Fluid dynamics is one of the two categories of fluid mechanics, a branch in physics concerned with fluids in either a rested state or in motion. In this article, we will dive into the basics of fluid dynamics, the subdiscipline of fluid mechanics focused on fluid in motion.

Fluid dynamics is a complex field of study, with a wide range of applications. Engineers and scientists use fluid dynamics to solve critical problems, improve existing technologies, and innovate new solutions. Understanding these principles led to advancements in areas such as aerodynamics, hydrodynamics, meteorology, and technologies in our everyday lives.

What is Fluid Dynamics?

Fluid dynamics is a branch of physics and mathematics that focuses on the behavior of fluids (liquids and gasses) in motion. It examines the forces and interactions that influence how fluids flow and change. In layman's terms, fluid dynamics looks at how fuel moves through an engine, how air moves around an airplane wing, and how blood circulates through our bodies. It answers questions like how submarines navigate underwater, why weather systems form, and how to make pipelines more efficient.

Fluids and Their Properties

A fluid is a substance that can flow and take the shape of the container that it is in. Liquids and gasses are both considered “fluids” with each of them having their own distinct properties. The main difference between the two types of fluids is their molecular structure and behavior.

Difference Between Liquids and Gasses

Liquids are made up of tightly packed molecules that are attracted to each other. The compact molecules give liquids a definite volume. They will take the shape of the container they are in, but they don’t easily compress. Think of a glass of water. The water takes the shape of the glass, filling it from the bottom up and spreading out to the sides. If you pour the water into a different container, it will take the shape of the new container with the volume remaining the same.

Gasses are made up of molecules that are widely spaced from one another and constantly moving and colliding with each other. Unlike liquids, gasses do not have a definite shape or volume and will expand to fill any container they're in. They are also highly compressible. Think of a balloon filled with air. The molecules inside spread out to fill the entire space of the balloon. When you squeeze the balloon, the gas inside gets compressed, pushing the molecules closer together and reducing the volume of the balloon. If you let the air out, the gas escapes and spreads out to fill the room, showing how gasses can expand to occupy any available space.

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Key Properties of Fluids

Fluids possess different properties which are classified as kinematic properties (motion of fluids without considering the forces causing the motion), thermodynamic properties (state of the fluid and its energy content), and physical properties (physical state and appearance of the fluid).

Kinematic Properties

• Velocity: Speed and direction the fluid particles are moving with respect to time
• Acceleration: Rate of change of the fluid's velocity with respect to time

Thermodynamic Properties

• Temperature: Average kinetic energy of the fluid molecules
• Pressure: Force exerted by the fluid per unit area on its surroundings
• Density: Mass of the fluid per unit volume

Physical Properties

• Viscosity: The internal resistance to flow
• Surface Tension: The elastic tendency of fluid surfaces
• Buoyancy: Ability of fluids to exert an upward force on objects

Types of Fluid Flow

Fluid flow is the movement of liquid or gas particles in a particular environment. The primary types of flow are laminar and turbulent. These two types are classified based on the nature of the flow itself.

Primary Types of Fluid Flow (Based on Behavior)

Image source - NASA Glenn Research Center

Laminar (Streamline) Flow

Liquid flows in smooth, parallel layers, with minimal mixing between the layers. This type of flow is characterized by low velocities and high viscosity.

Turbulent Flow

Whereas laminar flow is smooth and predictable, turbulent flow is chaotic and random. The fluid flow is irregular with eddies, swirls, and fluctuations in velocity and pressure. This type of flow is characterized by high velocities and low viscosity.

Additional Classifications (Based on Properties)

There are additional fluid flow types which are classified based on specific characteristics such as steadiness, compressibility, and viscosity.

Steady vs. Unsteady Flow

• Steady Flow: Fluid properties (velocity, pressure, etc.) remain constant at any given point over time.
• Unsteady Flow: Fluid properties vary with time at a given point.

Compressible vs. Incompressible Flow

• Compressible Flow: Fluid density varies significantly with pressure (common in gasses)
• Incompressible Flow: Fluid density is constant (common in liquids)

Viscous vs. Inviscid Flow

• Viscous Flow: Fluid molecules transfer momentum between layers due to their viscous properties. Layers nearer the surface move slower than the layers further away.
• Inviscid Flow: An idealized model that assumes the fluid has zero viscosity and viscous forces are negligible. (ideal fluid flow)

Transitional Flow

Transitional Flow: Mixes characteristics of both laminar and turbulent flows. It often occurs during the transition between the two.

Beyond the Basics

Most of this article covers the basics of fluid dynamics, but there are a few terms and principles worth briefly touching on when discussing fluid dynamics.

Bernoulli's Principle

Image - Jacques and Jean Bernoulli working on geometrical problems

This principle describes the relationship between the pressure and velocity of a fluid in motion. Basically, as the speed of a fluid increases, its pressure decreases. This is how airplane wings generate lift, why shower curtains pull inward when water is running, and how a pitcher can get a curveball to drop down.

Reynold's Number

Reynold's Number (Re) is a dimensionless number used to predict the type of flow (laminar or turbulent) in different situations. Low Reynold's numbers indicate laminar flow, while high Reynold's numbers indicate turbulent flow. This is useful for determining things like the appropriate pipe diameter and pumping pressure for transporting fluids like oil or water and in aircraft design to make wings that minimize drag and maximize lift.

A dimensionless number is a number that represents a relationship between two or more things, without being tied to any specific units of measurement.

The Reynolds number is calculated using the following formula:

Re = (ρ * V * L) / μ

Where:

• Re is the Reynolds number, which is dimensionless
• ρ (kg/m³) is the density of the fluid
• V (m/s) is the characteristic velocity of the flow
• L (m) is the characteristic length scale of the flow (e.g., diameter of a pipe)
• μ (Pas) is the dynamic viscosity of the fluid

Pascal's Law

Pascal's Law states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid and to the walls of the containing vessel. This principle is the basis for hydraulic systems, such as hydraulic lifts and brakes, which use fluids to transmit force and power.

Continuity Equation

What goes in must come out. The continuity equation states that, for any incompressible fluid, the mass flow rate must remain constant from one cross-section of a pipe to another. As a section narrows, the fluid must speed up to maintain the same flow rate. For example, when a river flows through a canyon, the water speeds up to maintain the same flow rate.

Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a powerful tool for predicting and visualizing fluid flow. It uses computers to simulate and analyze fluid flow using complex calculations and algorithms. This allows engineers and scientists to test and optimize designs virtually before building physical prototypes, saving time and resources. CFD plays a crucial role in various industries where designing more efficient and reliable products is paramount, including aerospace, automotive, and energy.

Examples - How are Fluid Dynamics Used in Real Life?

Fluid dynamics isn't just a theoretical concept that you’ll only find in college textbooks and labs. It's all around us, playing a major role in everyday life and cutting-edge technology:

• Transportation:
  • Airplanes: The shape of airplane wings are designed using principles of fluid dynamics to create lift. This is what allows these massive vehicles to soar through the air. The principles of fluid dynamics are also applied in the design of pneumatic systems in aircraft, where pneumatic solenoid valves play a crucial role in controlling airflow
  • Cars and Trucks: Fluid dynamics helps optimize the design of vehicles to reduce drag and improve fuel efficiency.
  • Ships and Submarines: The shape of a ship's hull and the design of submarines are carefully crafted to minimize resistance to move smoothly through water.
• Weather and Climate:
  • Weather Forecasting: Fluid dynamics models are used by meteorologists to predict weather patterns, including the formation and movement of storms.
  • Climate Modeling: Scientists use fluid dynamics to understand ocean currents, atmospheric circulation, and other complex phenomena that influence our planet's climate.
• Energy:
  • Wind Turbines: The design of wind turbine blades relies on fluid dynamics to maximize energy capture from the wind.
  • Hydroelectric Dams: The flow of water through turbines in dams generates electricity, and fluid dynamics principles play a major part in designing efficient hydroelectric systems.
• Medicine and Biology:
  • Blood Flow: Understanding how blood flows through our arteries and veins is crucial for diagnosing and treating cardiovascular diseases.
  • Drug Delivery: Fluid dynamics helps design drug delivery systems that ensure medications reach their target sites in the body effectively.
• Everyday Life:
  • Plumbing Systems: The flow of water through pipes in our homes and cities is governed by fluid dynamics. Understanding fluid dynamics allows engineers to design plumbing systems with the most efficient water flow that also prevents leaks and other problems.
  • Sports: Fluid dynamics plays a role in the design of sports equipment like golf balls and swimsuits, aiming to reduce drag and enhance performance.
  • Inkjet Printers: These printers use tiny nozzles to eject precise droplets of ink onto paper, a process governed by fluid dynamics.

Simple Experiments to Try at Home

Just for fun, here are some ways to see fluid dynamics in action at home.

Bernoulli’s Principle with a Piece of Paper

• Materials Needed: A piece of paper.
• Steps: Hold the paper by the edges and blow across the top surface. Watch how the paper rises.
• Explanation: Blowing across the top of the paper increases the airspeed above the paper, reducing pressure and causing the paper to lift. This demonstrates Bernoulli's Principle in action.

Laminar vs. Turbulent Flow with Food Coloring

• Materials Needed: Clear glass, water, food coloring, a spoon.
• Steps: Fill a clear glass with water. Add a drop of food coloring without stirring and observe how it moves through the water. Then, stir the water with a spoon and observe how the food coloring spreads.
• Explanation: Initially, the food coloring moves slowly and smoothly, showing laminar flow. When you stir, the movement becomes chaotic and mixes quickly, illustrating turbulent flow.

Surface Tension with a Needle

• Materials Needed: A bowl of water, a needle, tissue paper.
• Steps: Fill the bowl with water. Place a small piece of tissue paper on the water's surface, and then carefully place a needle on top of the tissue paper. Once the tissue sinks, the needle should stay afloat.
• Explanation: The needle floats due to the surface tension of the water, which creates a 'skin' strong enough to support the needle.

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