# Applications of the Venturi Effect Equation

### Key Takeaways

• What does the Venturi effect equation actually mean?

• Where is the Venturi effect observed?

• How to best implement the Venturi effect for CFD.

Graphical view of Venturi effect equation

It is often stated that mathematics is the universal language. This assertion is probably derived from the fact that physical phenomena and theoretical concepts may be described by symbols and equations. Although mathematics may be considered a language, its reliance upon graphics is what makes it understandable.

In fact, the ease with which an observation can be expressed in equation form contributes greatly to its usability. For example, equations comprised of often observed and/or used parameters tend to be easily recognizable (graphically) and widely applied (as equations). One such case is where fluid flowing through a pipe is constricted, resulting in corresponding changes in its common parameters–velocity, density, and pressure. This graphic is well understood to represent the Venturi effect equation which is applied widely.

## What Does the Venturi Effect Equation Actually Mean?

The Venturi effect, named after Giovanni Baptiste Venturi–a Renaissance scientist from Italy–is an important concept in fluid dynamics and is applicable to many scientific disciplines. The concept is best exhibited by the Venturi effect equation, shown below.

The equation relates three important fluid parameters: pressure, density, and velocity, as a fluid flow changes from state 1 to state 2 due to a decrease in the area through which it flows. The equation is mathematically equivalent to the following definition:

Definition:

The Venturi effect equation shows that the difference in pressure of a fluid that flows through a reduced cross-sectional area is equal to the change in velocity squared of the fluid–as a result of the constriction–times half of the fluid density.

The Venturi effect equation demonstrates the conservation of mass and momentum for fluids and is utilized to explain fluid behavior for various systems. For example, when applying Bernoulli’s principle to incompressible inviscid flows. As this equation reinforces basic physical laws, it is observable naturally and widely applicable.

## Where Is The Venturi Effect Observed or Applicable?

Believe it or not, river rapids are an example of the Venturi effect occurring

There are many natural occurrences where a fluid flow is forced through a narrower region resulting in increased velocity with decreased pressure.

Venturi effect occurrences in nature:

• Through mountain passes
• Through rapids in rivers
• Increased flow through blood vessels in the body

Additionally, everyday events like doors slamming on their own in windy conditions and the increased wind gusts around tall buildings are examples of the Venturi effect. Many common products also leverage this phenomenon, as listed below.

Common applications of the Venturi effect:

•  Musical instruments
•  Vacuum cleaners
•  Nozzles
•  Carburetors
•  Atomizers
•  Wind tunnels (to study aerodynamics)

The list above is far from exhaustive but does show the wide range of applicability of the Venturi effect for commercial products where fluid flow is involved.

Many systems take advantage of the increased energy that can be produced in conjunction with the Venturi effect equation utilization. For example, hydro and pneumatic energy systems use turbines to generate higher levels of power due to the increasing speed of the fluid flow. The Venturi effect is also employed for system design for CFD simulation and analysis.

## How to Best Implement the Venturi Effect for CFD

For many applications, the Venturi effect is an integral aspect of designing systems that incorporate or are influenced by internal or external fluid flow regimes. This includes energy systems; such as motors, generators or other turbine based equipment. Analyzing the behavior of these systems; however, can be complex, requiring accurate modeling and precise calculations.

Therefore, the best method of applying the Venturi effect equation starts with employing capable analysis tools; such as Cadence’s advanced CFD solvers for turbomachinery. This includes various mesh generation techniques integrated with computational speed and evaluation tools to significantly improve the efficiency of your design and development process.

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Subscribe to our newsletter for the latest CFD updates or browse Cadence’s suite of CFD software, including Fidelity and Fidelity Pointwise, to learn more about how Cadence has the solution for you.

# About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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