What is Fluid Mechanics?

A branch of mechanics, which mainly studies the interaction and flow laws of the fluid when it is at rest and in motion, and when the fluid and the solid boundary wall have relative motion under the action of various forces.

Chinese name: Fluid mechanics

Foreign name: fluid mechanics

A brief history of the development of fluid mechanics

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Fluid mechanics is gradually developed in the struggle between man and nature and in production practice. There is a legend in China that Dayu manages the river and clears the rivers. Father Qin Dynasty Li Bing (3rd century BC) led the working people to build Dujiangyan, and it still plays a role. Around the same time, the Romans built a large-scale water supply system.

The first contribution to the formation of the discipline of fluid mechanics was Archimedes in ancient Greece. He established the theory of liquid equilibrium including the buoyancy theorem of the object and the stability of the floating body, and laid the foundation for hydrostatics. In the following thousand years, there has been no major development in fluid mechanics.

In the 15th century, the works of Italian Leonardo da Vinci addressed water waves, pipe flow, hydraulic machinery, and the principle of bird flight.

In the 17th century, Pascal clarified the concept of pressure in a stationary fluid. But fluid mechanics, especially fluid mechanics, as a rigorous science, gradually formed after the establishment of the three laws of conservation: mass, momentum, and energy. Classical mechanics established the concepts of speed, acceleration, force, and flow field. of.

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The founder of mechanics in the 17th century I. Newton studied the resistance of an object moving in a liquid, and obtained that the resistance is directly proportional to the density of the fluid, the cross-sectional area of the object, and the square of its speed. He also put forward the following assumptions on the internal frictional force of viscous fluids: that the frictional stress between two fluid layers is proportional to the relative sliding speed of the two layers and inversely proportional to the distance between the two layers (ie, Newton's law of viscosity).

Later, H. Pito of France invented the pitot tube for measuring the flow velocity; D'Alembert carried out many experimental work on the resistance of ships in the canal, confirming the square relationship between resistance and the speed of object movement; L. Euler of Switzerland adopted The concept of continuum is extended, the concept of pressure in statics is extended to moving fluids, the Euler equation is established, and the motion of inviscid fluid is correctly described by differential equations. Bernoulli starts from the energy conservation of classical mechanics. The flow of water in the water supply pipeline was studied, and experiments were carefully arranged and analyzed, and the relationship between the flow velocity, pressure, and pipeline elevation under the steady motion of the fluid was obtained-Bernoulli's equation.

The establishment of Euler's equation and Bernoulli's equation is a sign of the establishment of fluid dynamics as a branch of science. From this point on, the phase of quantitative research on fluid motion using differential equations and experimental measurements has begun.

Since the 18th century, the potential flow theory has made great progress, and many laws have been clarified in water waves, tides, vortex motion, and acoustics. French J.-L. Lagrange made no research on vortex motion, and German H. von Helmholtz made a lot of research on vortex motion. In the above research, the viscosity of the fluid does not play an important role, which is considered. Is a non-viscous fluid, so this theory cannot clarify the effect of viscosity in fluids.

Scientists who have made outstanding contributions to the development of fluid mechanics (15 photos)

Theoretical basis

The equation of fluid motion taking viscosity into account was established by French C.-L.-M.-H. Navier in France in 1821 and GG Stokes in England in 1845. Tox's equation is the theoretical basis of fluid dynamics.

Since the Navier-Stokes equation is a set of nonlinear partial differential equations, it is very difficult to study the fluid motion using analytical methods. In order to simplify the equation, scholars have adopted the assumption that the fluid is incompressible and inviscid, but have obtained the Dallemian paradox that runs counter to the fact that the drag of an object in the fluid is equal to zero. Therefore, by the end of the 19th century, although great progress had been made in the use of analytical fluid dynamics, it was not easy to promote production.

Parallel to fluid dynamics is hydraulics (see Fluid Dynamics). This is to meet the needs of production and engineering. Some empirical formulas are summarized from a large number of experiments to express the empirical science of the relationship between flow parameters.

What makes the above two approaches unified is the boundary layer theory. It was founded by German L. Plant in 1904. The Prandt School gradually simplified the NS equation from 1904 to 1921. From various angles such as reasoning, mathematical reasoning, and experimental measurement, the boundary layer theory was established. It can actually calculate the flow state and fluid in the boundary layer in simple cases. Viscous force with solids. At the same time, Planck put forward many new concepts and widely used in the design of aircraft and steam turbines. This theory not only clarifies the applicable range of ideal fluids, but also calculates the frictional resistance encountered when an object moves. These two situations have been unified.

Bernoulli's theorem

Development of aircraft and aerodynamics

In the early 20th century, the emergence of aircraft greatly promoted the development of aerodynamics. The development of the aviation industry is expected to reveal the pressure distribution around the aircraft, the force conditions and resistance of the aircraft, and this has promoted the development of experimental and theoretical analysis of fluid mechanics. At the beginning of the 20th century, scientists represented by Zhukovsky, Chaplygin, and Plant, etc., pioneered the theory of wing based on the theory of potential flow of incompressible incompressible fluid, and explained how the wing is subject to Lift so that the air can lift a heavy aircraft into the sky. The correctness of the wing theory makes people re-understand the theory of inviscid fluid, affirming its great significance in guiding engineering design.

The establishment and development of wing theory and boundary layer theory is a major advance in fluid mechanics, which makes the inviscid fluid theory and the boundary layer theory of viscous fluids well combined. With the improvement of the steam turbine and the increase of the aircraft's flight speed to more than 50 meters per second, the experimental and theoretical research on the effect of air density changes, which has begun since the 19th century, provides theoretical guidance for high-speed flight. After the 1940s, due to the application of jet propulsion and rocket technology, the speed of the aircraft exceeded the speed of sound, and the space flight was realized. The research on the high-speed flow of gas has made rapid progress, and branch disciplines such as gas dynamics, physics-chemical fluid dynamics have been formed .

Formation of branches and interdisciplines

Since the 1960s, fluid mechanics has begun to cross-penetrate fluid mechanics and other disciplines, forming new interdisciplinary or marginal disciplines, such as physical-chemical fluid dynamics, magnetohydrodynamics, etc .; originally it was basically described qualitatively The problem is gradually being studied quantitatively, and biorheology is an example.

Based on these theories, in the 1940s, a new theory was formed on detonation waves in explosives or natural gas. In order to study the propagation of shock waves in air or water after the detonation of atomic bombs and explosives, they developed Explosive wave theory. Since then, fluid mechanics has developed many branches, such as hypersonic aerodynamics, supersonic aerodynamics, lean aerodynamics, electromagnetic fluid mechanics, computational fluid dynamics, two-phase (gas-liquid or gas-solid) flow and so on.

These huge advances are inseparable from the use of various mathematical analysis methods and the establishment of large, sophisticated experimental equipment and instruments. Since the 1950s, electronic computers have been constantly improved, making it difficult to conduct research with analytical methods, which can be performed by numerical methods. A new branch of computational fluid mechanics has emerged. At the same time, due to the needs of civilian and military production, great progress has been made in hydrodynamics and other disciplines.

In the 1960s, according to the needs of structural mechanics and solid mechanics, a finite element method for calculating elastic mechanics problems appeared. After more than ten years of development, the new calculation method of finite element analysis has begun to be applied to fluid mechanics, especially in low-velocity flows and fluid boundary shapes with very complicated problems. Since the 21st century, the use of finite element methods to study the problem of high-speed flow has also begun to appear. The mutual penetration and fusion of finite element methods and differential methods have also appeared.

Subjects of fluid mechanics

Basic assumptions

Continuum hypothesis

Substances are composed of molecules. Although the molecules are discretely distributed and perform irregular thermal motion, both theory and experiments have shown that within a small range, the statistical average value of fluid molecular micelles that perform thermal motion is stable. Therefore, it can be approximated that the fluid is composed of continuous matter, and the physical quantities such as temperature, density, and pressure are all continuously distributed scalar fields.

Conservation of mass

The purpose of mass conservation is to establish a system of equations describing fluid motion. Euler's method is described as: the mass flowing into any closed surface in the absolute coordinate system is equal to the mass flowing out of this surface. That is: the divergence of the product of density and velocity is zero (no divergence field). It is described by Euler's method as: the change rate of the derivative of the mass of the fluid micelles with time is zero.

Momentum theorem

Fluid mechanics belongs to the category of classical mechanics. Therefore, momentum theorem and moment theorem are suitable for fluid microelements.

Stress tensor

The forces acting on fluid microelements are mainly surface and volume forces. Surface and volume forces are measures of force on a unit area and a unit volume, respectively, so they are bounded. Since we consider fluid microelements with very small size when establishing the basic equations of fluid mechanics, the force on the surface of the fluid micelles is a second-order small amount of size, and the volume force is a third-order small amount of size. When the volume is small, the effect of the bulk force can be ignored. It is thought that fluid micelles are only affected by surface forces (surface stresses). In non-isotropic fluids, the fluid micelles have different positions, different surface normals, and different stresses. The stress is described by a second-order tensor and the inner product of the surface normal. Only three quantities are independent, so as long as you know the stress on three different faces of a point, you can determine the stress distribution at that point.

Sticky hypothesis

The fluid is viscous, and the stress tensor can be derived using the viscosity theorem.

Conservation of energy

The specific expression is: the work done by the volume force per unit time on the fluid micelles plus the product of the surface force and the deformation velocity of the fluid micelles is equal to the increment of the internal energy of the fluid micelles plus the kinetic energy increase of the fluid micelles.

Branch of fluid mechanics

Fluid is a general term for gas and liquid. Fluids can be encountered anytime, anywhere in people's lives and production activities. Therefore, fluid mechanics is closely related to human daily life and production.

Atmospheric and water are the two most common fluids. The atmosphere surrounds the entire earth, and 70% of the earth's surface is water. Atmospheric motion, seawater motion (including waves, tides, mesoscale vortices, circulation, etc.) and even the flow of molten plasma in the depths of the earth are the contents of hydrodynamic research, and belong to the scope of earth hydrodynamics.
Hydrodynamics
The movement of water in pipes, channels and rivers has been the object of research since ancient times. People also use water for work, such as ancient water striders and modern highly developed turbines. Ships have always been a means of transportation for people. Various resistances encountered by ships moving in water, ship stability, and cavitation caused by hulls and thrusters in water have always been research topics for ship hydrodynamics. These sub-disciplines that study the laws of water movement are called hydrodynamics.
Aerodynamics
Since the appearance of the first aircraft in the world in the early 20th century, aircraft and various other aircraft have developed rapidly. The space flight that began in the 1950s extended human activity to other planets and the Milky Way. The vigorous development of the aerospace industry is closely linked to the development of aerodynamics and aerodynamics, a branch of fluid mechanics. These disciplines are the most active and productive fields in fluid mechanics.
Seepage mechanics
The exploitation of oil and natural gas and the development and utilization of groundwater require people to understand the movement of fluids in porous or gap media. This is one of the main subjects of percolation mechanics research in the branch of fluid mechanics. Percolation mechanics also involves technical issues such as the prevention and control of soil salinization, concentration, separation and porous filtration in the chemical industry, and cooling of the combustion chamber.
Physical-chemical fluid dynamics
By burning coal, oil, natural gas, etc., you can get thermal energy to promote machinery or for other purposes. Combustion is inseparable from gas. This is a fluid mechanics problem with chemical reactions and thermal energy changes, and is one of the contents of physical-chemical fluid dynamics. Explosion is a violent transient energy change and transfer process, involving aerodynamics, thus forming explosion mechanics.
Multiphase fluid mechanics
Desert migration, river sediment movement, pulverized coal transportation in pipelines, and gas catalyst movement in chemical fluidized beds all involve issues such as solid particles in fluids or bubbles in liquids. This type of problem is the scope of multiphase fluid mechanics research.
Plasma dynamics and electromagnetic fluid mechanics
Plasma is a collection of free electrons, ions with an equal amount of positive charge, and neutral particles. Plasma has a special law of movement under the action of a magnetic field. The disciplines that study the laws of plasma motion are called plasma dynamics and electromagnetic fluid mechanics (see Current Fluid Dynamics, Magnetic Fluid Mechanics). They have a wide range of applications in controlled thermonuclear reactions, magnetic fluid power generation, and cosmic gas motion (see Cosmic Gas Dynamics).
Environmental fluid mechanics
The effects of wind on buildings, bridges, cables, etc. cause them to bear loads and excite vibration; emissions of waste gas and wastewater cause environmental pollution; river bed scouring and coastal erosion; study the movement of these fluids and their interaction with humans, animals and plants The interdisciplinary discipline is called environmental fluid mechanics (which includes ambient aerodynamics, building aerodynamics). This is an emerging fringe discipline involving classical fluid mechanics, meteorology, oceanography and hydraulics, and structural dynamics.
Biorheology
Biorheology studies hydrodynamic issues in the human body or other animals and plants, such as blood flow in blood vessels, physiological fluid motion in the heart, lungs, and kidneys (see Circulatory System Dynamics, Respiratory System Dynamics), and in plants Transport of nutrient solution (see flow in plants). In addition, the flight of birds in the air (see the flight of birds and insects), the swimming of animals (such as dolphins) in the water, and so on.

Therefore, fluid mechanics includes both the basic theory of natural sciences and the application of engineering and technical sciences. The above mainly explains the contents and branches of fluid mechanics from the perspective of the research object. In addition, from the perspective of fluid force, it can be divided into hydrostatics, fluid kinematics, and fluid dynamics; from the study of different "mechanical models", there are ideal fluid dynamics, viscous fluid dynamics, Incompressible fluid dynamics, compressible fluid dynamics, and non-Newtonian fluid mechanics.

Research Methods in Fluid Mechanics

It can be divided into four aspects: field observation, laboratory simulation, theoretical analysis, and numerical calculation:

Fluid mechanics field observation

The natural flow phenomenon or the full-scale flow phenomenon of existing projects is systematically observed by various instruments, so as to summarize the laws of fluid movement and predict the evolution of flow phenomena. Observations and forecasts of the weather in the past have basically been done this way. However, the occurrence of on-site flow phenomena cannot be controlled, and the occurrence conditions are almost impossible to completely reappear, which affects the study of flow phenomena and laws; on-site observations will also take a lot of material, financial and human resources. Therefore, people have established laboratories to make these phenomena appear under controllable conditions for the convenience of observation and research.

Fluid mechanics laboratory simulation

In the laboratory, the flow phenomenon can be repeated many times in a much shorter time and in a much smaller space. Multiple parameters can be isolated and the experimental parameters can be changed systematically. In the laboratory, people can also cause special conditions rarely encountered in nature (such as high temperature and high pressure), which can make the original invisible phenomenon visible. On-site observations are often observations of existing things and existing projects, while laboratory simulations can observe things that have not yet appeared and phenomena that have not yet occurred (such as engineering to be designed, machinery, etc.) to improve them. Therefore, laboratory simulation is an important method for studying fluid mechanics. However, in order for the experimental data to be consistent with the on-site observations, the conditions of flow similarity (see the law of similarity) must be fully satisfied. However, for scale models, some similar quasi numbers such as Reynolds number and Froude number are not easy to meet at the same time, and large Reynolds numbers for some engineering problems are also difficult to achieve. Therefore, in the laboratory, it is usually aimed at specific problems, try to meet some major similar conditions and parameters, and then verify or correct the experimental results through field observations.

Analysis of fluid mechanics

According to the general laws of fluid motion such as conservation of mass, conservation of momentum, conservation of energy, etc., mathematical analysis is used to study the motion of fluids, explain known phenomena, and predict possible results. The steps of theoretical analysis are roughly as follows:

Establish "Mechanical Model"

The general approach is: in view of the mechanics of the actual fluid, analyze the various contradictions and grasp the main aspects, simplify the problem and establish a "mechanical model" that reflects the essence of the problem. The most commonly used basic models in fluid mechanics are: continuous media (see continuum hypothesis), Newtonian fluids, incompressible fluids, ideal fluids (see viscous fluids), and planar flow.

Establish the governing equation

According to the characteristics of fluid motion, the laws of mass conservation, momentum conservation, and energy conservation are expressed in mathematical language to obtain continuity equations, momentum equations, and energy equations. In addition, some relational equations (such as equations of state) or other equations relating to the flow parameters are added. These equations together are called the basic equations of fluid mechanics. Fluid motion often has certain restrictions in space and time. Therefore, boundary conditions and initial conditions should be given. The mathematical model of the entire flow problem is to establish a closed system of equations that must be satisfied by the flow parameters, and give the appropriate boundary conditions and initial conditions.

Solving the system of equations

Under the given boundary conditions and initial conditions, the mathematical method is used to find the solution of the system of equations. Since this system of equations is a non-linear system of partial differential equations, it is difficult to obtain analytical solutions and must be simplified. This is one of the reasons for the establishment of mechanical models. After years of effort, mechanics have created many mathematical methods or techniques to solve these equations (mainly simplified equations) and get some analytical solutions.

Analyze and explain the solution

After finding the solutions of the system of equations, combined with the specific flow, explain the physical meaning and flow mechanism of these solutions. These theoretical results are usually compared with experimental results to determine the accuracy of the solutions obtained and the applicability of mechanical models.

Numerical calculation of fluid mechanics

The aforementioned equations using the simplified model or closed fluid mechanics basic equations are solved numerically. The emergence and development of electronic computers have made it possible for many complex fluid mechanics problems that could not be solved by theoretical analysis to obtain numerical solutions. Numerical methods can partially or completely replace some experiments, saving experimental costs. Numerical calculation methods have developed rapidly recently and their importance is increasing day by day.

Relationship between four research methods:

When solving fluid mechanics problems, field observations, laboratory simulations, theoretical analysis, and numerical calculations are complementary. Experiments need theoretical guidance to draw regular conclusions from scattered, superficially unrelated phenomena and experimental data. Conversely, theoretical analysis and numerical calculations also rely on field observations and laboratory simulations to give physical patterns or data to establish mechanical and mathematical models of flow. Finally, experiments must be used to verify the integrity of these models and models. In addition, the actual flow is often extremely complicated (such as turbulence), and theoretical analysis and numerical calculations will encounter huge mathematical and computational difficulties. No specific results can be obtained, and research can only be performed through field observations and laboratory simulations.

Related books (4)

Fluid Mechanics Outlook

For more than 2,000 years from Archimedes to the present, especially since the 20th century, fluid mechanics has developed into a part of the basic science system, and it has also been used in industry, agriculture, transportation, astronomy, geoscience, biology, medicine, etc. Has been widely used. In the future, on the one hand, people will conduct research on the application of fluid mechanics according to the needs of engineering technology, and on the other hand, they will carry out more in-depth basic research to explore the complex flow laws and mechanisms of fluids. The latter aspect mainly includes: understanding the structure and establishing a computational model through theoretical and experimental studies of turbulence; multiphase flow; interaction of fluids and structures; boundary layer flow and separation; biogeography and environmental fluid flow; related issues; Various experimental equipment and instruments.

Research areas of fluid mechanics include:

Theoretical fluid mechanics

Hydrodynamics

Gas dynamics

aerodynamics

Suspension mechanics

Turbulence theory

Viscous fluid mechanics

Multiphase fluid mechanics

Seepage mechanics

Physics-chemical fluid mechanics

Plasma dynamics

Electromagnetic fluid mechanics

Non-Newtonian fluid mechanics

Fluid mechanics fluid mechanics

Rotation and layered fluid mechanics

Radiation fluid mechanics

Computational Fluid Dynamics

Experimental fluid mechanics

Environmental fluid mechanics

Microfluidics

Biological fluid mechanics