What is Fluid Mechanics?

The search for the knowledge of fluid phenomena started when human began his search for water, waterpower, navigation and irrigation. In general, matter exists in two states in our surroundings: solids and fluids. Fluid state is further bifurcated as liquids and gases. The main differences between these states are the spaces and movement between the respective molecules. The spaces and movement of the molecules is found high in gases, medium in liquids and very less in gases indicating high cohesive forces in solids and least in gases.

Fluid mechanics is a branch of continuum mechanics (study of continuous materials) deals with the study about the forces and mechanics of fluids such as liquids, gases and plasmas. As fluids play important role in day-to-day life, its studies have wide range of application in various fields such as meteorology, biology, oceanography, biomedical engineering and other fields of engineering. Fluid mechanics is bifurcated as fluid statics and fluid dynamics. Fluid statics is the study of fluids which are at rest and fluid dynamics which rolls around the effect of forces on fluids when in motion. Fluid mechanics designs matter in the point of macroscopic and not under microscopic viewpoint.

History

Fluid mechanics got importance long bank in the days of ancient Greece, when fluid statics and buoyancy were investigated and formulated a famous law named ‘Archimedes principle’. Further advancement was developed by Leonardo Da Vinci, barometer by Evangelista Torricelli, viscosity by Isaac Newton, Pascal’s law and hydrostatics by Blaise Pascal and Hydrodynamics by Daniel Bernoulli. Further many scientists worked on in viscid flow, viscous flow, fluid viscosity and turbulence.

What are Fluid Statics and Fluid Dynamics?

The branch of fluid mechanics which deals with the study of the properties of fluids during their rest state is termed as fluid statics or hydrostatics. Few physical day-to-day examples for this phenomenon are changes in atmospheric pressure with altitude, floating of wood and oil on water, why fluid takes the containers shape etc. It is the fundamental phenomenon involved in hydraulics which is equipment for transportation and usage of fluids.

The other major sub-discipline of fluid mechanics that deals with the properties of fluids while in motion is termed as fluid dynamics. This phenomenon involves determining the various properties of fluids such as velocity, pressure, density, and temperature etc., as a function of time or space. It is further divided into sub-disciplines such as aerodynamics and hydrodynamics. It has wide range of applications such as determining forces, aircraft movements, mass flow rate of petroleum, predicting weather patterns, modelling explosions, crowd dynamics and traffic engineering. 

Archimedes Principle

The fundamental law of physics in fluid mechanics is the Archimedes principle postulated by Archimedes which states that when an object is immersed fully or partially in a liquid or fluid the upward buoyant force exerted on the object should be equal to the weight of the displaced fluid. Thus, if the fluid is uniform then the weight of the displaced fluid is proportional to the volume of the fluid displaced. In short, it is explained as the buoyant force (F_b) of the immersed object is determined from the product of the weight of the fluid displaced or the density (ρ) of the fluid displaced and the volume (V) of the submerged body to its gravity (g) times.

$$F_{a }= \rho gV$$

where, $F_{a }$ - buoyant force of the submerged body

ρ – density of fluid

g – acceleration due to gravity

V – volume of the fluid displaced 

In fluid mechanics, to derive various equations, four major primary dimensions such as mass, time, length and force are involved. A square bracket with the term i.e. [M] means dimension of mass. Similarly [T], [L] and [F] are related to the dimensions of time, length and force, respectively. From Newton’s second law of motion, the dimension force is proportional to mass and acceleration. Further acceleration is proportional to the dimensions of length and time. Thus, the dimension of force is given as

                                         [F]= [MLT^-2]

The dimension of specific mass [ρ] i.e. the amount of liquid or fluid in a particular volume is expressed in terms of dimensions of mass, length and time. Thus, it is expressed in terms of mass per unit volume.   

$\left[{\rm P}\right]= \left[\frac{M}{L^3}\right] = \left[\frac{F{T}^2}{L^4}\right]$

  The dimension specific weight [γ] is expressed in terms of the dimension of force, length and time i.e. force per unit volume. 

$\left[\gamma \right]= \left[\frac{F}{L^3}\right] = \left[\frac{M}{L^2{T}^2}\right]$

Based on the Newton’s second law of motion, the force (F) or weight (W) is related to its mass (M). Thus, in similar fashion, the specific weight (γ) and specific mass (ρ) are related to each other. 

F=W=Mg

So,

γ=ρg

What is Bernoulli’s Principle?

Bernoulli’s principle was postulated by Daniel Bernoulli and the equation stating Bernoulli’s theorem was derived by Leonhard Euler. This principle holds good for isentropic flows in which the effect of non-adiabatic process and the irreversible process are negligible. Thus, it states that the decrease in the pressure or the fluids potential energy is simultaneously related to increase in speed of the fluid. 

Practice Problems

1. Calculate the specific mass of water at 4 ºC, whose specific weight is 2000 kg/m³.

    Solution: Given specific weight (γ) = 2000 kg/m³ 

                   Gravity of water at 4 ºC = 9.81 m/sec²         

                   Substituting the given values in the formula

γ = ρg

ρ = 1000 / 9.81

= 203.87 kg sec² / m⁴

Thus, the specific mass of water is found to be 203.87 kg sec² / m⁴.

2. Determine the mass of an object whose weight is 500 kg at standard earth gravity.

    Solution: Given weight (W) = 5000 kg

                  Standard earth gravity (g) = 9.81 m/sec²

                  Substituting the given value in the appropriate formula

                     W = mg 

                    M = W / g

                         = 500 / 9.8

                          = 50.968 kg sec² / m⁴

Thus, the mass of the object is 50.968 kg sec² / m⁴.

Context and Applications  

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• B. Tech in Chemical engineering  

• B. Tech in Chemical engineering