Vortex Flow Meter Formula

To understand the principles and formulas behind the vortex flow meter we need to have a basic knowledge of the history behind it. The pioneers of the study of the behavior of liquids are the ancient Greeks, mainly Archimedes and Aristotle. They understood the motion as something, let’s call it a medium, following, rushing behind the body to assure the flow, ergo preventing the formation of a vacuum.

The next big step came in the person of John Philoponos in the sixth century, who theorized that the body gains impetus, which is a property of the moving body, and when it seizes to exist the body stops.

We can’t have a background lesson on flow meters without mentioning Sir Isaac Newton’s name, especially since a type of flow meters is directly based on his angular motion law, and in 1742 it was proven by Rond d’Alambert that Newton’s third law applies to objects in motion too.

The breakthrough was achieved by Bernoulli’s Hydrodynamica published in 1783. Bernoulli’s theorem states that an increase in velocity creates a decrease in static energy, and that is why a flow restriction causes an elevated flowing velocity and low value of static pressure of the same flowing fluid.

The last breakthrough came with the name of Theodore van Karman, whose observations led at a hike subsequently led to the development of vortex flow meters. He realized that if he puts a non-streamlined object in the water or other fast-flowing streams, this fluid will separate and flow on the object’s sides and at the end it curves back.  He used rocks as object and found that these create traveling vortices, which had constant distance between them. He was the one that looked up and saw the same principle in the movement of a flag. His book was published in 1968 and the first vortex flow meter was sold in 1979.

Nowadays the formula for the volume flow rate is:

Where fv = frequency of vortex shedding

w = width of the bluff/pipe

D = diameter of the pipe

S = Strouhal numbers (determined experimentally)

K = the compensation for the non-uniform state of the pipe flow

As you could see the formula is not a child’s play, and that is one reason why usually the flow is calculated by a computer or other machines, this ensures the accurate, and reliable result.