Fluid mechanics is a branch of physics that deals with the study of fluids and their behavior under different conditions. All the fluids are substances that can flow and take the shape of their container. This article is an introduction to basic ideas of fluid mechanics, including the properties, classifications, principles, and applications of fluid mechanics.

What are Fluids?

A fluid is a substance that is able to flow and takes the form of its container. In a broader sense, it is of two types: liquid and gas. Liquids are incompressible and have a definite volume, while gases are compressible and do not have a definite volume. Water, air, and oil are some examples of fluids occurring in nature.

Characteristics of Fluids

• A fluid can flow and fill up the shape of the container.
• These materials could be either compressible or incompressible.
• They have a constant volume or have a volume that can change.
• The states in which they can exist are liquid, gas, or plasma.

Classification of Fluids

Fluids can be broadly classified into the following main types based on their physical properties and behavior:

• Liquids: Incompressible fluids of a definite volume that take the shape of their container. Examples include water, oil, and mercury.
• Gases: Fluids with a variable volume that would expand to fill the container completely and take its shape. Common examples include air, oxygen, and nitrogen.
• Plasmas: Plasmas are ionized gases that possess electrical conductivity. Examples include the solar wind and the ionosphere.
• Two-phase fluids: Mixtures of vapours and liquids, for example, steam and its vapours in the air above boiling water.

What is Fluid Mechanics?

Fluid mechanics is the science of fluids under specified conditions, including a change of conditions in pressure, temperature, and flow rate. In its simplest terms, it includes Bernoulli’s equation, Pascal’s law, and conservation of mass, momentum, and energy. These basic definitions help in understanding the behavior of fluids in different situations, for example, in pipes, channels, or open environments.

Fundamental Theorem of Fluid Mechanics

The basic theorem of fluid mechanics is based on the principles of mass, momentum, and energy conservation. It can be derived by:

• Conservation of Mass: For an incompressible fluid, the mass entering a pipe must equal the mass leaving the pipe. Mathematically, this is written:

mass in – mass out = mass accumulating

• Conservation of Momentum: Summation of partial velocity components with respect to space and time equals the fluid density times the acceleration due to gravity. Mathematically, this is written:

∂????/∂???? + ∂????/∂???? + ∂????/∂???? + ∂????/∂???? = ????????

• Conservation of Energy: The total energy of fluid remains constant along a streamline. Mathematically, this can be written as:

???? + 1/2????????² + ????????ℎ = ????????????????????????????????

Where, 

• p is the pressure
• v is the velocity
• h is the height
• g is the acceleration due to gravity.

Formulas of Fluid Mechanics

Some of the important concepts and their formulas is mentioned below:

Bernoulli’s equation

Bernoulli’s equation is one of the basic principles in fluid mechanics. Bernoulli’s Principle yields a relation of pressure, velocity, and potential energy of the fluid in motion. It is given that the sum of the fluid energy at all points across a streamline is constant, and the pressure, kinetic energy, and potential energy summed at all points are equal to a constant. This is derived from the equation of motion and is applied in the analysis of fluid flow in various areas. The formula is as follows:

P + (1/2)ρv² + ρgh = constant

Pascal’s law

Another important principle of fluid mechanics is Pascal’s law, which states that the pressure exerted by a fluid on a surface is directly proportional to the surface area. The law is applied very widely when the fluid is at rest and pressure at some depth in a fluid of constant density is to be ascertained. The law is also used when pressure distribution in any system of fluids is to be analyzed. The mathematical expression is:

P1 = P2

Conservation of Mass

According to the principle of mass conservation in fluid mechanics, mass is conserved within a fluid for a fluid of constant density inside a control volume. This essentially means that the sum of the total mass entering a control volume will be equal to the sum of the total mass leaving the control volume plus the mass stored within the control volume.

This principle is used in the study of fluid flow in those systems in which mass is conserved, such as in open channels and pipes. It has been given as :

ρvA = m

Conservation of Momentum

The conservation of momentum states that, in fluid mechanics, the sum of partial derivatives of the velocity components with respect to space and time is equal to the multiplication of the fluid density and the acceleration due to gravity. The equation is in the form:

 ρvA(v + v’) = m(v’ – v)

Conservation of Energy

The principle of conservation of energy for fluid mechanics is the principle that the total energy of a fluid is conserved down a streamline, suggesting that the summation of internal, kinetic, and potential energy per unit volume is the same. Such a conservation law can be applied to the analysis of the flow of fluids under some conditions in which energy is conserved, such as hydrodynamics and fluid dynamics. The equation is written as:

ΔE = ΔU + ΔK + ΔP

Applications of Fluid Mechanics

Fluid mechanics has numerous applications in various fields. Some of the applications of fluid mechanics is mentioned below:

• Aerospace engineering: Aerospace engineers develop and implement fluid mechanics in the design and analysis of aircraft and spacecraft.
• Civil engineering: Fluid mechanics finds its application in the design and analysis of several structures in the field of civil engineering.
• Chemical engineering: Fluid mechanics deals with designing and analyzing chemical engineering systems like separation and mixing.
• Environmental Engineering: It helps study and predict how natural systems, such as rivers and oceans, will behave.

Conclusion

Fluid Mechanics is defined as a fundamental part of Physics that describes fluids and the way they work under various conditions. The areas where fluid mechanics is applied include aerospace, civil, chemical, and environmental engineering. Good knowledge of the basics of fluid mechanics is one of the prerequisites that need to be in place before you design and analyze a system concerning the fluid.

Also, Check

• Stoke’s Law
• Surface Tension
• Reynolds Number

FAQs on Fundamentals of Fluid Mechanics

What is the basic principle of fluid mechanics?

The basic principle of fluid mechanics is the conservation of mass, momentum, and energy, which governs fluid behavior.

What is fluid mechanics used for?

Fluid mechanics is a science that deals with the study of the behavior of fluids when in motion. It forms the basis of work in many fields, including engineering, meteorology, and biology.

Which method is most commonly used in fluid mechanics for analysis?

The analysis is based mainly on the Navier-Stokes equations, the method of analysis mostly applied in fluid mechanics, which describes the motion of viscous fluid substances.

Is Bernoulli’s principle a concept of fluid mechanics?

Yes, Bernoulli’s principle is a fundamental concept in fluid mechanics that describes the relationship between the pressure and velocity of a fluid in motion.