Fluid flow. Velocity, pressure, flow rate and Bernoulli’s principle

Properties of fluid flow

The fluid flow is described in terms of velocity, pressure and flow rate. Flow velocity refers to how fast the fluid particles move in a given direction. It can be measured in terms of average velocity or velocity at a specific point. Pressure, on the other hand, is the force that the fluid exerts on a surface. As the fluid flows, pressure can change due to varying velocity and flow geometry. Flow rate is the amount of fluid passing through a given point in a given time interval and is measured in volume per unit time.

Types of flow

The fluid flow  can be laminar or turbulent.

Laminar flow

In a laminar flow, the fluid particles move in orderly and parallel layers, without significant interruptions.

Turbulent flow

On the other hand, in a turbulent flow, the fluid particles move chaotically and eddies and vortices are generated. The type of flow depends on factors such as fluid velocity, viscosity and system geometry.

Fundamental principles of fluid flow

To understand how fluids behave in motion, it is essential to know two basic principles: conservation of mass and conservation of energy. These principles are expressed by the continuity equation and Bernoulli’s principle, which allow us to analyze and predict the behavior of flow in different situations.

Fluid flow continuity equation

The continuity equation is fundamental to understanding fluid flow because it states that the amount of fluid entering a pipe or conduit is equal to the amount leaving it, provided there are no leaks or accumulation. Mathematically, it is written as follows:

A₁ × v₁ = A₂ × v₂

where

A₁ and A₂ are the cross-sectional areas of the conduit at two different points

v₁ and v₂ are the fluid velocities at those points

This equation indicates that the product of area and velocity remains constant, i.e., if the conduit narrows (smaller area), the fluid velocity increases so that the amount of fluid passing through the conduit remains the same. This is essential for understanding how fluids behave in pipes, rivers, or any system where the space for flow changes.

Bernoulli’s principle

Bernoulli’s principle states that for an ideal fluid moving along a streamline, the sum of the pressure P, the kinetic energy per unit volume 1/2ρv2, and the gravitational potential energy per unit volume ρgh remains constant. Mathematically, it is expressed as follows:

P + 1/2ρv2 +ρgh = constant

Where:

P is the fluid pressure,

ρ is the fluid density,

v is the fluid velocity,

g is the acceleration due to gravity,

h is the height relative to a reference point.

This equation shows that if the fluid velocity increases, the pressure or height must decrease to conserve total energy. It is essential for understanding phenomena such as lift on airplane wings, the operation of Venturi tubes, and the dynamics of rivers and pipes.

Applications of fluid flow

The study of fluid flow has applications in a variety of areas. In engineering, it is crucial to understand the flow of liquids and gases in systems such as pipes, ducts and channels to design efficient systems and prevent problems such as clogging or corrosion. In addition, fluid flow is fundamental in aerodynamics, in the design of vehicles, aircraft and turbines, as well as in meteorology, to understand the behavior of the atmosphere.