The methodical manual "Basic laws of hydraulics" is a short theoretical course that sets out the basic terms and provisions.
The manual is recommended to help students of the specialty "Installation and operation of gas supply systems and equipment" in classroom or extracurricular independent work and teacher of the disciplines "Fundamentals of hydraulics, heat engineering and aerodynamics", "Hydraulics".
At the end of the manual there is a list of questions for self-study and a list of literature recommended for study.
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"Basic laws of hydraulics"
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The methodical manual "Basic laws of hydraulics" is a short theoretical course that sets out the basic terms and provisions.
The manual is recommended to help students of the specialty "Installation and operation of gas supply systems and equipment" in classroom or extracurricular independent work and the teacher of the disciplines "Fundamentals of hydraulics, heat engineering and aerodynamics", "Hydraulics".
At the end of the manual there is a list of questions for self-study and a list of literature recommended for study.
Introduction…………………………………………………………………….....4
- Hydrostatics, basic concepts………………………………………......5
- The basic equation of hydrostatics…………………………………………7
- Types of hydrostatic pressure .................................................................... ........eight
- Pascal's law, application in practice………………………………...9
- Law of Archimedes. Bodies floating condition………………………………..11
- Hydrostatic paradox……………………………………………..13
- Hydrodynamics, basic concepts………………………………………..14
- The equation of continuity (continuity)………………………………16
- Bernoulli's equation for an ideal fluid…………………….......17
- Bernoulli's equation for a real fluid………………………….20
- Questions for self-preparation of students………………..22
Conclusion…………………………………………………………………...23
References……………………………………………………..............24
Introduction
Given Toolkit covers the sections "Hydrostatics" and "Hydrodynamics" of the discipline "Fundamentals of hydraulics, heat engineering and aerodynamics". The manual outlines the basic laws of hydraulics, discusses the basic terms and provisions.
The material is presented in accordance with the requirements curriculum of this discipline and an educational and methodological complex in the specialty "Installation and operation of gas supply systems and equipment."
The manual is a theoretical course, it can be used in the study of individual topics academic discipline as well as for extracurricular independent work.
Please note that the final stage of this methodological manual is a list of questions for self-preparation of students on all the topics presented.
1. Hydrostatics, basic concepts
Hydrostatics is a section of hydraulics that studies the laws of equilibrium of fluids and their interaction with bounding surfaces.
Consider a liquid in a state of absolute equilibrium, i.e. at rest. Let us single out some infinitesimal volume inside the liquidΔ V and consider the forces acting on it from the outside.
There are two types of external forces - surface and volumetric (mass).
Surface forces are the forces acting directly on the outer surface of the selected volume of liquid. They are proportional to the area of this surface. Such forces are due to the influence of neighboring volumes of liquid on a given volume or the influence of other bodies.
Volume (mass) forcesare proportional to the mass of the selected volume of liquid and act on all particles inside this volume. Examples of body forces are gravity, centrifugal force, inertia force, etc.
To characterize the internal forces acting on a selected volume of liquid, we introduce a special term. To do this, consider an arbitrary volume of liquid in equilibrium under the action of external forces.
We select a very small area inside this volume of liquid. The force acting on this area is normal (perpendicular) to it, then the ratio:
represents the average hydrostatic pressure occurring at the siteΔω . Otherwise, it can be characterized that under the action of external forces, a stressed state of the liquid occurs, characterized by the occurrence of hydrostatic pressure.
To determine the exact value of p at a given point, it is necessary to determine the limit of this ratio at. which will determine the true hydrostatic pressure at a given point:
The dimension of [p] is equal to the dimension of voltage, i.e.
[p]= [Pa] or [kgf/m 2 ]
Hydrostatic pressure properties
On the outer surface of the liquid, the hydrostatic pressure is always directed along the internal normal, and at any point inside the liquid, its value does not depend on the angle of inclination of the platform on which it acts.
A surface in which the hydrostatic pressure is the same at all points is calledequal pressure surface. These surfaces includefree surface, i.e., the interface between a liquid and a gaseous medium.
Pressure is measured for the purpose of continuous monitoring and timely regulation of all technological parameters. For each technological process, a special regime map is developed. There are cases when, with an uncontrolled increase in pressure, a multi-ton drum of an energy boiler flew away like a soccer ball for several tens of meters, destroying everything in its path. The decrease in pressure does not cause damage, but leads to:
- defective products;
- fuel overrun.
- Basic equation of hydrostatics
Figure 1 - Demonstration of the basic equation of hydrostatics
For any point of a fluid in a state of equilibrium (see Fig. 1), the equality
z+p/γ = z 0 +p 0 /γ = ... = H ,
where p is the pressure at a given point A (see Fig.); p 0 - pressure on the free surface of the liquid; p/γ and p 0 /γ is the height of the liquid columns (with specific gravity γ) corresponding to the pressures at the considered point and on the free surface; z and z 0 - coordinates of point A and the free surface of the liquid relative to an arbitrary horizontal comparison plane (x0y); H - hydrostatic head. From the above formula follows:
p = p 0 +γ(z 0 -z) or p = p 0 +γ h
where h is the immersion depth of the considered point. The above expressions are calledthe basic equation of hydrostatics. The value γ h representsliquid column weight height h.
Conclusion: hydrostatic pressure p at a given point is equal to the sum of the pressure on the free surface of the liquid p 0 and the pressure produced by a liquid column with a height equal to the point's immersion depth.
3. Types of hydrostatic pressure
Hydrostatic pressure is measured in the SI - Pa system. In addition, hydrostatic pressure is measured in kgf/cm 2 , the height of the liquid column (in m water column, mm Hg, etc.) and in physical (atm) and technical (at) atmospheres.
absolute called the pressure created on the body by a single gas without taking into account other atmospheric gases. It is measured in Pa (pascals). Absolute pressure is the sum of atmospheric and gauge pressures.
Barometric(atmospheric) refers to the pressure of gravity on all objects in the atmosphere. Normal atmospheric pressure is created by a 760 mm column of mercury at a temperature of 0°C.
vacuum called the negative difference between measured and atmospheric pressure.
Difference between absolute pressure p and atmospheric pressure p a is called excess pressure and is denoted by p hut:
p izb \u003d p - p a
or
R izb / γ \u003d (p - p a) / γ \u003d h p
h p in this case is calledpiezometric height, which is a measure of excess pressure.
On fig. 2 a) shows a closed reservoir with a liquid, on the surface of which the pressure p 0 . Piezometer connected to the tank P (see figure below) determines the excess pressure at the point BUT .
Absolute and gauge pressures, expressed in atmospheres, are denoted respectively ata and ati.
Vacuum pressure, or vacuum, - lack of pressure to atmospheric (pressure deficit), i.e. the difference between atmospheric or barometric and absolute pressure:
p wak \u003d p a - p
or
R wack /γ = (p a - p)/γ = h wak
where h vac - vacuum height, i.e. vacuum gauge reading AT connected to the reservoir shown in fig. 2 b). Vacuum is expressed in the same units as pressure, as well as fractions or percentages of the atmosphere.
Figure 2 a - Piezometer readings Figure 2 b - Vacuum gauge readings
From the last two expressions it follows that the vacuum can vary from zero to atmospheric pressure; maximum h value wack at normal atmospheric pressure (760 mm Hg) is equal to 10.33 m of water. Art.
4. Pascal's law, its application in practice
According to the basic equation of hydrostatics, the pressure on the liquid surface p 0 is transmitted to all points of the volume of the liquid and in all directions equally. This is what Pascal's law.
This law was discovered by the French scientist B. Pascal in 1653. It is sometimes called the fundamental law of hydrostatics.
Pascal's law can be explained in terms of the molecular structure of matter. In solids, molecules form a crystal lattice and vibrate around their equilibrium positions. In liquids and gases, molecules are relatively free, they can move relative to each other. It is this feature that allows you to transfer the pressure produced on a liquid (or gas) not only in the direction of the force, but in all directions.
Pascal's law has found wide application in modern technology. The work of modern superpresses is based on Pascal's law, which allows creating pressures of the order of 800 MPa. Also, this law is based on the operation of hydraulic automation systems that control spaceships, jet airliners, numerical control machines, excavators, dump trucks, etc.
Pascal's law is not applicable in the case of a moving liquid (gas), as well as in the case when the liquid (gas) is in a gravitational field; for example, it is known that atmospheric and hydrostatic pressure decreases with height.
Figure 3 - Demonstration of Pascal's law
Consider the most famous device that uses Pascal's law in principle. This is a hydraulic press.
The basis of any hydraulic press are communicating vessels in the form of two cylinders. The diameter of one cylinder is much smaller than the diameter of the other cylinder. The cylinders are filled with liquid, such as oil. From above they are tightly closed by pistons. As can be seen from fig. 4 below, single piston area S 1 many times smaller than the area of the other piston S 2 .
Figure 4 - Communicating vessels
Suppose a force is applied to a small piston F1 . This force will act on the liquid, distributing over the area S1 . The pressure exerted by a small piston on a liquid can be calculated by the formula:
According to Pascal's law, this pressure will be transmitted unchanged to any point in the fluid. This means that the pressure exerted on the large piston p 2 will be the same:
This implies:
In this way , the force acting on the large piston will be as many times greater than the force applied to the small piston as the area of the large piston more area small piston.
As a result, the hydraulic machine allows you to get gain in strength equal to the ratio of the area of the larger piston to the area of the smaller piston.
5. Law of Archimedes. Bodies floating condition
A body immersed in a liquid, in addition to gravity, is affected by a buoyant force - the Archimedes force. The fluid presses on all faces of the body, but the pressure is not the same. After all, the lower face of the body is immersed in the liquid more than the upper, and the pressure increases with depth. That is, the force acting on the lower face of the body will be greater than the force acting on the upper face. Therefore, a force arises that tries to push the body out of the liquid.
The value of the Archimedean force depends on the density of the liquid and the volume of that part of the body that is directly in the liquid. The Archimedes force acts not only in liquids, but also in gases.
Law of Archimedes : a body immersed in a liquid or gas is subjected to a buoyant force equal to the weight of the liquid or gas in the volume of the body.
The Archimedes force acting on a body immersed in a liquid can be calculated by the formula:
where ρ w is the liquid density, V Fri is the volume of the part of the body immersed in the liquid.
Two forces act on a body that is inside a liquid: the force of gravity and the force of Archimedes. Under the influence of these forces, the body can move. There are three conditions for floating bodies (Fig. 5):
- if gravity is greater than the Archimedean force, the body will sink, sink to the bottom;
- if the force of gravity is equal to the force of Archimedes, then the body can be in equilibrium at any point in the fluid, the body floats inside the fluid;
- if the force of gravity is less than the Archimedean force, the body will float, rising up.
Figure 5 - Conditions for floating bodies
Archimedes' principle is also used for aeronautics. First Balloon in 1783 the Montgolfier brothers created it. In 1852, the Frenchman Giffard created an airship - a controlled balloon with an air rudder and propeller.
6. Hydrostatic paradox
If the same liquid is poured to the same height into vessels of different shapes, but with the same bottom area, then, despite the different weight of the poured liquid, the pressure force on the bottom is the same for all vessels and is equal to the weight of the liquid in the cylindrical vessel.
This phenomenon is calledhydrostatic paradoxand is explained by the property of a liquid to transmit pressure produced on it in all directions.
In vessels of various shapes (Fig. 6), but with the same bottom area and the same liquid level in them, the pressure of the liquid on the bottom will be the same. It can be calculated:
P = p ⋅ S = g ⋅ ρ ⋅ h ⋅ S
S - bottom area
h is the height of the liquid column
Figure 6 - Vessels of various shapes
The force with which the liquid presses on the bottom of the vessel does not depend on the shape of the vessel and is equal to the weight of the vertical column, the base of which is the bottom of the vessel, and the height is the height of the liquid column.
In 1618, Pascal amazed his contemporaries by breaking a barrel with just a mug of water poured into a thin tall tube inserted into the barrel.
7. Hydrodynamics, basic concepts
Hydrodynamics is a section of hydraulics that studies the laws of motion of fluids under the action of applied external forces and their interaction with surfaces.
The state of a moving fluid at each of its points is characterized not only by density and viscosity, but also, most importantly, by the velocity of fluid particles and hydrodynamic pressure.
The main object of study is the fluid flow, which is understood as the movement of a fluid mass bounded in whole or in part by some surface. The bounding surface can be solid (for example, river banks), liquid (interface between states of aggregation), or gaseous.
Fluid flow can be steady and unsteady. Steady-state movement is such a movement of a fluid in which at a given point in the channel the pressure and speed do not change with time
υ = f(x, y, z) and p = f(x, y, z)
Motion, in which the speed and pressure change not only from the coordinates of space, but also from time, is called unsteady or non-stationary υ \u003d f (x, y, z, t) and p \u003d f (x, y, z, t)
An example of a steady motion is the outflow of a liquid from a vessel with a constant level maintained through a conical tube. The speed of the fluid in different sections of the tube will vary, but in each of the sections this speed will be constant, not changing in time.
If, in such an experiment, the liquid level in the vessel is not maintained constant, then the movement of the liquid along the same conical tube will have an unsteady (unsteady) character, since the velocity in the tube sections will not be constant in time (it will decrease with decreasing liquid level in the vessel).
Distinguish between pressure and non-pressure fluid movement. If the walls completely restrict the fluid flow, then the movement of the fluid is called pressure (for example, the movement of fluid through completely filled pipes). If the restriction of the flow by the walls is partial (for example, the movement of water in rivers, canals), then such movement is called non-pressure.
The direction of velocities in the flow is characterized by a streamline.
Streamline - an imaginary curve drawn inside the fluid flow in such a way that the velocities of all particles located on it in this moment time are tangent to this curve.
Figure 7 - Current line
The streamline differs from the trajectory in that the latter reflects the path of any one particle over a certain period of time, while the streamline characterizes the direction of movement of a set of fluid particles at a given time. With steady motion, the streamline coincides with the trajectories of motion of fluid particles.
If in the cross section of the fluid flow to select an elementary area∆S and draw a streamline through the points of its contour, then you get the so-called current tube . The fluid inside the current tube formsan elementary trickle. The fluid flow can be considered as a set of all moving elementary jets.
Figure 8 - Current tube
The living section ω (m²) is the cross-sectional area of the flow, perpendicular to the direction of flow. For example, the living section of a pipe is a circle.
Wetted perimeter χ ("chi") - part of the perimeter of the living section, bounded by solid walls (in the figure it is highlighted by a thickened line).
Figure 9 - Living section
Hydraulic flow radius R - the ratio of the open area to the wetted perimeter
The flow rate Q is the volume of liquid V flowing per unit time t through the open area ω.
The average flow velocity υ is the velocity of the liquid, determined by the ratio of the liquid flow rate Q to the open area ω
Since the speed of movement of various particles of a liquid differs from each other, therefore, the speed of movement is averaged. In a round pipe, for example, the velocity on the axis of the pipe is maximum, while at the walls of the pipe it is equal to zero.
- Continuity (continuity) equation
The equation of the continuity of flows follows from the law of conservation of matter and the constancy of the flow rate of the liquid throughout the flow. Imagine a pipe with a variable free cross section.
Figure 10 - Demonstration of the jet continuity equation
The fluid flow through the pipe in any of its sections is constant, because the law of conservation of energy is satisfied. We also assume that the fluid is incompressible. So Q 1 = Q 2 = const, whence
ω 1 υ 1 = ω 2 υ 2
Or another way to write this equation is:
Those. average speeds v1 and v2 are inversely proportional to the corresponding areas of living sections w 1 and w 2 fluid flow.
So, the continuity equation expresses the constancy of the volume flow Q , and the condition of fluid jet continuity along the length of the steady fluid flow.
9. Bernoulli's equation for an ideal fluid
Daniil Bernoulli's equation, obtained in 1738, shows the relationship between pressure p, average velocity υ and piezometric height z in various sections of the flow and expresses the law of conservation of energy of a moving fluid.
Consider a pipeline of variable diameter located in space at an angle β (see Fig. 10)
Figure 11 - Demonstration of the Bernoulli equation for an ideal fluid
Let us randomly choose two sections on the pipeline section under consideration: section 1-1 and section 2-2. Up the pipeline from the first section to the second one moves a liquid with a flow rate Q.
To measure the pressure of a liquid, piezometers are used - thin-walled glass tubes in which the liquid rises to a height. In each section, piezometers are installed, in which the liquid level rises to different heights.
In addition to piezometers, in each section 1-1 and 2-2, a tube is installed, the bent end of which is directed towards the fluid flow, which is called the Pitot tube. The liquid in the pitot tubes also rises to different levels, if counted from the piezometric line.
The piezometric line can be constructed as follows. If we put several of the same piezometers between sections 1-1 and 2-2 and draw a curve through the readings of the liquid levels in them, we will get a broken line (shown in the figure).
But the height of the levels in Pitot tubes relative to an arbitrary horizontal line 0-0 (the reference plane of coordinates), called the plane of comparison, will be the same.
If a line is drawn through the readings of the liquid levels in the Pitot tubes, then it will be horizontal and will reflect the level of the total energy of the pipeline.
For two arbitrary sections 1-1 and 2-2 of the flow of an ideal fluid, the Bernoulli equation has the following form:
Since sections 1-1 and 2-2 are taken arbitrarily, the resulting equation can be rewritten differently:
The formulation of the equation is as follows:
The sum of the three terms of the Bernoulli equation for any section of the flow of an ideal fluid is a constant value.
From an energy point of view, each term in the equation represents certain types of energy:
z1 and z2 - specific position energies characterizing the potential energy in sections 1-1 and 2-2;- specific pressure energies characterizing the potential energy of pressure in the same sections;- specific kinetic energies in the same sections.
It turns out that the total specific energy of an ideal fluid in any section is constant.
There is also a formulation of the Bernoulli equation from a geometric point of view. Each term of the equation has a linear dimension. z 1 and z 2 - geometric heights of sections 1-1 and 2-2 above the comparison plane;- piezometric heights;- high-speed heights in the specified sections.
In this case, the Bernoulli equation can be read as follows: the sum of the geometric, piezometric and velocity heights for an ideal fluid is a constant.
10. Bernoulli's equation for a real fluid
The Bernoulli equation for the flow of a real fluid is different from the Bernoulli equation for an ideal fluid.
When a real viscous fluid moves, friction forces arise, for example, due to the fact that the surface of the pipeline has a certain roughness, to overcome which the fluid expends energy. As a result, the total specific energy of the liquid in section 1-1 will be greater than the total specific energy in section 2-2 by the value of the lost energy.
Figure 12 - Demonstration of the Bernoulli equation for a real fluid
Lost energy (lost head) are denotedhas a linear dimension.
The Bernoulli equation for a real fluid will look like:
As the fluid moves from section 1-1 to section 2-2, the lost head increases all the time (the lost head is marked with vertical shading).
Thus, the level of initial energy, which the liquid has in the first section, for the second section will be the sum of four components: geometric height, piezometric height, velocity height and lost head between sections 1-1 and 2-2.
In addition, two more coefficients α appeared in the equation 1 and α 2 , which are called Coriolis coefficients and depend on the fluid flow regime (α = 2 for laminar regime, α = 1 for turbulent regime).
Lost Heightconsists of the head loss along the length of the pipeline, caused by the friction force between the layers of the liquid, and the losses caused by local resistances (changes in the flow configuration, for example, a gate valve, a pipe turn)
H lengths + h places
With the help of the Bernoulli equation, most problems of practical hydraulics are solved. To do this, choose two sections along the length of the flow, so that for one of them the values \u200b\u200bof p, ρ are known, and for the other section one or the values \u200b\u200bare to be determined. With two unknowns for the second section, the equation of constancy of fluid flow υ is used 1 ω 1 = υ 2 ω 2 .
11. Questions for self-preparation of students
- What forces cause a body to float in water? Explain the conditions under which a body begins to sink.
- What do you think is the difference between an ideal liquid and a real one? Does an ideal liquid exist in nature?
- What types of hydrostatic pressure do you know?
- If we determine the hydrostatic pressure at a point in the liquid at a depth h , then what forces will act on this point? Name and explain your answer.
- What physical law underlies the continuity equation and the Bernoulli equation? Explain the answer.
- Name and briefly describe the devices, the principle of which is based on Pascal's law.
- What is the physical phenomenon called the hydrostatic paradox?
- Coriolis coefficient, average flow rate, pressure, head loss along the length of the pipeline .... Explain which equation relates all these quantities, and what is not yet indicated in this listing.
- Name the formula relating specific gravity and density.
- The fluid jet continuity equation plays a rather important role in hydraulics. What kind of liquid is it true for? Explain your answer.
- Name the names of all the scientists named in this methodological manual, and briefly explain their discoveries.
- Do ideal fluid, streamline, vacuum exist in the world around us? Explain your answer.
- Name the instruments for measuring various kinds pressure according to the scheme: "Type of pressure ... .. - device ... ..".
- Give examples from Everyday life types of pressure and non-pressure fluid movement, stationary and unsteady.
- For what purposes are piezometers, barometers, and pitot tubes used in practice?
- What happens if, when measuring pressure, it is found that it is much higher than the normative values? What if it's less? Explain your answer.
- What is the difference between the objects of study of the sections "hydrostatics" and "hydrodynamics"?
- Explain the geometric and energetic meaning of the Bernoulli equation?
- Wetted perimeter, clear section... Continue this list and explain what the listed terms characterize.
- List what laws of hydraulics you learned from this methodological manual, and what physical meaning do they carry?
Conclusion
I hope that this manual will help students to better understand educational material disciplines "Hydraulics", "Fundamentals of hydraulics, heat engineering and aerodynamics" and most importantly - to get an idea of the most "bright" moments of the discipline being studied, i.e. about the fundamental laws of hydraulics. The operation of many devices that we use at work and in everyday life are based on these laws, often without even realizing it.
Sincerely, Markova N.V.
Bibliography
- Bryukhanov O.N. Fundamentals of hydraulics and heat engineering: A textbook for students. inst. avg. prof. education / Bryukhanov O.N., Melik-Arakelyan A.T., Korobko V.I. - M.: ITs Academy, 2008. - 240 p.
- Bryukhanov O.N. Fundamentals of Hydraulics, Heat Engineering and Aerodynamics: A Textbook for Students. inst. avg. prof. education / Bryukhanov O.N., Melik-Arakelyan A.T., Korobko V.I. - M.: Infra-M, 2014, 253 p.
- Gusev A. A. Fundamentals of hydraulics: A textbook for students. inst. avg. prof. education / A. A. Gusev. - M.: Yurayt Publishing House, 2016. - 285 p.
- Ukhin B.V. Hydraulics: A textbook for students. inst. avg. prof. education / Ukhin B.V., Gusev A.A. - M.: Infra-M, 2013, 432 p.
The theoretical foundations of refrigeration plant and machine processes as well as air conditioning concepts are mainly based on two fundamental sciences: thermodynamics and hydraulics.
Definition 1
Thermodynamics is a science that studies the patterns of transformation of internal energy into various chemical, physical and other processes considered by scientists at the macro level.
Thermodynamic provisions are based on the first and second laws of thermodynamics, which were first formulated at the beginning of the 19th century and became the development of the foundations of the mechanical hypothesis of heat, as well as the law of transformation and conservation of energy, formulated by the great Russian researcher M.V., Lomonosov.
The main direction of thermodynamics is technical thermodynamics, which studies the processes of mutual transformation of heat into work and the conditions under which these phenomena occur most efficiently.
Definition 2
Hydraulics is a science that studies the laws of equilibrium and movement of fluids, as well as developing methods for using them to solve complex engineering problems.
The principles of hydraulics are often used in solving many issues related to the design, design, operation and construction of various hydraulic pipelines, structures and machines.
The outstanding founder of hydraulics is the ancient Greek thinker Archimedes, who wrote scientific work"On floating bodies". Hydraulics as a science arose much earlier than thermodynamics, which is directly related to the social intellectual activity of man.
Development of hydraulics and thermodynamics
Figure 1. Hydraulic flow measurement. Author24 - online exchange of student papers
Hydraulics is a complex theoretical discipline that carefully studies issues related to the mechanical movement of various fluids in natural and man-made conditions. Since all elements are considered as indivisible and continuous physical bodies, hydraulics can be considered one of the sections of continuum mechanics, to which it is customary to include a special substance - a liquid.
Already in ancient China and Egypt, people knew how to build dams and water mills on rivers, irrigation systems in huge rice fields, in which powerful water-lifting machines were used. Rome, six centuries BC. e. a water pipe was built, which speaks of the ultra-high technical culture of that time. The first treatise on hydraulics should be considered the teachings of Archimedes, who was the first to invent a machine for lifting water, which was later called the “Archimedean screw”. It is this device that is the prototype of modern hydraulic pumps.
The first pneumatic concepts arose much later than hydraulic ones. Only in the XVIII century. n. e. in Germany, a machine for the "movement of gas and air" was introduced. With the development of technology, hydraulic systems were modernized and the scope of their practical application quickly expanded.
In the development of thermodynamics in the 19th century, scientists distinguish three main periods, each of which had its own distinctive properties:
- the first one was characterized by the formation of the first and second thermodynamic principles;
- the second period lasted until the middle of the 19th century and was distinguished by the scientific works of outstanding European physicists such as the Englishman J. Joule, the German researcher Gottlieb, and W. Thomson;
- The third generation of thermodynamics is opened by the famous Austrian scientist and member of the St. Petersburg Academy of Sciences, Ludwig Boltzmann, who, through numerous experiments, established the relationship between the mechanical and thermal forms of motion.
Further, the development of thermodynamics did not stand still, but advanced at an accelerated pace. Thus, the American Gibbs developed chemical thermodynamics in 1897, that is, he made physical chemistry an absolutely deductive science.
Basic concepts and methods of two scientific directions
Figure 2. Hydraulic resistance. Author24 - online exchange of student papers
Remark 1
The subject of research in hydraulics is the basic laws of equilibrium and the chaotic movement of fluids, as well as methods for activating hydraulic systems for water supply and irrigation.
All these postulates were known to man long before our era. The term "fluid" in fluid mechanics has a broader meaning than is commonly believed in thermodynamics. The concept of "fluid" includes absolutely all physical bodies that can change their shape under the influence of arbitrarily small forces.
Therefore, this definition means not only ordinary (drop) liquids, as in thermodynamics, but also gases. Despite the difference in the branches of physics under study, the laws of motion of dropping gases and liquids under certain conditions can be considered the same. The main of these conditions is the speed indicator compared to the same sound parameter.
Hydraulics studies primarily the flow of fluids in various channels, that is, flows limited by dense walls. The concept of "channel" includes all devices that restrict the flow itself, including the flow parts of pumps, pipelines, gaps and other elements of hydraulic concepts. Thus, in hydraulics, mainly internal flows are studied, and in thermodynamics, external ones.
Remark 2
The subject of thermodynamic analysis is a system that can be separated from the environment by some control surface.
The research method in thermodynamics is a macroscopic method.
To accurately characterize the macrostructural properties of the system, the values of the macroscopic concept are used:
- nature:
- temperature;
- pressure;
- specific volume.
The peculiarity of the thermodynamic method lies in the fact that its base is the only fundamental law of nature - the law of transformation and conservation of energy. This means that all the key relationships that form the basis of the mathematical apparatus are derived only from this provision.
Fundamentals of hydraulics and thermodynamics
When studying the basics of hydraulics and thermodynamics, it is necessary to rely on the representations of those sections of physics that will help to better master and understand the principle of the functionality of hydraulic machines.
All physical bodies are made up of atoms that are in constant motion. Such elements attract at a relatively short distance and repel at a fairly close one. At the center of the smallest particle is a positively charged nucleus, around which electrons randomly move, forming electron shells.
Definition 3
A physical quantity is a quantitative description of the properties of a material body, which has its own unit of measurement.
Almost a century and a half ago, the German physicist K. Gauss proved that if you choose independent units of measurement for several parameters, then on their basis, by means of physical laws, it is possible to establish units of quantities included in absolutely any section of physics.
The unit of speed in hydraulics is a derived unit of concept derived from the system units of the meter and second. The considered physical quantities (acceleration, speed, weight) are determined in thermodynamics using the basic units of measurement and have a dimension. Despite the presence of molecular forces, water molecules are always in constant motion. The higher the temperature of a liquid, the faster its constituent parts move.
Let us dwell in more detail on some physical properties of liquids and gases. Liquids and gases in a hydraulic system can easily deform while retaining their original volume. In a thermodynamic system, things look completely different. For such a deformation in thermodynamics, it is not necessary to perform any mechanical work. This means that the elements operating in a certain concept weakly resist a probable shift.
MINISTRY OF AGRICULTURE AND FOOD OF THE REPUBLIC OF BELARUS
EE "GORODOKSKY STATE AGRARIAN AND TECHNICAL COLLEGE"
BASICS OF HEAT ENGINEERING AND HYDRAULICS
student guide correspondence department
in questions and answers
partI
Town
"Reviewed"
at a meeting of the methodological commission
general professional disciplines
Protocol No. ____ dated ________________
Chairman: ________
The manual is intended for students of the correspondence department of specialties 2-74 06 01 "Technical support of agricultural production processes" and 2-74 06 31 "Energy support of agricultural production" for self-study discipline "Fundamentals of heat engineering and hydraulics".
Introduction. 5
Fuel and energy complex of the Republic of Belarus. 6
Working body and its parameters.. 11
Basic gas laws.. 12
Basic equations of thermodynamics. fourteen
gas mixtures. Dalton's Law. 16
Heat capacity: its types, calculation of heat consumption for heating. eighteen
Heat capacity in processes at constant pressure and at constant volume 19
The first law of thermodynamics and its analytical expression. 21
The concept of a thermodynamic process, their types.. 22
isochoric process. Its graph in - coordinates and basic equations 23
isobaric process. Its plot in - coordinates and basic equations 24
isothermal process. Its plot in - coordinates and basic equations 26
adiabatic process. Its plot in - coordinates and basic equations 28
circular process. Its schedule and efficiency.. 30
Carnot cycle and its efficiency.. 31
Water vapor. Basic definitions. 33
The process of vaporization in - coordinates. 35
The ideal cycle of a steam power plant and its efficiency.. 37
C. Their classification. 40
Ideal cycles for D.V.S. Their efficiency.. 42
Real ICE cycles, power determination. 45
Heat balance and specific fuel consumption in internal combustion engines.. 48
Operation diagram and indicator diagram of a single-stage compressor 49
The indicator diagram of a virtual compressor. 51
Multistage reciprocating compressors.. 53
The concept of the operation of centrifugal, axial and rotary compressors 56
Heat transfer methods. 58
Heat transfer by thermal conduction through a single-layer flat wall 60
Heat conduction through a multilayer wall. 62
Heat conduction through cylindrical walls. 64
convective heat transfer. 66
Heat transfer by radiation.. 67
Heat exchangers. Their types.. 70
Fundamentals of calculation of heat exchangers. 72
Complex heat transfer through a flat wall. 75
Heat transfer through a cylindrical wall. 78
Introduction
The discipline "Fundamentals of heat engineering and hydraulics" provides for the study by students of the basics of thermodynamics and hydraulics, the principles of operation of boilers and drying plants, internal combustion engines, compressors, refrigeration machines, solar water heaters and pumps. The main energy problem facing science is to improve the technical and economic performance of heat engineering and power equipment, which will undoubtedly lead to a reduction in fuel consumption and an increase in efficiency.
Thermal power engineering is the main industry and Agriculture, which is engaged in the transformation of natural thermal resources into thermal, mechanical and electrical energy. An integral part thermal power industry is technical thermodynamics, which deals with the study of physical phenomena associated with the transformation of heat into work. Based on the laws of thermodynamics, calculations are made for heat engines, heat exchangers. The conditions for the greatest efficiency of power plants are determined. A great contribution to the development of heat engineering was made by those who created the classic works on thermodynamics.
Systematized the laws of convective and radiant heat transfer.
They laid the foundations for the design and construction of steam boilers and engines.
Knowledge of the laws of technical thermodynamics and the ability to apply them in practice makes it possible to improve the operation of heat engines and reduce fuel consumption, which is very important at the present time, when prices for hydrocarbon raw materials are increasing and consumption volumes are increasing.
Question 1
Fuel and energy complex of the Republic of Belarus
The highest priority of the energy policy of the Republic of Belarus, along with the sustainable provision of the country with energy carriers, is the creation of conditions for the functioning and development of the economy with the most efficient use of fuel and energy resources.
Own reserves of fuel and energy resources in the Republic of Belarus are insufficient and amount to approximately 15-20% of the consumed amount. In sufficient quantities there is peat and wood, brown coal, slates are rather low-calorie.
Oil is produced in the Republic of Belarus about 2 million tons per year. Gas about 320-330 thousand tons of fuel equivalent The remaining energy carriers are purchased abroad, mainly from Russia.
The price of energy carriers has seriously increased. So for 1000 m3 of gas 115u. e, oil - for one ton 230 c.u. e. In a year Belarus buys about 22 billion natural gas and about 18 million oil. So that the country's energy security does not depend on one supplier, negotiations are underway with Azerbaijan, the Middle East, and Venezuela, which in the future will sell hydrocarbon raw materials in the form of oil.
At present, the government and the energy saving committee put great emphasis on the use of local fuels, and by 2010 they should reduce the consumption of purchased energy resources by 20-25%.
Peat.
More than 9,000 peat deposits have been explored in the republic with total area within the boundaries of the industrial depth of the deposit of 2.54 million hectares and the initial reserves of peat 5.65 billion tons. To date, the remaining geological reserves are estimated at 4.3 billion tons, which is 75% of the original.
The main reserves of peat lie in the deposits used agriculture(1.7 billion tons and 39% of the remaining reserves) or classified as environmental objects (1.6 billion tons or 37%).
Peat resources included in the developed fund are estimated at 260 million tons, which is 6% of the remaining reserves. The reserves recoverable during the development of deposits are estimated at 110-140 million tons.
Burning shale.
The predicted reserves of oil shale (Lubanskoye and Turovskoye deposits) are estimated at 11 billion tons, industrial - 3 billion tons. t.
The most studied is the Turovskoye deposit, within which the first mine field with reserves of 475-697 million tons was previously explored, 1 million tons of such shale is equivalent to about 220 thousand tons. here. Calorific value - 1000-1500 kcal / kg, ash content -75%, resin yield 6 - 9.2%, sulfur content 2.6%
According to their quality indicators, Belarusian oil shale is not an efficient fuel due to the high ash content and low calorific value. They require preliminary thermal processing with the release of liquid and gaseous fuels. Taking into account the fact that the cost of the products obtained is higher than world prices and oil, as well as taking into account the environmental damage due to the emergence of huge ash dumps and the content of carcinogenic substances in the ash. The extraction of shale and the forecast period is inappropriate.
Brown coals.
The total reserves of brown coal is 151.6 million tons
Two deposits of the Zhitkovichskoye field have been explored in detail and prepared for industrial development: Severnaya (23.5 million tons) and Naidinskaya (23.1 million tons), two other deposits (South - 13.8 million tons and Kolmenskaya - 8.6 million tons). .t) explored beforehand.
The use of brown coal is possible in combination with peat in the form briquettes.
Estimated cost of coal reserves is estimated at 2 tons of fuel equivalent. in year.
Firewood.
In general, in the republic, the annual volume of centralized procurement of firewood and sawmill waste is about 0.94 - 1.00 million tons of fuel equivalent. m. Part of the firewood is supplied to the population through self-procurement, the volume of which is estimated at the level
0.3-0.4 million tons of equivalent fuel
The maximum capacity of the republic for the use of firewood as fuel can be determined based on the natural annual growth of wood, which is approximately estimated at 25 million cubic meters. m or 6.6 mln. tons per year (if you burn everything that grows), including in contaminated areas. Gomel region- 20 thousand cubic meters. m or 5.3 thousand tce To use wood from these areas as fuel, it is necessary to develop and implement gasification technologies and equipment. Given the fact that by 2015 it is planned to double timber harvesting for the production of heat energy, the projected annual volume of wood fuel by 2010 may increase to 1.8 million tons of fuel equivalent.
Renewable energy sources.
The potential capacity of all watercourses in Belarus is 850 MW, including technically available capacity - 520 MW, and economically viable - 250 MW. Due to hydro resources, by 2010 it is possible to generate 40 million kWh and, accordingly, to displace 16 thousand tons of fuel equivalent.
On the territory of the Republic of Belarus, 1840 sites have been identified for the placement of wind turbines with a theoretical potential of 1600 MW and an annual electricity generation of 16 thousand tons of fuel equivalent.
However, in the period up to 2015, the technically possible and economically feasible use of the wind potential will not exceed 5% of the installed capacity e and will amount to 720-840 million kWh.
World reserves of energy carriers.
