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 at kth. This text is an outgrowth of lectures i have given to civil engineering students at. F 6f fforce exerted in the direction of the fluid by a. This material relates predominantly to modules elp034, elp035. The propeller is a mechanical devise that is used to increase the fluid momentum. This book should be used by many different engineering disciplines. The vector sum of the momenta momentum is equal to the mass of an object multiplied by its velocity of all the objects of a system cannot be changed by interactions within the system. These forces can be determined, as in solid mechanics, by the use of newtons second law, or by the momentum equation.
Linear momentum equation for fluids can be developed using newtons 2nd law which states that sum of all forces must equal the time rate of change of the momentum. In fluid mechanics, a system is defined as the chunk of fluid particles whose. Fluid mechanics 4th edition white solutions manual. Three basic tools for the solution of fluid flow problems. Basic equations, mathematical theory of viscous incompressible flow, compressible flow. Define the average density of this volume element by the ratio. Download file pdf fluid mechanics 4th edition white solutions manual fluid mechanics 4th edition white solutions manual reynolds transport theorem angular momentum example 1 lectures adapted from professor maria tomassone, rutgers university problem 3. In general, when solving fluid mechanics problems, one should. Develop impulse momentum equation, the third of three basic equations of fluid mechanics. Lecture 3 conservation equations applied computational. F 5f vforce exerted in the direction of the fluid by any. Chapter 6 the impulsemomentum principle snu open courseware. Mcdonough departments of mechanical engineering and mathematics.
The momentum equation for a control volume can be used to determine reaction forces and thrust forces, among other things. The magnitude of the force f per meter of width to keep the gate closed is most nearly r is onethird from the bottom centroid of a triangle from the ncees handbook. For a unit system using gc, the manometer equation would be written as. Many times it is used for propulsion purposes of airplanes, ships and other devices thrust as shown in figure 6. Solve problems involving pressure and momentum changes. The impulsemomentum equation for fluid flow can be derived from the wellknown. The momentum equation is a statement of newtons second law and relates the sum of the forces acting on an element of fluid to its acceleration or rate of change of momentum. The equations can take various di erent forms and in numerical work we will nd that it often makes a di erence what form we use for a particular problem.
In general, the law of conservation of momentum or principle of momentum conservation states that the momentum of an isolated system is a constant. Derivationif the flow crossing the cs occurs through a series of inlet and outlet ports,and the velocity vis uniformly distributed across each port. Substituting all the momentum, momentum flow, and force definitions into newtons second law 2 gives the integral momentum. Navierstokes equations, conservation of energy examples 15 of. The navierstokes equations classical mechanics classical mechanics, the father of physics and perhaps of scienti c thought, was initially developed in the 1600s by the famous natural philosophers the codename for physicists of the 17th century such as isaac newton. The momentum of a system remains constant when the net force acting on it is zero, and thus the momentum of such systems is conserved. The impulsemomentum principle to summarize what weve done thus far we first considered fluid statics, in which case a mass balance is of little value it would simply tell us that the amount of mass in a static system remains constant. The rectangular gate shown is 3 m high and has a frictionless hinge at the bottom. Professor fred stern fall 20 1 chapter 5 finite control.
A continuity equation is useful when a flux can be defined. To define flux, first there must be a quantity q which can flow or move, such as mass, energy, electric charge, momentum, number of molecules, etc. The bernoulli equation is the most famous equation in fluid mechanics. An alternative which can still be employed to simplify calculations is the momentum integral method of karman. Momentum equation application engineering libretexts. Fluid mechanics is a traditional cornerstone in the education of civil engineers. Linear momentum equation and bernoulli equation examples 11 of 34 0. Consider a steady, incompressible boundary layer with thickness. Fundamentals of fluid mechanics chapter 5 flow analysis. The momentum and energy equations, in tensor notation, for the raleighbenard problem are as follows. Momentum transfer in a fluid involves the study of the motion of fluids and the forces that produce these motions. We continue with the development of the energy equation in a form suitable for use in fluid mechanics and introduce the concept of head loss.
Fluid mechanics problems for qualifying exam fall 2014 1. Then we derive the bernoulli equation by applying newtons second law to a fluid element along a streamline and demonstrate its use in a variety of applications. Fluid dynamics continuity equation linear momentum equation angular momentum equation energy equation bernoulli equation egl and hgl dimensional analysis buckingham pi theorem common dimensionless parameters dynamic similitude applications pipe flow reynolds number, laminar and turbulent flows, entrance length, darcyweisbach. File type pdf fluid mechanics white 5th solution mechanics. This book describes typical issues that are taught and cover in first year class of fluid mechanics with various examples. In fluid mechanics, the conservation of mass relation written for a differential control volume is usually called the. And introduction to linear momentum and how we can use it to find forces on systems.
As numerous books on this subject suggest, it is possible to introduce fluid mechanics to students in many ways. It is used frequently in fluid mechanics in the same manner as conservation of momentum in rigid body dynamics. Fluid mechanics pdf notes fm pdf notes smartzworld. In fluid mechanics it is not clear what mass of moving fluid we should use so we use a different form of the equation.
In this section we will consider the following examples. Erik st alberg and ori levin has typed most of the latexformulas and has created the electronic versions of most gures. Lecture 1 governing equations of fluid motion nptel. Subject fluid mechanics topic module 4 momentum equation lecture 31 faculty venugopal sharma gate academy plus is an effort to initiate free online digital resources for the first.
The rate of change of momentum of a body is equal to the resultant force acting on the body, and takes place in the direction of the force. The study of these forces is essential to the study of fluid mechanics and hydraulic machinery. Boundary layer theory with a general pressure gradient the boundary layer equations can be solved by a variety of modern numerical means. The laws apply to either solid or fluid systems ideal for solid mechanics, where we follow the same system for fluids, the laws need. Next we will use the above relationships to transform those to an eulerian frame for fluid elements. The branch of engineering science that studies the behaviour of fluid. Introduction to dimensions and units physical properties of fluids specific gravity, viscosity, surface tension, vapor pressure and their influences on fluid motion pressure at a point, pascals law, hydrostatic law. The force exerted by a jet of fluid on a flat or curve surface can be resolved by applying the momentum equation. You will probably recognise the equation f ma which is used in the analysis of solid mechanics to relate applied force to acceleration. Fluid mechanics study of fluids at rest, in motion, and the effects of fluids on. If you are enjoying these videos and finding them useful, please make sure to. Momentum equation in three dimensions we will first derive conservation equations for momentum and energy for fluid particles.
The equations of fluid dynamicsdraft the equations of uid mechanics are derived from rst principles here, in order to point out clearly all the underlying assumptions. This would make it easy for you if you are searching for fluid mechanics solved problems covering a. Momentum, heat and mass transfer are called transport phenomena what is momentum transfer fluid mechanics. To summarize what weve done thus far we first considered fluid statics, in which case a mass balance is of little value it would simply tell us that the amount of mass in a static system remains constant. The linear momentum equation is mainly governed by newtons. Based on a control volume analysis for the dashed box, answer the following.
In describing the momentum of a fluid, we should note that in the case of a solid body, its mass is. Bookmark file pdf fluid mechanics white 7th solutions fluid mechanics white 7th solutions my favorite fluid mechanics books facebook page. The cornerstone of computational fluid dynamics is the fundamental governing equations of fluid dynamicsthe continuity, momentum and energy equations. We introduce the equations of continuity and conservation of momentum of fluid flow, from which we derive the euler and bernoulli equations. This equation is one of the most important equations in fluid mechanics and. Therefore, in fluid mechanics, newtons second law is usually referred to as the linear momentum equation. Solved problems in fluid mechanics and hydraulics, bernoullis principle, theory and numerics for problems of fluid dynamics. Fluid mechanics problems and solutions free download. The product of the mass and the velocity of a body is called the linear momentum or just the momentum. This easy to apply in particle mechanics, but for fluids, it gets more complex due to the control volume and not individual particles.
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