Hydraulics and Pneumatics Transmission1 Fluid Properties 2 Mechanics of fluids at rest 3 Mechanics of fluids in motion 4 Energy loss of fluids in motion 5 Flow of fluids in clearances and orifices 6 Hydraulically sticking 7 Hydraulically shocking 8 CavitationFLUID MECHANICS WITH HYDRAULICS1.1 DensityFluid density was defined as mass per unit volume 1 Fluid Propertieshydraulic oil =890-910kg/m3 1.1 Compressibility and expansibilitySuppose the volume is the function of pressure and temperature , or V=f(t,p ) , and tV,pVThe volumetric increment can be approximated by is total differential, thusIn hydraulic transmission problems, p32Mpa, the volume variation caused by pressure variation isConsequently, hydraulic oil may be regarded as uncompressible. - Found by experiment:whereexpansibility coefficientcompressibility coefficient1 Fluid Properties1.3.1 cohesion force and adhesion force1.3 Viscosity1.3.2 dynamic viscosityThere 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 platesThe 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 fluidsIf 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 constantwhich 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 Properties1.3.3 Kinematic viscosityIn many problems including viscosity there frequently appear the value of viscosity divided by density. This is defined as kinematic viscosityE.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 Properties1.3.3 Relative viscositya. Definition : E= t1 /t2b. Transposed relationt1 -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 PropertiesThe 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 octane The diesel oil is named according to its freezing point2 Mechanics of fluids at restFluid 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 propertya. The pressure is defined as the force exerted on a unit area b. The pressure is the same in all directionNote geometric relation and neglect higher order term, thus2.2 Basic differential equationAssume 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 restAx yzdxdydzAx yzdxdydzNewtons second law is writtenin vector for constant mass system.F=maThis results in three componentequations,Where ax, ay, and az are the components of the acceleration of the element.2 Mechanics of fluids at restDivision by the elements volume dxdydz yieldsThe equation expresses the relation between pressure variation and acceleration.(2)2 Mechanics of fluids at rest2.3 Examples included in fluid statics. E1: liquid at restp0SolutionThe quantity is referred to as the piezometric headAnother form is written asWhere p-the pressure at a point;gh-the pressure caused by liquid c