[工学]液压与气压传动课件

Hydraulics and Pneumatics Transmission,1 Fluid Properties2 Mechanics of fluids at rest3 Mechanics of fluids in motion4 Energy loss of fluids in motion5 Flow of fluids in clearances and orifices6 Hydraulically sticking7 Hydraulically shocking8 Cavitation,FLUID MECHANICS WITH HYDRAULICS,1.1Density Fluid density was defined as mass per unit volume,1 Fluid Properties,hydraulic oil =890-910kg/m3,1.1Compressibility and expansibility,Suppose the volume is the function of pressure and temperature , or V=f(t,p ) , and tV,pV,The volumetric increment can be approximated by is total differential, thus,In hydraulic transmission problems, p32Mpa, the volume variation caused by pressure variation is,Consequently, hydraulic oil may be regarded as uncompressible.-,Found by experiment:,where expansibility coefficient compressibility coefficient,1 Fluid Properties,1.3.1 cohesion force and adhesion force,1.3 Viscosity,1.3.2 dynamic viscosity,There are cohesion forces among fluid particles, while there are adhesion forces among fluid particles and solid wall.Adhesion forces are usually greater than cohesion force except mercury.,Consider two parallel plates, placed a small distance Y apart, the space between the plates being filled with the fluid.,The lower surface is assumed to be stationary, while upper one is moved parallel to it with a velocity U by the application of a force F, corresponding to some area A of the moving plates,The particles of the fluid in contact with each plate will adhere to it. The velocity gradient will be a straight line. The action is much as if the fluid were made up of a series of thin sheets.,Experiment has shown that for a large class of fluids,If a constant of proportionality is now introduced, the shear stress between any two thin sheets of fluid may be expressed by,(1),Above equation is called Newtows equation of viscosity and in transposed form it serves to define the proportional constant,which is called the dynamic viscosity.,The viscosity is the natural property of fluids, but shown only in fluid flow. The viscosity is a measure of resistance to shear or angle deformation. The viscosity accounts for energy losses associated with the transport of fluids in ducts and pipes.,The friction forces in fluid flow result from the cohesion and momentum interchange between molecules in the fluid.,1 Fluid Properties,1.3.3 Kinematic viscosity,In many problems including viscosity there frequently appear the value of viscosity divided by density. This is defined as kinematic viscosity,E.g. the kinematic viscosity of 30# mechanic oil is 30 厘斯,As temperature increases, the viscosity of all liquids decreases, while the viscosity of all gases increase. This is because the force of cohesion, which diminishes with temperature, predominates with liquids; while with gases the predominating factor in the interchange of molecules between layers of different velocity.,1 Fluid Properties,1.3.3 Relative viscosity,a. Definition : E= t1 /t2,b. Transposed relation,t1 -time the measured liquid (200mL, TC) passes through the viscosity-meter orifice(2.8mm);t2 time the pure water (200mL, 20C) passes through the viscosity-meter orifice(diameter=2.8mm).,1 Fluid Properties,The lubrication oil is named according to its kinematic viscosity E.g. For 30#mechanical oil, its kinematic viscosity is 30 厘斯,The gasoline is named according to its octaneThe diesel oil is named according to its freezing point,2 Mechanics of fluids at rest,Fluid statics is the study of fluids there is no relative motion between fluid particles. The only stress is normal stress, pressure, so it is the pressure that is of primary interest in fluid statics.,2.1 static pressure property,a. The pressure is defined as the force exerted on a unit area,b. The pressure is the same in all direction,Note geometric relation and neglect higher order term, thus,2.2 Basic differential equation,Assume the pressure is the function of space coordinates, or p=f( x, y, z ) . Consider a infinitesimal element in the figure.,Assume that a pressure p exists at the center A of this element, the pressure each of sides can be expressed by using chain rule from calculus with p( x, y, z ),2 Mechanics of fluids at rest,Newtons second law is writtenin vector for constant mass system. F=ma,This results in three componentequations,Where ax, ay, and az are the components of the acceleration of the element.,2 Mechanics of fluids at rest,Division by the elements volume dxdydz yields,The equation expresses the relation between pressure variation and acceleration.,(2),2 Mechanics of fluids at rest,2.3 Examples included in fluid statics.,E1: liquid at rest,Solution,The quantity is referred to as the piezometric head,Another form is written as,Where p-the pressure at a point; gh-the pressure caused by liquid column weight; p0-the pressure caused by external force (either gas or liquid or solid).,(3),(4),2 Mechanics of fluids at rest,(4),Explanation: The term is used to convert pressure to a height of liquid. Neglect the pressure caused by the fluid weight when studying gases. Neglect the pressure caused by the liquid weight and the pressure caused by atmosphere on hydraulic transmission. The equal-pressure surface is a horizontal plane. The free surface is a special equal-pressure surface (p=pa).,2 Mechanics of fluids at rest,E2: Trolley in a linear acceleration,Solution The liquid is at rest relative to the trolley, so the reference frame is established on the trolley. According to Equation (1),When x=z=0, p=pa, thus,The equal-pressure surface is not a horizontal plane but a slope surface.,2 Mechanics of fluids at rest,E3: Rotating container,Solution The the reference frame is established on the container. According to Equation (1),When x=y=z=0, p=pa, thus,The constant-pressure surface is a parabaloid of revolution,2 Mechanics of fluids at rest,2.4 Absolute pressure, gage pressure and vacuum,If pressure is measured relative to absolute zero, it is called absolute pressure.,When measured relative to atmosphere as a base, it is called gage pressure.,If the pressure is below that of the atmosphere, it is designated as a vacuum.,2 Mechanics of fluids at rest,fuchsin,2.5 Forces on plane Areas and on curved surface,a. Forces on plane Areas,b.Forces on curved surfaces,Where Ax, Ay and Az are project areas in three directions-,2 Mechanics of fluids at rest,3 fluid kinematics and dynamics,3.1 Description of fluid motion,a. Lagrangian description,In the study of particle mechanics, attention is focused on individual particles, motion is observed as a function of time. The position, velocity, and acceleration of each particle are listed,where x, y and z are transient position coordinates。,This description is easily acceptable but difficult as the number of particles becomes extremely large in a fluid flow.,1736 1813,b. Eulerian description,An alternative to following each fluid particle separately is to identify points in space and the observe the velocity of particles pass each point. The flow properties, such as velocity, are functions of both space and time.,where x, y and z are the position coordinates of the flow field,1707 1783,3 Mechanics of fluids in motion,3.2 Key concepts,a. Ideal fluid:,b. Incompressible and compressible fluid,c. Steady flow:,Where the quantities of interest do not depend on time.,d. Path line:,A path line is the locus of points traversed by a given particle as it travels in the flow field. Note that a path line is a history of the particles locations (Lagrange description),A fluid is presumed to have no viscosity,An incompressible fluid is the one whose density remains relatively constant. Generally speaking, liquids can be considered as incompressible fluids while gases as compressible fluids,3 Mechanics of fluids in motion,e. Streamline:,A streamline is a curved line possessing following property: the velocity vector of each particle occupying a point on the streamline is tangent to the streamline (Eulerian description),In a steady flow, path lines and streamlines are all coincident.,3 Mechanics of fluids in motion,f. Stream tube:,A stream tube is a tube whose walls are steamlines.,Note that no fluid can cross the walls of a stream tube since the velocity is tangent to a stream line People often sketch a stream tube with a infinitesimal cross section in the interior of flow for demonstration purposes.,g. Flow cross section,A plane or curved surface at right (angle) to the direction of velocity.,3 Mechanics of fluids in motion,h. Flow rate and mean velocity,The quantity of fluid flowing per unit time across any section is called the flow rate.,In dealing with incompressible fluids, volume flow rate is commonly used, whereas mass flow rate is more convenient with compressible fluids.,The mean value of the velocity in a cross section is called the mean velocity.,This indicates that the volume flow rate is equal to the magnitude of the mean velocity multiplied by the flow area at right to the direction of velocity.,3 Mechanics of fluids in motion,3.3 Equation of continuity,Assume an incompressible fluid steadily flows in the infinitesimal stream tube.,The following figure represents a short length of a stream tube,The fixed volume between the two fixed sections of the stream tube is called the control volume.,According to mass conservation law, in the time dt, the mass flowing in the control volume must be equal to the mass flowing out the control volume.,3 Mechanics of fluids in motion,The equation can be simplified, thus,The equation can be integrated along flow cross section, yielding,The equation indicates the mean velocity is inversely proportional to the flow area.,3 Mechanics of fluids in motion,3.4 Differential equation of steady flow for ideal fluid,Consider steady flow of an ideal fluid.,Use a infinitesimal cylindrical element, with length ds andcross-section dA, in the s-direction of the stream.,The forces acting on the element are pressure forces and the weight.,Summing up the forces in the s-direction, there results,The acceleration of the s-direction,3 Mechanics of fluids in motion,Apply Newtons second law , we have,a. The Bernoulli equation on following assumptions:,The equation is called Eulerian equation,3.5 Bernoulli equation,Consider geometric relation,Thus,(1) Ideal fluid; (2) Steady flow; (3) An infinitesimal stream tube; (4) Constant density; (5) Inertial reference frame.,3 Mechanics of fluids in motion,simplifying the expression, we have,3 Mechanics of fluids in motion,or,where,The physical significance of the equation:,Bernoulli equation indicates that the total energy of a fluid flowing from 1 cross section to 2 cross section remains constant though one energy form can be converted into another.,Bernoulli Daniel(1700-1782), Swiss mathematician, who showed that as the velocity of a fluid increases, the pressuredecreases, a statement known as the Bernoulli principle.,3 Mechanics of fluids in motion,E1: Manufacture a shower,In order to suck hot water into the tube, the pressure inside the tube need be lower than atmospheric pressure.,A good idea is to increase kinematic energy, that is to say, to decrease the diameter of the tube.,E2: The lift force of an airplane,In order to make an airplane lift, the pressure under the wing need be higher than that on the wing.,A good idea is to make the wing have different curve surfaces-,3 Mechanics of fluids in motion,b. The Bernoulli equation on following assumptions:,(1) Real fluid; (2) Steady flow; (3) An infinitesimal stream tube; (4) Constant density; (5) Inertial reference frame.,The ideal fluid flow or inviscid flow does not cause energy losses; while a real fluid flow or viscous flow will cause energy losses.,If energy losses are considered the Bernoulli equation can be written as following,where henergy losses caused by friction forces,3 Mechanics of fluids in motion,c. The Bernoulli equation on following assumptions:,(1) real fluid; (2) steady flow; (3) a real pipe; (4) constant density; (5) inertial reference frame; (6) cross sections of gradually varied flow,A real tube can be considered as consisting of countless infinitesimal stream tubes. Consequently, we can integrate the above equation along the cross-section of a real tube,Rewrite the integration,3 Mechanics of fluids in motion,Note that in the cross section of gradually varied flow,Hence,Let,We can obtain,where v1 and v2 -mean velocities; 1 and2-kinetic energy correction factors, =12.,The selected cross sections should ensure that the stream lines across the cross section are approximately parallel (gradually varied flow),3 Mechanics of fluids in motion,d. Example Venturi meter A Venturi meter consists of one tube with a constricted throat which produces an increased velocity accompanied by a reduction in pressure. The meter is used for measuring the flow rate of both compressible and incompressible. Assuming D1=200mm, D2=100mm,the height of the mercury column h=45mm, Calculate the flow rate of water.,3 Mechanics of fluids in motion,Solution First, selecting two flow cross section I-I and II-II; Second, select potential energy base line O-O; Then, writing the Bernoulli equation between cross section I-I and II-II;,We can obtain,Next, calculating parameter z1=z2=0, let ,3 Mechanics of fluids in motion,Use continuity equation,Inserting this value of v2 in foregoing expression, we obtain,3 Mechanics of fluids in motion,According to static pressure equation, select equal pressure planeO1O1，,thus,Finally, the flow rate is,3 Mechanics of fluids in motion,As there is some friction losses between cross section 1-1 and 2-2, the true velocity is slightly less than the value given by the expression. Hence, we may introduce a discharge coefficient C, so that the flow rate is given,Substituting data for these variables, we obtain the ideal throat flow rate,3 Mechanics of fluids in motion,a. Momentum theorem and dAlembert principle,The expression of momentum theorem is,3.6 momentum equation,The dAlembert principle expression of momentum theorem is,3 Mechanics of fluids in motion,b. The derivation of momentum equation,Assumptions: (1) Incompressible fluid; (2) Steady flow; (3) An infinitesimal stream tube; (4) Constant density; (5) Inertial reference frame.,Use a infinitesimal stream tube between section 1-1, with a velocity u1 and cross-section dA1 , and 2-2, with a velocity u2 and cross-section dA2, as the control volume.,It may be note that the control volume is fixed.,3 Mechanics of fluids in motion,Assume that time t lapses，the fluid flows from cross section1-1 and 2-2 to cross section 1-1 and 2-2.,Both sides are divided by t, then taking limit,The variation of the fluid momentum is,3 Mechanics of fluids in motion,Momentum change rate caused by time variation,The expression is written into dAlembert principle equation,Transient flow force,Momentum change rate caused by position variation,Steady flow force,3 Mechanics of fluids in motion,The momentum change rate caused by time variation is equal to zero when flowing steadily. The momentum change rate caused by position variation is calculated as following,The integration of momentum change rate,3 Mechanics of fluids in motion,Where v1, v2 -mean velocity on cross section 1-1 and 2-2 respectively； 1, 2 -momentum correction factors on cross section 1-1 and 2-2 respectively， =14/3.,External forces The external forces acting on the fluid inside the control volume can be classified three types: (1)pressure forces on cross sections;(2) weight force of the fluid inside the control volume;(3) Restrictive force of the control volume, that is,3 Mechanics of fluids in motion,Solution steps Select a control volume； Express all external forces in a figure； Select a reference frame； Write component momentum equations； calculate parameters;Sometimes the Newtons third law is applied.,Explanation: The resultant force acting on the fluid inside the control volume is equal to that in unit time the momentum fluxing out the control volume is subtracted by the momentum fluxing in the control volume.,It may be noted that the equation is vector equation.,c. Momentum equation of incompressible fluid,Assumptions: (1) Incompressible fluid; (2) Steady flow; (3) An real tube.,3 Mechanics of fluids in motion,E1: Calculate the force acting on the tube, assume followings are known:,c. Examples,SolutionSelect the “y” shaped tube as a control volume.Express all external forces as shown in the FigureSelect the reference frame as shown in the Figure-,3 Mechanics of fluids in motion,c. List component equations of momentum,In x direction:,Consequently,According to Newtons third law, the forces acting on the tube are,3 Mechanics of fluids in motion,In y direction:,-,E2: Stablility analysis of directional control valve,Solution,Both are stable.,3 Mechanics of fluids in motion,Synthetical application of three equations,To sum up, solve the equation including one unknown numberso as to exhibit your clear mind of thoughts.,Energy loss is usually called power loss or head loss. Head loss is the measure of the reduction in the total head (sum of