### 2D monostatic velocity measurement

The monostatic technique consists in measuring the projection of the velocity vectors over two different beam axis and to combine pairs of measuring cells in order to compute the velocity components of the profile in an orthonormal coordinate system (x, y).

The figure below presents an example of installation adapted to the 2D velocity profile measurement in a pipe (diameter 1000 mm). Two transducers (diameter 20mm) oriented symmetrically to the cross-section of the flow (yellow acoustic beams oriented with angles of 75° and 105°). The transducers are plugged into the UB-Lab laboratory profiler. The measurement cells of each beam (yellow slice in the below figure) are gathered by pairs along the main flow axis and become the 2D measurement cell (blue slice), leading to a profile of 2D vectors. The fluid's velocity V in a cell, with an angle α to the main flow direction, can be observed through its two projections V_{p1} et V_{p2} along the acoustic beam axes. The norm V and the angle α of the velocity vector can then be calculated through trigonometric relations. This technique can also be used with the UB-Flow field profiler, which has 2 transducers with angles 65° and 97°.

With the UB-Flow for example (see illustration below), for each pair of measurement cell, the two projection V_{1} and V_{3} of the velocity vector can give the following two components (in the (X_{v};Y_{v}) orthonormal coordinate system) :

V_{x} = 1.873 V_{1} − 1.710 V_{3}

V_{y} = −0.2300 V_{1} − 0.7975 V_{3}

The norm V and the angle α of the velocity vector are then given by:

∣V∣=√(V_{x}² + V_{y}²)

α = arctan( V_{y} / V_{x} )

This technique only works when combining average velocity values. In turbulent flows, the instantaneous velocity values are too different in the two cells.