Fluid mechanics Lectuer: Sun Gang
Fluid Mechanics Lectuer:Sun Gang
Introduction 1-2 Definition of a fluid Fluid mechanics the behavior of The solid object will no chang fluids at rest and in motion inside the a closed container a fluid is a substance that deforms continuously under the application The liquid will change its shape of a shear(tangential)stress no to conform to that of the matter how small the shear stress container and will take on the may be same boundaries as the a solid deforms when a shear stress container up to the maximum is applied does not continue to depth of the liquid increase with the time F/A Dye maker to outline a fluid clement
Introduction • 1-2 Definition of a Fluid • The solid object will no change inside the a closed container • The liquid will change its shape to conform to that of the container and will take on the same boundaries as the container up to the maximum depth of the liquid • Fluid mechanics:the behavior of fluids at rest and in motion • A fluid is a substance that deforms continuously under the application of a shear(tangential) stress no matter how small the shear stress may be • A solid deforms when a shear stress is applied does not continue to increase with the time • Dye maker to outline a fluid element = F / A
Introduction The deformation of solid Experience a Deformation Finite(solid Continuously increasing Shear stress is proportional To the rate of change of · The deformation
Introduction • The deformation of solid • Experience a Deformation • Finite(solid) • Continuously increasing • Shear stress is proportional • To the rate of change of • The deformation
At the atomic and molecular level Solid: the molecular are packed so closely together that their nuclei and electrons form a rigid geometric structure, glued together by powerful intermolecular forces Liquid the space between molecular is large, the intermolecular forces allow enough movement of the molecules to give the liquid its“ fluidity Gas the spacing between molecular is much larger, the influence of the intermolecular forces is much weaker and the motion of the molecules occurs rather freely throughout the gas
At the atomic and molecular level: Solid:the molecular are packed so closely together that their nuclei and electrons form a rigid geometric structure,”glued”together by powerful intermolecular forces. Liquid:the space between molecular is large,the intermolecular forces allow enough movement of the molecules to give the liquid its “fluidity” Gas:the spacing between molecular is much larger, the influence of the intermolecular forces is much weaker,and the motion of the molecules occurs rather freely throughout the gas
Introduction 1-4 Basic equation The Basic laws governing the flow The ideal gas equation of state motion include I The conservation of mass P=ORT ·2、 Newton' s second law of motion 3 The principle of angular momentum 4 The first law of theromdynamics 5 The second law of theromdynamics
Introduction • 1-4 Basic Equation • The ideal gas equation of state • The Basic laws governing the flow motion include: • 1、The conservation of mass • 2、Newton’s second law of motion • 3、The principle of angular momentum • 4、The first law of theromdynamics • 5、The second law of theromdynamics p = RT (1.1)
Introduction 1-5 Methods of analysis The system that you are attempting to analyze Basic mechanics: free-body diagram thermod ynamics: closed system(terms: system and control volume)
Introduction • 1-5 Methods of analysis • The system that you are attempting to analyze Basic mechanics : free-body diagram thermodynamics: closed system(terms: system and control volume)
1-5. 1 System and Control Volume a system is defined as a fixed identifiable quantity of mass; the system boundaries separate the system from the surroundings(fixed or movable), no mass crosses the system boundaries A control volume is an arbitrary volume in space through which fluid flows. The geometric boundary of the comtrol volume is called the control surface (include real or imaginary)
1-5.1 System and Control Volume • A system is defined as a fixed, identifiable quantity of mass; the system boundaries separate the system from the surroundings(fixed or movable), no mass crosses the system boundaries. • A control volume is an arbitrary volume in space through which fluid flows. The geometric boundary of the comtrol volume is called the control surface.(include real or imaginary)
1-5.2 Differential versus Integral Approach The basic laws can be formulated in terms of infinitesimal or finite systems and control volumes The first case the resulting equation are differential equation The integral formulations of basic laws are easier to treat analytically, for deriving the control volume equation, we need the basic laws of mechanics and thermodynamics, formulated in terms of finite systems
1-5.2 Differential versus Integral Approach • The basic laws can be formulated in terms of infinitesimal or finite systems and control volumes. • The first case the resulting equation are differential equation. • The integral formulations of basic laws are easier to treat analytically, for deriving the control volume equation , we need the basic laws of mechanics and thermodynamics ,formulated in terms of finite systems
1-5.3 Methods of Description Use of the basic equations applied to a fixed, identifiable quantity of mass, keep track of identifiable elements of mass(in particle mechanics the lagrangian method of description) Example: th eapplication of Newton's second law to a particle of fixed mass Consider a fluid to be composed of a very large number of particle whose motion must be described With control volume analyses, the Eulerian on the properties of a flow at a given point in space as a function of time
1-5.3 Methods of Description • Use of the basic equations applied to a fixed , identifiable quantity of mass, keep track of identifiable elements of mass(in particle mechanics: the Lagrangian method of description) • Example: th eapplication of Newton’s second law to a particle of fixed mass • Consider a fluid to be composed of a very large number of particle whose motion must be described • With control volume analyses, the Eulerian on the properties of a flow at a given point in space as a function of time
EXAMPLE PROBLEM 1.1 GIVEN: Piston-cylinder containing O2, m-0.95Y 71=27CT2=627C p= constant= 150 kPa(abs FIND: Q SOLUTION We are dealing with a system, m=0.95 kg Basic equation: First law for the system, Q12-Wn2- E2-Er Assumptions: (1) E= U, since the system is stationary (2) Ideal gas with constant specific heats Under the above assumptions, E2-E1=U2-U1=m(-)=mcn(T2-1 The work done during the process is moving boundary work P v=p(H2-V1) For an ideal gas, Pt a mRT. Hence Wn= mR(T2-T1). Then from the first law equation, On= E2-E+Wn T1)+mR(2-T) Q12=m(T2-71)c+R Q12=mcp(72-71){R=cp-c From the Appendix, Table A 6, for O2, Cp =909. 4 J/(kg. K). Solving for @n2, we obtain 095kg909Jx60K =518kJ K The purpose of this problem was to review the use of () the first law of thermodynamics for a system, and (i) the equation of state for an ideal gas