# Velocimetry

Velocimetry is the measurement of the velocity of fluids, as often used to solve fluid dynamics problems, or to study fluid networks, as well as in industrial and process control applications, or in the creation of new kinds of fluid flow sensors. Methods of velocimetry include particle image velocimetry and particle tracking velocimetry, Molecular tagging velocimetry, laser-based interferometry, ultrasonic Doppler methods, Doppler sensors, and new signal processing methodologies. Temporal integration of velocimetric information can be used to totalize fluid flow. For measuring velocity and length on moving surfaces, laser surface velocimeters are used.

In general, velocity measurements are made in the Lagrangian or Eulerian frames of reference (see Lagrangian and Eulerian coordinates). Lagrangian methods assign a velocity to a volume of fluid at a given time, whereas Eulerian methods assign a velocity to a volume of the measurement domain at a given time. A classic example of the distinction is particle tracking velocimetry, where the idea is to find the velocity of individual flow tracer particles (Lagrangian) and particle image velocimetry, where the objective is to find the average velocity within a sub-region of the field of view (Eulerian).

## Methods

Velocimetry can be traced back to the days of Leonardo da Vinci, who would float grass seeds on a flow and sketch the resulting trajectories of the seeds that he observed (a Lagrangian measurement). Today the basic idea is the same; the flow must be seeded with particles that can be observed by the method of choice. The seeding particles depend on many factors including the fluid, the sensing method, the size of the measurement domain, and sometimes the expected accelerations in the flow.

The fluid generally limits the particle selection according to its specific gravity; the particles should ideally be of the same density as the fluid. This is especially important in flows with a high acceleration (for example, high-speed flow through a 90-degree pipe elbow). Heavier fluids like water and oil are thus very attractive to velocimetry, whereas air ads a challenge in most techniques that it is rarely possible to find particles of the same density as air.

Still, even large-field measurement techniques like PIV have been performed successfully in air. Particles range from droplets of oil or water generated with an atomizer (diameters in the micrometre range) to helium-filled soap bubbles (diameters in the millimetre range). For point measurements like laser Doppler velocimetry, particles in the nanometre diameter range, such as those in cigarette smoke, are sufficient to perform a measurement.

In water and oil there are a variety of inexpensive industrial beads that can be used, such as silver-coated hollow glass spheres manufactured to be conductive powders (tens of micrometres diameter range) or other beads used as reflectors and texturing agents in paints and coatings. The particles need not be spherical; in many cases titanium dioxide particles can be used.