Introduction to basic principles of fluid mechanics. Mass balance equations are formal statements of the law of conservation of mass, and it is no exaggeration to think of them as the f ma of environmental engineering. Yasar demirel, in nonequilibrium thermodynamics, 2002. Mass balance rate of increase of mass in fluid element equals the net rate of. Fluid statics treats fluid in the equilibrium state no motion fluid dynamics treats fluids when portion of the fluid are in motion concerned with the relation between the fluid velocity and the forces acting on it compressible fluids means that the fluid density is sensitive to any change in temperature. This note will be useful for students wishing to gain an overview of the vast field of fluid dynamics. Multiphase particleincell coupled with population balance. Brief introduction to rich topic, of which people spend lifetimes studying one small part. Acidbase eqilibrium systems for all the acid base equilibrium systems we can write down mass balance equation charge balance equation. When fluid flow occurs in a single direction everywhere in a system, shell balances are. Lagrangian and eulerian representations of fluid flow.
In this context, this equation is also one of the euler equations fluid dynamics. Therefore, to solve the mass balance equation, we need to define a cv in which the concentration is uniform. This is the equation for the energy density of a continuous at rest medium. The equations of fluid dynamicsdraft where n is the outward normal. Local balance equations mass balance balance of mechanical and thermodynamic quantities boundary conditions global form of the balance equations. The equation is a rearrangement of the form used in chemistry.
These conservation laws are often written in integral form for a. The time rate of change of mass within the control volume plusthe net mass flow rate through the control surface is equal to zero. The mass flow rate is mt and at any given moment this is dmdt or m and for a constant flow rate, only the velocity changes. Computational fluid dynamics of incompressible flow. We can derive the relationship between the equations for a fluid particle lagrangian and a fluid. In this case the turbine operates at steady state with inlet. Basic equations hydrostatic equilibrium in centrifugal. Highspeed supercomputers are used to perform the calculation that is required to simulate the interaction of liquids and gases.
The navierstokes equations form a vector continuity equation describing the conservation of linear momentum. Examples are the gravitational force or thermal radiation. Here, the left hand side is the rate of change of mass in the volume v and the right hand side. Change due to the fact that it moves to a different location in the fluid. Since then i have taken numerous courses in the broad field of fluid mechanics and my phd focuses on the flow of fluid through nanochannels with the fluid being driven by an electric force. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective. Computational fluid dynamics is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. For instance, a flow field is characterized by balance in mass, momentum, and total energy described by the continuity equation, the navierstokes equations, and the total energy equation. Understand the use and limitations of the bernoulli equation, and apply it to solve a variety of fluid. To fully describe fluid flow, more information is needed, how much depending on the assumptions made. Fluid mechanics problems for qualifying exam fall 2014 1.
Chapter 1 governing equations of fluid flow and heat transfer. Pressure loss and head loss due to friction in ducts and tubes major loss head loss or pressure loss due to friction in pipes and ducts. A continuity equation in physics is an equation that describes the transport of some quantity. This additional information may include boundary data noslip, capillary surface, etc. Continuity equation totalenergy balance mechanicalenergy balance velocity of sound ideal gas equations acoustical velocity and nma ma of an. Continuity equation fluid dynamics with detailed examples. This body can be translating and possibly rotating, but not deforming. Similar to problem b, the equation is linear but it appears that the coefficients are nonlonger constants.
Shu the physics of astrophysics volume ii gas dynamics 3. As before we will consider open and closed systems and steadytransient flows engr 5961 fluid mechanics i. Particles of mass crossing a surface within the fluid with random atomic velocity relative to the bulk velocity contribute. The bernoulli equationis concerned with the conservation of kinetic, potential, and flow energies of a fluid stream and their conversion to each other in. Fluid dynamics continuity mass conservation mass is conserved. They correspond to the navierstokes equations with zero viscosity, although they are usually written in the form shown here because this emphasizes the fact that they directly represent conservation of mass, momentum, and energy. Lecture 3 conservation equations applied computational.
You will probably recognise the equation f ma which is used in the analysis of solid mechanics to relate applied force to acceleration. Introduction to basic principles of fluid mechanics i. Understand the use and limitations of the bernoulli equation, and apply it to solve a variety of fluid flow problems. The mass equa tion is an expression of the conservation of mass principle. Lecture 3 conservation equations applied computational fluid dynamics instructor. In fluid mechanics it is not clear what mass of moving fluid we should use so we use a different form of the equation. The navierstokes equations are strictly a statement of the balance of momentum. Fluid dynamics 122 summary of the equations of fluid dynamics reference. Consider a steady, incompressible boundary layer with thickness. This is an essential production of partial mass by chemical reactions. Integrating the source term over the volume leads to 3. The continuum hypothesis, kinematics, conservation laws. This can get very complicated, so well focus on one simple case, but we should briefly mention the different categories of fluid flow.
This kind of equation is called an euler differential equation 1. Lets now consider a general control volume immersed in a fluid. The mass balance for this case can be written in the following form. The energy balance for a control volume follows a similar approach to that for conservation of mass, but has additional considerations. In fluid dynamics, the euler equations govern the motion of a compressible, inviscid fluid. Shell balances in fluid mechanics clarkson university. Fluid mechanics has to be taken in bitesized pieces, topics, but i also had the uneasy.
Fluid dynamics equations fundamentals of fluid mechanics. In this case assume a simple cycle without reheat and without with condensing steam turbine running on saturated steam dry steam. Finally, we apply the energy equation to various engineering systems. The differential equations of flow are derived by considering a differential volume element of fluid and describing mathematically a the conservation of mass of fluid entering and leaving the control volume. Fluid statics, kinematics of fluid, conservation equations and analysis of finite control volume, equations of motion and mechanical energy, principles of physical similarity and dimensional analysis, flow of ideal fluids viscous incompressible flows, laminar boundary layers, turbulent flow, applications of viscous flows. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. The equations can be derived easily by applying the laws of mass conservation and newtons second law to an elementary fluid volume volumelet, in the charming terminology of sauro succis the lattice boltzmann equation for fluid dynamics and beyond incorporating the assumption that.
Mass balance equation mass balance equation the quantity of all species in a solution containing a particular atom or group atoms must equal the amount of that atom or group atoms delivered to the solution. Compressible fluid flow an overview sciencedirect topics. Fluid mechanics has to be taken in bitesized pieces, topics, but i. Recognize various forms of mechanical energy, and work with energy conversion efficiencies. The inner passage is filled with fluid with pressure p1 at inlet and p2 at outlet. Change due to changes in the fluid as a function of time. Let assume the rankine cycle, which is the one of most common thermodynamic cycles in thermal power plants. The momentum equation for a control volume can be used to determine reaction forces and thrust forces, among other things. Mass, bernoulli, and energy equations this chapter deals with three equations commonly used in fluid mechanics. It is used frequently in fluid mechanics in the same manner as conservation of momentum in rigid body dynamics. Fluid dynamics fluid dynamics equations bernoullis equation. A moving fluid particle experiences two rates of changes. It expresses the equivalence between energy and mass densities in the field of fluid dynamics. In rigid body mechanics the motion of a body is described in terms of the bodys position in time.
Mass balance equation mass balance equation the quantity of all species in a solution containing a particular atom or group atoms must equal the. Compressible fluid flows have long been a topic of study in the fluid dynamics community. Solving these equations is done in a similar manner to problem b except that the homogeneous solution now has the following form. Application of these basic equations to a turbulent fluid. Salih department of aerospace engineering indian institute of space science and technology, thiruvananthapuram february 2011 this is a summary of conservation equations continuity, navierstokes, and energy that govern the ow of a newtonian uid. First law of thermodynamics conservation of energy. Conservation of mass of a solute applies to nonsinking particles at low concentration. Fundamental equations 2178 the point to remember from this analysis is that pressure in a fluid is the result of a flux of momentum resulting from the microscopic motions of the particles. We can write a 2d mass balance equation for the fluid entering and exiting the control. Mass leaving volume in t the control mass entering interval t in a time control volume mass in the change of a j 1. Amount of component produced or consumed inside a unit volume per unit time is the result of chemical reactions. Based on a control volume analysis for the dashed box, answer the following. Deriving the differential equations of mass transfer. The continuity equation in fluid dynamics describes that in any steady state process, the rate at which mass leaves the system is equal to the rate at which mass enters a system.
It is clear that as h is the energy per unit volume and. The lattice boltzmann equation for fluid dynamics and. A mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. Fluid dynamics and balance equations for reacting flows. Many flow situations do exist, however, where such changes.
Introductory fluid mechanics l12 p2 differential equations of mass conservation. Lifshitz 1 introduction emission processes give us diagnostics with which to estimate important parameters, such as the density, and. The multiphase particleincell coupled with population balance equation mppicpbe method is introduced for simulating multiscale multiphase particulate flows. Whether in engineering or geophysical flows, there is probably some mass density change in any physical flow. Contents 5 preface these lecture notes has evolved from a cfd course 5c1212 and a fluid mechanics course 5c1214 at the department of mechanics and the department of numerical analysis and computer science nada. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique. Therefore, all these equations are closely coupled to each other. In particular, if the cv contains fluid with varying concentrations, then the rate of reaction will also vary from point to point, and the average rate might not be the same as the rate based on the average concentration.
Correction of bernoulli equation for fluid friction. The massenergy equivalence principle in fluid dynamics. Chapter 1 governing equations of fluid flow and heat transfer following fundamental laws can be used to derive governing differential equations that are solved in a computational fluid dynamics cfd study 1 conservation of mass conservation of linear momentum newtons second law. The differential form of the continuity equation is. Mass and heat balances 9 mars 2017 the transport equations for mass and heat are obtained from conservation laws of mass, on one hand, and energy, on the other hand. Department of chemical and biomolecular engineering. They correspond to the navierstokes equations with zero viscosity, although they are usually written in the form shown here. Lagrangian and eulerian representations of kinematics. You will likely be confused at the end of this lecture, come to get it over the next two or three.
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