Introduction

I.1. Introduction

Fluid Mechanics consist of two main categories. The first one refers to the quantitative and qualitative analysis and study of fluids in motion, the velocity or acceleration as well as the forces exerted by nature. The second category analyzes the physical forces that are developed on solid-fluid interfaces, where the solids represent the containers. The first category can be called Theoretical Fluid Mechanics, while the second one is called Applied Fluid Mechanics.

This book primarily presents the aspects and problems of internal and external flows, including certain fundamental principles of fluids.

To develop an extended study of Applied Fluid Mechanics problems, mathematical modeling and analysis is considered necessary. On the other hand, the empirical or experimental investigation of fluid phenomena only provides us with certain measurements and information about individual cases, and it is often difficult to generalize our conclusions. Hence, the appropriate way to study fluid flows is to investigate the related phenomena with a combined analytical-computational and experimental approach in order to improve step by step the proposed fluid theories or solutions.

Industrial engineers have raised various issues related to the main assumption that all fluids are considered to be ideal. In order to overcome these issues, every technological problem is considered to be an individual one, resulting in a lack of theoretical background. Year after year, a huge gap has been created between theoretical and practical hydrodynamics researchers, which exists even today. This book bridges this gap between various industrial flows, and an attempt has been made to present a common strategy. The flows inside pipes or channels as well as the flows around bodies are considered to be real life applications, setting the appropriate theoretical background simultaneously.

I.2. Fluid Mechanics sections

The Fluid Mechanics study comprises fluid motion and fluid balance. During the last decades, it has evolved in two major directions. Theoretical Fluid Mechanics includes the mathematical exploitation of fluid phenomena, and Technical Fluid Mechanics includes the applications of mechanical engineering, aeronautics, shipbuilding and meteorology. Technical Fluid Mechanics is considered an applied science, and hence it is often referred to as Applied Fluid Mechanics, which includes the possible solutions of fluid problems and the explanation of natural phenomena. Moreover, it aims to produce numerical predictions or experimental validation for direct practical applications.

Classic Fluid Mechanics can be derived from various areas according to the mechanical condition or fluid properties. The categories presented in Table I.1 are based on the motion of fluids as well as on compressibility, where the density varies according to the fluid condition.

Table I.1. Fluid Mechanics categories

Fluid mechanics Fluids at rest Fluids in motion Hydrodynamics (?=ct) Hydrostatics Hydrodynamics Aeromechanics (??ct) Aerostatics Aerodynamics

I.3. Systems of units

I.3.1. Definitions and general considerations

Units are fundamental for physics, especially for all the applied sciences such as mechanical engineering. The number without units means absolutely nothing for Fluid Mechanics, as it represents a natural quantity such as pressure, velocity or force.

Historically, various systems of units have been developed according to the theoretical principle demands or to practical applications. In most countries (not including the USA), the metric system is the official system of measurement, which is accepted by both scientists and engineers. The International System of Units (SI) was defined and established at the 11th General Conference on Weights and Measures, where more than 36 countries accepted it to be the most complete and appropriate one, including the USA. Since then, the USA has made huge progress in introducing SI units to engineering. For example, many NASA laboratories use SI units for their technical research results, and the AIAA (American Institute of Aeronautics and Astronautics) also supports the SI in its research papers.

Therefore, students who want to study engineering have to know both unit systems. The following table presents the corresponding basic units in both systems based on the theory that all the derived units at the metric system can be produced by the base ones.

Table I.2. Base units in SI and BS (British system)

Base quantity SI BS Length Meter (m) Foot (ft) Time Second (s) Second (sec) Mass Kilogram (kg) Pounds of mass (lbm) or slug Temperature Celsius (°C) Fahrenheit (°F) Absolute temperature Kelvin (K) Rankine (R)

As we have just mentioned, the derived units can be produced by the base units following the nature of interrelationships or the basic formulas with the need for adding any conversion factor, as in the following, using Newton's law:

[I.1]

Thus, we further confirm the definition of Newton as the force that is required to accelerate a mass of 1 kg at a rate of 1 m/s2. Similarly, the ideal gas constant for air (R=287 J/(kg·K) can also be expressed in the following way:

[I.2]

The BS is also a consistent system, and the same procedure can be followed for the derived quantities:

[I.3] [I.4]

However, more systems of units are not consistent; therefore, it is necessary to use a factor in order to produce the required conversion as shown below. These systems have been used in the past by engineers but have often not been convenient to be applied:

[I.5] [I.6]

The various temperature units are of high importance. We often denote absolute temperature by T, where the minimum temperature value can be zero. Kelvin (K) and Rankine (R) are the absolute temperature units, where 0 R = 0 K indicates the temperature at which all the molecular motion theoretically stop. In addition, the relationships among the temperature units are:

[I.7] [I.8]

It is worth mentioning that the temperature T in the ideal gas equation of state (equation [I.9]) is absolute:

[I.9]

where ? is the pressure, ? is the density of gas and the other symbols are defined as above.

I.3.2. Definitions and fundamental units in fluids

Table I.3. Units of common quantities in physics and fluids

Natural quantity Units Symbol Force Newton N = kg m/s2 Energy Joule J = N m Power Watt W = J/s

Table I.4. Common metric prefix in SI

10-6 micro µ 10-3 milli m 103 kilo k 106 mega M

Table I.5. Length, area and volume conversion factors

Length l 1 in 25.4 mm 1 ft 0.3048 m 1 yd 0.9144 m 1 mile 1.6093 km Area S 1 in2 645.16 mm2 1 fr2 0.0929 m2 1 yd2 0.8361 m2 1 mile2 2.590 km2 1 acre 4046.9 m2 Volume v 1 in3 16387 mm3 1 ft3 0.02832 m3 1 UK gal 0.004546 m3 1 US gal 0.003785 m3

Table I.6. Conversion factor mass, density, force, viscosity and pressure

Mass m 1 kg 103 g 1 oz 28.352 g 1 lb 453.592 g 1 cwt 50.802 kg 1 ton (UK) 1016.06 kg Density...