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Exploring the Venturi Effect: Pressure and Velocity Relations

Key Takeaways

  • The Venturi effect explains how the increase in velocity of a fluid causes the pressure to decrease. 

  • The Venturi effect and Bernoulli’s principle fulfill the principle of conservation of energy, mass, and momentum.

  • CFD simulations provide deeper insight into the Venturi effect on the relationship between pressure and velocity, facilitating design efficiency. 

A water flow channel depicting the Venturi effect on pressure

A Venturi flow channel

Have you felt the water pressure when placing your thumb at the end of a garden hose? This has to do with the pressure and velocity of a flowing fluid when passing over a reduced cross-sectional area. This phenomenon can be explained by the Venturi effect, which states that the increase in velocity of a fluid causes the pressure to decrease following the principle of conservation of mechanical energy. The design of aircraft wings or natural ventilation systems in buildings is based on this principle. In this article, we will explore Bernoulli’s principle and the Venturi effect, pressure, and velocity relations for subsonic flow. 

Bernoulli’s Principle and the Venturi Effect

The basic assumption made for the pressure and velocity relation of a fluid is that when a fluid flows at a high speed through a narrow constriction, the pressure of the fluid should increase as well. However, fluids act differently from this assumption.

Bernoulli’s principle is based on the principle of conservation of energy, according to which, in a  steady, streamlined flow, the sum of all energy (kinetic, potential, and internal energy) should remain constant at all points. This means for an increase in kinetic energy, there should be a decrease in potential energy, i.e., the static pressure. This is Bernoulli’s principle, which can be expressed mathematically as:

Bernoulli’s equation

The above equation is true for incompressible, steady, and viscous flow. Note that:

v is the velocity of the fluid

g is the gravitational acceleration  

z is the elevation of the reference point

p is the pressure at the reference point

ρ is the density of the fluid

This principle is useful in explaining the Venturi effect, which establishes how the pressure and velocity of the fluids change when passed through a reduced cross-sectional area.

Let us explain this using a Venturi meter as an example. The Venturi meter enables the flow within but has a convergent cross-section in the middle called the throat. Following the principle of conservation of mass, the pressure build-up at the inlet tries to push the fluid with higher velocity. A significant pressure difference can be noted between the pipe inlet and at the throat. At the throat, a significant drop in pressure is seen to accommodate for the increase in flow velocity. 

  Illustration of pressure and velocity relation in a Venturi meter

This is the Venturi effect

The Venturi Effect, Pressure, and Velocity 

In order to better understand the Venturi effect and pressure and velocity relations, we can consider the following mathematical equation:

 The Venturi effect–pressure and velocity relations

The above equation is derived from Bernoulli’s principle to address the Venturi effect. The equation illustrates that with a drop in pressure, there is an increment in velocity and vice-versa. 

Understanding this relationship is important in process control and for the safer operation of industrial plants. The flow rate can also be identified, deriving from the above formula as:

Flow rate formula in a Venturi tube

CFD Simulation Simplifies Pressure and Velocity Relations

When studying water flow through a pipe or airflow behavior along an airfoil, the pressure drop and velocity relations are important parameters to be exploited. When the flow system consists of a varied cross-section, this relation can be explained by the Venturi effect.

Using a CFD model to simulate the Venturi effect is an ideal way to analyze the relationship between pressure and velocity. CFD tools facilitate the numerical modeling of the Venturi effect, which allows engineers to analyze the relationship between pressure and velocity for a wide range of Reynolds numbers. In the analysis of the Venturi effect, pressure contours and velocity contours can be visualized, which explains the pressure gradient and flow rate across the Venturi flow system. By analyzing these attributes of the Venturi effect, pressure and velocity limits can be set to ensure design efficiency.

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