Chapter 1 Introduction

§1.1 Summary

1.1.1 Task of fluid mechanics

Fluid mechanics is an independent branch of mechanics that studies the mechanics of fluids (liquids, gases, and plasma)and the forces on them.

Fluid mechanics includes two branches.The first one deals with the fluids at rest, which embraces the study of the conditions under which fluids are at rest and in stable equilibrium.This branch is called fluid statics or hydrostatics.The second one deals with fluid flow—the natural science of fluids (liquids and gases)in motion.This branch is called fluid dynamics.

Fluid mechanics can be also divided into (1)theoretical fluid mechanics and (2)applied fluid mechanics (also called engineering fluid mechanics)according to the research contents.The first one focuses on theoretical research and mathematical reasoning.The second one focuses on how to solve practical engineering problems.This book belongs to the second one.

1.1.2 Development of fluid mechanics

1．Maj or phases for fluid mechanics development

Fluid mechanics originates from a book On Floating Bodies written by Archimedes, a Greek scholar who lived in Sicily.He summarized mechanical properties of stationary liquid for the first time.

In 1687, Newton discussed about fluid resistance and wave movement in the famous book Philosophiae Naturalis Principia Mathematica, indicating fluid mechanics stepped into main development periods.

Phase Ⅰ:Energy estimation of liquid motion proposed by Daniel Bernoulli and analytic method of liquid movement proposed by Leonhard Euler laid a solid foundation for the studies of the law of liquid motion.As a result, a classical“Hydrodynamics”which belongs to mathematics was formed.

Phase Ⅱ:Based on the classical“Hydrodynamics”, Claude-Louis Navier and ·1 ·George Gabriel Stokes proposed a famous basic motion equation of viscous fluid, which laid a theoretical foundation for the long-term development of fluid mechanics. However, engineering problems cannot be solved due to the complexity of mathematical solution and the limitations of fluid model.Therefore,“experimental fluid mechanics”which used experimental methods to summarize empirical formula was formed.The development of initial“experimental fluid mechanics”is limited due to a lack of theoretical foundation.

Phase Ⅲ: The contents of classical hydrodynamics and experimental fluid mechanics had been continually renewed since the late 19th century.In the meantime, the combination of theoretical analytic methods and experimental analytic methods leads to the generation of modern fluid mechanics which emphasizes both theory and practice. Since 1960s, fluid mechanics has been applied increasingly widely due to the development and popularity of computer science.

2．Maj or events in the field of fluid mechanics

In 1738, Daniel Bernoulli, a Swiss mathematician and physicist proposed Bernoulli equation in his famous book H ydrodynamica.

In 1757, Leonhard Euler proposed an important set of equations for inviscid flow, now known as the Euler equations.

In 1781, Joseph-Louis Lagrange proposed a concept“stream function”for the first time.

In 1822, Claude-Louis Navier, a French engineer and physicist, and in 1845, George Gabriel Stokes, an English mathematician and physicist proposed Navier-Stokes equations.

In 1876, Osborne Reynolds, an English physicist, found two states of fluid flow:laminar flow and turbulent flow.

In 1886, Hermann von Helmholtz, a German physician and physicist, proposed Helmholtz's theorems for vortex dynamics in inviscid fluids.

In the late 19th century, the theory of similarity was proposed.

In 1904, Ludwig Prandtl, a German engineer, described the boundary layer in his groundbreaking paper“Fluid Flow in Very Little Separation”.

Since 1960s, computational fluid mechanics was developed rapidly, and the connotation of fluid mechanics has also been continuously enriched and improved.

China has a long history of water conservancy.People gradually deepen the understanding of the law of fluid motion through long-term practice.For example:

“Dayu flood control”already knew water control should follow the nature of water before 4000 years.

Three water conservancy projects (Dujiang Weir, Zhengguo Canal and Ling Canal) were built from 256 B.C.to 210 B.C. ·2 ·

The Grand Canal was built from A.D.587 to 610, indicating people knew the water flow and weir flow of open canal very well.

Depending on the cognition and utilization of ocean current and air currents, Zheng He's seven voyages to western countries was a miracle in the history of human voyage.

During Yong Zheng years of the Qing Dynasty, He Mengyao proposed the flow of water was equal to the area of the cross section multiplied by the average velocity of water in his book Suandi.

1.1.3 The methodology of fluid mechanics

1．Theoretical methodology

Theoretical methodology is:reasonable theoretical model is proposed through scientific abstraction of physical properties and flow characteristic of liquid, and closed equations of controlling liquid motion are built according to universal law of mechanical motion.As a result, specific flow issues can be transformed to mathematical problems which can be worked out under corresponding boundary conditions and initial conditions.The key of theoretical methodology lies in proposing ideal model and working out theoretical results through mathematical methods in order to reveal the law of fluid motion.However, it is hard to solve many practical flow issues accurately due to mathematical difficulties.

Among the theoretical methods, major laws cited in fluid mechanics.

(1)Conservation of mass:

(2)Momentum law:

(3)Newton's second law of motion:F=ma

(4)Mechanical energy transformation and conservation law:kinetic energy+pressure energy+potential energy+energy loss=constant

Because pure theoretical methodology suffers mathematical difficulties, a set of analytic methods which combines theory and experiment are gradually perfected during the era when computer has not yet developed.This set of analytic methods is simple and practical.Today, with the computer more and more sophisticated, it is still applicable.

2．Experimental methodology

Applied fluid mechanics is a basic subj ect which combines theory and practice. Many practical formula and factors are derived from experiments.Many engineering problems which can be worked out through modern theoretical analysis and numerical calculation should also be examined and corrected with the help of experiments.

Major ways of experimental study:a.Prototype measurement (directly observe practical engineering or natural flow distribution); b.Systematic experiment (study ·3 ·artificial flow phenomenon systematically in the laboratory); c. Model study (simulation of the conditions for practical engineering and study through previewing or repeating flow phenomenon).

Basic theories for experimental study:similarity theory and dimensional analysis.

3．Numerical methodology

Numerical methodology is to build various numerical models by means of various discretization methods, and then to obtain a collection of many data in time and space through numerical calculation and numerical experiment, and eventually obtain numerical solution which describes flow field quantitatively.In the past two or three decades, this methodology has been greatly developed to form a new subj ect—computational fluid mechanics.

4．Simplification of flow analysis

Due to the complexity of fluid motion state, it is very difficult and it is not necessary to take account of all the factors involved in fluid motion.Thus, it is essential to categorize and simplify various movement states.For example, flow can be categorized into one dimensional and multi-dimensional flow, constant flow and unsteady flow, uniform flow and non-uniform flow, rapidly varied flow and gradually varied flow, laminar and turbulent flow.

1.1.4 Fluid mechanics in civil engineering

1．The nature and purpose of the course

(1)Nature

This course is a compulsory professional basic course for the majors of civil engineering and water conservancy. The obj ects of study are water, air and compressible fluid.Research contents include fluid equilibrium, fluid mechanical motion law and engineering application.

(2)Purposes

This course provides students with basic concepts, theories, computational methods and experimental skills.This course helps the cultivation of students'ability to analyze problems and the creative ability required in their future study and work.

(3)Status

This course provides many courses such as hydrology, hydraulics, soil mechanics, engineering geology, civil engineering, hydraulic structure and construction equipment with fluid mechanics principles, and helps students understand the relationship between civil engineering, water conservancy and atmosphere, water environment deeply.

(4)Others

This course is a compulsory course for professionals in the field of construction engineering. ·4·

2．Application of fluid mechanics in civil engineering

Fluid is a physical form which comes across to human life and production.Many scientific and technical departments concern fluid mechanics.The solution of flow problems in the fields of irrigation works, civil engineering, traffic transportation, machinery manufacturing, oil production, chemical industry, and bioengineering depends on fluid mechanics.Actually, it is impossible to find a course or field which is not involved with fluid mechanics.

(1)Application in construction engineering such as water lowering of groundwork, roadbed drainage, groundwater seepage, stress analysis of underwater and underground structures, cofferdam construction, buoyancy and resistance to external disturbance of offshore platform.

(2)Application in municipal engineering such as aperture design of bridge and culvert, water supply and drainage, calculation of pipe network, design of pump station and water tower, ventilation of tunnel.The theories of fluid mechanics are theoretical basis for design and operation control of water supply and drainage system.

(3)Application in flood control works such as discharge capacity of river course, the force and seepage of dike and dam, discharge capacity of gate dam controlling flood.

(4)Application in building environment and equipment engineering such as heat supply, ventilation and design of pump station.

(5)Application in water conservancy.Water conservancy is more dependent on fluid mechanics than other courses.For the professionals in the field of water conservancy, engineering hydraulics is also a compulsory course.

3．Basic requirements of this course

(1)Completely understand basic theories.

①Understand basic concepts in the field of fluid mechanics.

②Learn the analytic methods of gross flow, methods of combining dimension analysis and experiment and the ways to work out simple planar potential flow.

③Understand the rules of energy transformation and head loss of fluid motion.

(2)Have analytical and computational skills for general flow problems, including:

①Calculation of hydraulic load.

②Calculation of discharge capacity of tunnel, canal, and weir as well as seepage of wells.

③Analysis and calculation of head loss.

(3)Master the conventional methods for the measurements of water level, pressure, flow rate and flux well, and know how to observe flow phenomenon, analyze experimental data and write experimental report.

(4)Grasp basic concepts, basic equations and basic application, i.e.basic knowledge of fluid mechanics. ·5 ·