# The Venturi Effect and Bernoulli's Principle

### Key Takeaways

• The Venturi effect describes how the rate of fluid flow in an enclosed system changes as the flow enters a constricted channel.

• This change in fluid flow rate through a channel can be described using Bernoulli’s principle.

• The Venturi effect and Bernoulli’s equation makes statements about conservation of energy, conservation of momentum, and conservation of mass. These channels in this heat sink constrict airflow and cause the Venturi effect

An important effect from fluid dynamics that is used in heat sink design is the Venturi effect. The large posts and fins used in modern heat sinks certainly look interesting, but they have a practical purpose that encourages heat transfer into a nearby flowing fluid within the constricted channels in a heat sink. When heat sink designers create these channels in a heat sink, they are taking advantage of the Venturi effect to encourage higher heat transfer into the surrounding fluid flow.

The Venturi effect can be explained in terms of another important principle from fluid dynamics, known as Bernoulli’s principle. The Venturi effect and Bernoulli’s principle are related through fundamental conservation laws (energy, mass, and momentum) that underlie all areas of mechanics and dynamics. In this article, we’ll dig deeper into how these effects arise in CFD simulations and how simulation data can be used with Bernoulli’s principle.

## Explaining the Venturi Effect With Bernoulli’s Principle

The Venturi effect and Bernoulli’s principle are related to each other through conservation laws. Specifically, we have the Venturi effect arising from conservation of momentum and conservation of mass. Bernoulli’s principle is a general statement about conservation of energy in laminar flow. Taken together, we can explain one of these effects in terms of the other. Both effects can be derived from the Navier-Stokes equation if desired, or they can be identified in CFD simulations.

### Venturi Effect

The Venturi effect is a somewhat counterintuitive observation that the rate of laminar fluid flow through an enclosed system, such as a pipe, increases as the fluid encounters a constricted region. This is illustrated in the graphic below, where the laminar flow in a pipe is being driven by a pressure gradient, and the flow encounters a constricted region along the flow direction. Within this region, there is a pressure drop and a resulting flow rate increase within this section of the pipe. The Venturi effect relates the pressure along an enclosed flow (in a pipe) to the flow rate through the pipe.

This might seem counterintuitive because the constricted region looks like it should be an obstacle (such as a baffle), so one would be tempted to think that the flow rate should decrease rather than increase. However, this would violate conservation of mass and conservation of momentum. Instead, in order to ensure the mass flow rate is conserved, meaning the continuity condition in the Navier-Stokes equation is satisfied, the flow rate must increase through this region. This ensures that, once the constriction region is passed, the flow rate can be restored to its initial lower value and momentum is conserved throughout the flow region.

### Bernoulli’s Principle

Next, we can explain the Venturi effect in terms of Bernoulli’s principle. When studying steady incompressible inviscid flows, Bernoulli’s principle is used to describe the relationship between pressure, density, fluid velocity per unit mass, and potential energy (normally just gravitational) per unit mass along a given streamline in a laminar flow. The following equation can be derived for flows along a given streamline: Bernoulli’s principle

The gz term accounts for gravitational potential energy. However, in general, this could be a potential function for any conservative forces acting on the fluid.

The above equation defining Bernoulli’s principle is system-specific. In other words, the constant that is derived in one portion of the system is not the same constant found in every other system, thus the magnitudes of changes in flow parameters in different systems will not be the same. However, the polarity of changes will be consistent in any system, which should illustrate the universality of Bernoulli’s principle.

From Bernoulli’s principle, we should now see how the Venturi effect occurs. As the flow moves into the constricted region, there will be a pressure drop. If we have a decrease in pressure for an incompressible flow along a given streamline, then the velocity must increase in order to keep the RHS of Bernoulli’s principle constant. This explains why the flow rate increase observed in the Venturi effect occurs. Just from the basic flow rate solution in laminar flow, it should also be obvious that the pressure gradient increases in the constricted region, thus the flow rate should increase.

## Investigating the Venturi Effect in CFD Simulations

The Venturi effect isn’t quantified directly in CFD simulations, but it can be identified by looking at streamlines in a laminar flow simulation. A system that can drive a higher fluid flow along narrow channels is important in applications involving convective heat transfer. In a CFD simulation, the streamlines can be visualized directly from the flow’s velocity field, and a collapse of streamlines into a narrow channel indicates where the Venturi effect will become dominant.

Once these regions are found in the flow field results, one can read off the pressure, velocity, and density data from the simulation results. If you wanted, you could use these values in Bernoulli’s principle to calculate the associated constant for the flow field. This value will be important for system design because, if any of the parameters in the Venturi-dominant region were to change (such as cross-sectional area), you could calculate how the flow rate will change. Your CFD simulation software should extract streamlines so they can be visualized clearly.

This process gives a simple way to iterate through slight adjustments to a system and determine some changes to the flow behavior without running multiple simulations. Each CFD simulation that is run for a system requires significant computational power, even if implemented with low resolution. Applying some basic equations to laminar flow simulation results is one way to speed up analysis and infer important modifications to system-level design without sacrificing simulation accuracy.

When you need to investigate the Venturi effect and Bernoulli’s principle, you can build and run high-accuracy CFD simulations using Omnis from Cadence. Modern numerical approaches used in aerodynamics simulations, turbulent and laminar flow simulations, reduced fluid flow models, and much more can be implemented in Cadence’s simulation tools.