Fluid Mechanics(history of fluid mechanics)

Introduction

A fluid cannot resist a shear stress by a static deflection and it moves and deforms continuously as long as the shear stress is applied. Fluid mechanics is the study of fluids either in motion (fluid dynamics) or at rest (fluid statics). Both liquids and gases are classified as fluids. There is a theory available for fluid flow problems, but in all cases it should be backed up by experiment. It is a highly visual subject with good instrumentation. Since the earth is 75% covered with water and 100% with air, the scope of fluid mechanics is vast and has numerous applications in engineering and human activities. Examples are medical studies of breathing and blood flow, oceanography, hydrology, energy generation. Other engineering applications include: fans, turbines, pumps, missiles, airplanes to name a few. The basic equations of fluid motion are too difficult to apply to arbitrary geometric configurations. Thus most textbooks concentrate on flat plates, circular pipes, and other simple geometries. It is possible to apply numerical techniques to complex geometries, this branch of fluid mechanics is called computational fluid mechanics (CFD). Our focus, however, will be on theoretical approach in this course. Viscosity is an internal property of a fluid that offers resistance to flow. Viscosity increases the difficulty of the basic equations. It also has a destabilizing effect and gives rise to disorderly, random phenomena called turbulence.

History of fluid mechanics

Ancient civilization had enough knowledge to solve certain flow problems, e.g. sailing ships with oars, irrigation systems.

• Archimedes (285 – 212 B.C.) postulated the parallelogram law for addition of vectors and the laws of buoyancy and applied them to floating and submerged objects.
• Leonardo da Vinci (1452 – 1519) stated the equation of conservation of mass in one‐dimensional steady‐state flow. He experimented with waves, jets, hydraulic jumps, eddy formation, etc.
• Edme Mariotte (1620 – 1684) built the first wind tunnel and tested models in it.
• Isaac Newton (1642 – 1727) postulated his laws of motion and the law of viscosity of linear fluids, now called newtonian. The theory first yield the frictionless assumption which led to several beautiful mathematical solutions.
• Leonhard Euler (1707 – 1783) developed both the differential equations of motion and their integral form, now called Bernoulli equation.
• William Froude (1810 – 1879) and his son developed laws of model testing and Lord Rayleigh (1842 – 1919) proposed dimensional analysis.
• Osborne Reynolds (1842 – 1912) published the classic pipe experiment and showed the importance of the dimensionless Reynolds number, named after him.
• Navier (1785 – 1836) and Stokes (1819 – 1903) added newtonian viscous term to the equation of motion, the fluid motion governing equation, i.e., Navier‐Stokes equation is named after them.
• Ludwig Prandtl (1875 – 1953) pointed out that fluid flows with small viscosity, such as water flows and airflows, can be divided into a thin viscous layer (or boundary layer) near solid surfaces and interfaces, patched onto a nearly inviscid outer layer, where the Euler and Bernoulli equations apply.

Fluid Statics

Fluid Statics

Fluid statics is concerned with the balance of forces which stabilise fluids at rest. In the case of a liquid, as the pressure largely changes according to its height, it is necessary to take its depth into account. Furthermore, even in the case of relative rest (e.g. the case where the fluid is stable relative to its vessel even when the vessel is rotating at high speed), the fluid can be regarded as being at rest if the fluid movement is observed in terms of coordinates fixed upon the vessel.

Pressure- 

                   When a uniform pressure acts on a flat plate of area A and a force P pushes the plate, then 

                                                               p = P/A

Units of pressure- 

                                      The unit of pressure is the pascal (Pa), but it is also expressed in bars or metres of water column (mH,O).In addition, in some cases atmospheric pressure is used: 1 atm = 760mmHg(at273.15K,g = 9.80665m/s2) = 101 325Palatm is standard 1 atmospheric pressure in meteorology and is called the standard atmospheric pressure. 

Absolute pressure and gauge pressure-

                                                                             There are two methods used to express the pressure: one is based on the perfect vacuum and the other on the atmospheric pressure. The former is called the absolute pressure and the latter is called the gauge pressure. Then, gauge pressure = absolute pressure - atmospheric pressure In gauge pressure, a pressure under 1 atmospheric pressure is expressed as a negative pressure. This relation is shown in Fig.. Most gauges are constructed to indicate the gauge pressure.

                                                     

Characteristics of pressure -

                                                         The pressure has the following three characteristics.

1. The pressure of a fluid always acts perpendicular to the wall in contact with the fluid.

2. The values of the pressure acting at any point in a fluid at rest are equal regardless of its direction. Imagine a minute triangular prism of unit width in a fluid at rest. Let the pressure acting on the small surfaces dA,, dA, and dA be p,, p2 and p respectively. The following equations are obtained from the balance of forces in the horizontal and vertical directions:

                                                       

                                                         pldA, = pdAsin0

                                                         p2dA2 = pdAcos0  + idA,dA,pg

The weight of the triangle pillar is doubly infinitesimal, so it is omitted. From geometry, the following equations are obtained:

                                                           dA sin@ = dA,

                                                        dA COS 0 = dA,

Therefore, the following relation is obtained:

                                                         PI =P2=P 

Since angle 8 can be given any value, values of the pressure acting at one point in a fluid at rest are equal regardless of its direction.

3. The fluid pressure applied to a fluid in a closed vessel is transmitted to all parts at the same pressure value as that applied (Pascal’s law).

   when the small piston of area A, is acted upon by the force F,, the liquid pressure p = FI/A, is produced and the large piston is acted upon by the force F, = PA,.  

                                 

characteristics of Fluid

        CHARACTERISTICS OF FLUID 

FLUID-

                Fluids are divided into liquids and gases. A liquid is hard to compress and

as in the ancient saying ‘Water takes the shape of the vessel containing it’, it

changes its shape according to the shape of its container with an upper free

surface. Gas on the other hand is easy to compress, and fully expands to fill

its container. There is thus no free surface.

Consequently, an important characteristic of a fluid from the viewpoint

of fluid mechanics is its compressibility. Another characteristic is its viscosity.

Whereas a solid shows its elasticity in tension, compression or shearing stress,

a fluid does so only for compression. In other words, a fluid increases its

pressure against compression, trying to retain its original volume. This

characteristic is called compressibility. Furthermore, a fluid shows resistance

whenever two layers slide over each other. This characteristic is called

viscosity.

In general, liquids are called incompressible fluids and gases compressible

fluids. Nevertheless, for liquids, compressibility must be taken into account

whenever they are highly pressurised, and for gases compressibility may be

disregarded whenever the change in pressure is small. Although a fluid is an

aggregate of molecules in constant motion, the mean free path of these

molecules is 0.06pm or so even for air of normal temperature and pressure,

so a fluid is treated as a continuous isotropic substance.

Meanwhile, a non-existent, assumed fluid without either viscosity or compressibility

is called an ideal fluid or perfect fluid. A fluid with compressibility

but without viscosity is occasionally discriminated and called a perfect fluid,

too. Furthermore, a gas subject to Boyle’s-Charles’ law is called a perfect or

ideal gas. 

UNITS AND DIMENSIONS- 

                                                     A11 physical quantities are given by a few fundamental quantities or their combinations. The units of such fundamental quantities are called base 

Units and dimensions 7units, combinations of them being called derived units. The system in which length, mass and time are adopted as the basic quantities, and from which

the units of other quantities are derived, is called the absolute system of

units.  

                           Absolute system of unit system-

                                             MSK system of unit--

                                                                                     This is the system of units where the metre (m) is used for the unit of length, kilogram (kg) for the unit of mass, and second (s) for the unit of time as the base units.

                                             CGS System of unit--

                                                                                  This is the system of units where the centimetre (cm) is used for length, gram (g) for mass, and second (s) for time as the base units.

                                              International standard of unit(SI)-

                                                                                      SI, the abbreviation of La Systkme International d’Unites, is the system developed from the MKS system of units. It is a consistent and reasonable system of units which makes it a rule to adopt only one unit for each of the various quantities used in such fields as science, education and industry. There are seven fundamental SI units, namely: metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for mass quantity and candela (cd) for intensity of light. Derived units consist of these units.