used to compute k-factors based on hydraulic modelling. Additionally, reference measurements can be used to verify and correct modelled k-factors.

Cross-Sectional area

The cross-Sectional area A(W) as a function of the water level is calculated from the channel/river profile. A(W) values can be computed with the software SQ-Commander by Sommer Messtechnik.

Discharge calculation

The water discharge is calculated from the measured values of W and v_l using the discharge table stored in the SQ sensor. The following scheme illustrates this procedure:

Figure 5 Discharge calculation scheme