First, let's have some explanation For questions and remarks, don't hesitate to use the Forum !

Venturi's effect

The well-known phenomenon of mechanics of the fluids bears the name of an Italian physicist, Giovani Battista Venturi. This one established that when the flow of a fluid undergoes a contracting its pressure drops. Extremely of this report, G B Venturi designed a device making it possible to measure the flow passing in a drain. The famous conduit with divergent cones which bears its name had been born: VENTURI (c.f.: illustration below) This invention is always used - in particular in industry to control the flows of fluids. Nonintrusive, it is also appreciated for its reliability and its robustness (a differential barometer - today a differential sensor of pressure - is enough!).

How does it work ? Let's have some theory

The Swiss physicist Daniel Bernoulli (1700-1782) established the following simplified equation:

V²/2 + P/rho + g.z = Constant (known as "Bernoulli's equation")

- V : flow rate at some point (m/s)
- P : flow pressure at the same point (Pascals : Pa)
- z : altitude of the point (m)
- rho : density of the fluid (kg/m^3). A quick reminder: : 1000kg/m^3 for pure water, 1,2 kg/m^3 for air, in "normal" condition
- g : acceleration of gravity (about 10 m/s²)

Remark :

Let's note that the equation is valid for nonviscous fluids, incompressible and in permanent flow.
This formula can be shown starting from the Navier-Stokes equations subject to these assumptions. (Demonstration within request).

Let us consider the flow of a fluid in a drain between two items (noted 1 and 2).

The application of the theorem of Bernoulli leads to:

V1²/2 + P1/rho + g.z1 = Constant = V2²/2 + P2/rho + g.z2

Let's notice whereas the flow Q (in m^3/s) is equal to the product of the section S of the drain (in m²) by the speed V of the fluid (in m/s). Like there is no escape with the drain, the Q1 flow as in point 1 is equal to the flow as in point 2: Q2.

That's lead to : S1.V1 = S2.V2, or even : V2 = V1.S1/S2

With the Bernoulli's equation, we can deduce that:

V1² = 2.[ (P2-P1)/rho + g.(z2-z1) ] / [ 1 - (S1/S2)²]

And so, if we know :

- sections of the drain (S1 and S2),
- the possible difference in altitude (z2-z1) between the points of measurement (in practice often null),

it is enough to measure with a differential barometer (instrument very running in industry) the difference in pressure (P2-P1) to deduce the speed of the V1 fluid immediately in the drain.

Now, the simulator...

This simulator came from the Professor S.A. Kinnas (Courtesy of Prof. S.A. Kinnas, UT Austin). Many thanks to him!

Facts :

The difference in section between R1 and R2 generates a difference in pressure which one visualizes by the heights of water columns PH1 and PH2. Measurement TH corresponds to the impact pressure (on the level of the point located vis-a-vis at the flow, speed is null, therefore the pressure is maximum). Let us note that the pressure "TH" depends only on the flow and not on the S2 section of the drain.