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. Fluid 1 has a specific gravity of sg2, while fluid 2 has a density of 800 kgm3. Mcdonough departments of mechanical engineering and mathematics. Fluid statics fluid mechanics, spring term 2011 shear forces normal forces pressure where f is a force normal to area a flowing viscous fluid exert shear forces. Fundamentals of fluid mechanics, 6th edition by munson. In fluid mechanics and thermodynamics, the control volume is a volume fixed in space or moving with constant velocity no acceleration through which the fluid it could be gas or liquid flows. Mechanics is concerned with both stationary and moving bodies under the influence of loads. Integrating the last equation above then gives the total buoyancy force on the object. Continuum mechanics fluid mechanics solid mechanics newtonian nonnewtonian plastic elastic rheology.
Control volume of fluids flow in fluid mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. A collection of matter of fixed identity always the same atoms or fluid particles a specific, identifiable quantity of matter control volume cv. A volume in space through which fluid may flow a geometric entity independent of mass 57. Statics is the branch of mechanics that deals with bodies at rest.
Consider a general flow field as represented by the. This is essentially the same as the freebody concept employed in solid mechanics. May 20, 2018 the macroscopic momentum balance in the vertical direction is f mg, where f is the upward force that the base of the control volume including the dam exerts on the fluid within the control volume, and mg is the weight of the fluid in the control volume. We will present the analysis based on a control volume not differential element. Thus, we will have to write the most general case of the laws of mechanics to deal with control volumes. Leighton university of notre dame in order to walk the walk, it is useful to first be able to talk the talk. Lecture notes in fluid mechanics by laurent schoeffel. Integral relations for a control volume system and control volume. Figure 1 depicts something like a cylindrical syringe, or a grease gun, in which a solid piston of radius r1 is pushed at a speed ut into a fluidfilled cylinder with the same internal radius, forcing the fluid out through a tube with internal radius r2 and length l.
However, in fluid mechanics, it is difficult to analyze a system or volume from fluid by considering or tracking the same particle. Control volume is simply mathematical representation of 3d space. The piston, cylinder, and tube are inflexible and made of material with density s. The compiled slides of the introductory fluid mechanics course a fundamental course in mechanical engineering prepared by professors sankar kumar som of iit kharagpur and gautam biswas of iit kanpur.
Fluids a fluid is a substance that deforms continuously under the action of a shear force. The course concentrates on those aspects of fluid mechanics that can be studied analytically. Dynamics is the branch of mechanics that deals with bodies in motion. In fluid mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical. Six ways of applying the integral mass conservation theorem to a simple problem pdf assignments. Vapor pressure and their influences on fluid motion pressure at a point, pascals law, hydrostatic law, etc. Molecules are separated by voids and the percentage of volume occupied by molecules is very small compared to the total volume. Professor emer itus of mechanical engineering michigan state university david c.
Volume vl 3m orlliter ft3 velocityvl t m sft sec accelerational t 2 m s 2 ft sec2. Like any mathematical model of the real world, fluid mechanics makes some basic assumptions. Fluid element motion consists of translation, linear deformation, rotation, and angular deformation. Me 305 fluid mechanics i part 6 differential formulation of fluid flow. Professor fred stern fall 2014 1 chapter 6 differential. When applied to the arbitrary small rectangular volume depicted in fig. In an inertial frame of reference, it is a fictitious volume fixed in space or moving with constant flow velocity through which the continuum gas, liquid or solid flows. Professor emeritu sofcivil engineering michigan state university schaums outline series mcgr awhil l newyork chicago sanfrancisco lisbon london madrid mexicocity milannewdelhi sanjuan seoul singapore sydney. The control volume can be fixed or moving, and it can be rigid or deformable. Indeed, the idea of exploiting the laws of ideal fluid mechanics to. Figure 1 depicts something like a cylindrical syringe, or a grease gun, in which a solid piston of radius r1 is pushed at a speed ut into a fluid filled cylinder with the same internal radius, forcing the fluid out through a tube with internal radius r2 and length l.
In continuum mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. The rectangular gate shown is 3 m high and has a frictionless hinge at the bottom. Fluid mechanics pdf notes fm pdf notes smartzworld. Topics covered include hydrodynamics, surface tension, boundary layers, potential flow, aerodynamics, viscous flow, and waves. Jntuk syllabus bookall subject notes previous engineering physics. Fundamentals of fluid mechanics 4 chapter 1 definition of a fluid. Comparison of initial and final volume of a 3d fluid element provides an important quantity called dilation. Fluid mechanics problems for qualifying exam fall 2014 1. A mathematical introduction to fluid mechanics alexandre chorin department of mathematics university of california, berkeley berkeley, california 947203840, usa jerrold e. Fluid mechanics deals with the behavior of fluids at rest fluid statics and in motion fluid dynamics.
Fluid flow table of contents hydraulic and pneumatic knowledge fluid power equipment. Engineering fluid mechanics staffordshire university. The system and the control volume broken red line for methods 1 and 2. Control volume encloses the system or region of interest can have multiple inletsexits or none at all if it is a closed system as we have seen is important much like the free body diagram engr 5961 fluid mechanics i. Engineering fluid mechanics 4 contents contents notation7 1 fluid statics 14 1. Density density relates the mass and volume such that mv kg m3 pressure pressure is the result of compacting the molecules of a fluid into a smaller space than it would otherwise occupy. The macroscopic momentum balance in the vertical direction is f mg, where f is the upward force that the base of the control volume including the dam exerts on the fluid within the control volume, and mg is the weight of the fluid in the control volume. Flow of an unconfined viscous fluid down an incline. Continuum hypothesis, mathematical functions that define the fluid state, limits of the continuum hypothesis, closed set of equations for ideal fluids, boundary conditions for ideal fluids, nonlinear differential equations, eulers equations for incompressible ideal fluids, potential flows. A complete set of lecture notes for an upperdivision undergraduate fluid mechanics course. Two fluids of interest water air in some cases, fluid forces have little effect on an objects motion e. Continuum hypothesis, mathematical functions that define the fluid state, limits of the continuum hypothesis, closed set of equations for ideal fluids, boundary conditions for ideal fluids, nonlinear differential equations, eulers equations for incompressible ideal fluids. Each chapter comprises startofchapter learning objectives, a summary of basic theory, endofchapter summaries, a range of worked examples. Control volume relations for fluid analysis from consideration of hydrostatics, we now move to problems involving fluid flow with the addition of effects due to fluid motion, e.
Pressure is the force per unit area acting on a surface. You are to use an integral control volume analysis to dete4rmine the laminar boundary layer thickness u as a function of t. Thus, we provide the following glossary of terms used in cbe30355 transport i. Fundamentals of fluid mechanics, 6th edition by munson textbook coloured. Based on a control volume analysis for the dashed box, answer the following. Control volume theorems and applications advanced fluid. Mechanics me 305 fluid mechanics i part 1 fundamental fluid. Marsden control and dynamical systems, 10781 california institute. We can then suppose that the behaviour of the uid is the same as if the. From basics to the millennium problem laurent schoeffel 3 1. In most applications of uid mechanics the typical spatial scale l under consideration is much larger than the spacing between molecules d. In an inertial frame of reference, it is a volume fixed in space or moving with constant velocity through which the fluid gas or liquid flows. In an inertial frame of reference, it is a volume fixed in space or moving with.
There is three times as much mass of fluid 2 as there is of fluid 1. Material volumes, and control volumes pdf on choosing and using control volumes. Fluid mechanics notes pdf fm notes pdf starts with the topics covering introduction to dimensions and units physical properties of fluids specific gravity, viscosity, surface tension. Introduction fluid mechanics concerns the study of the motion of fluids in general liquids and gases and the forces acting on them. Masteringengineering for fluid mechanics is a total learning package that is designed to improve results through personalized learning. Principles of fluid mechanics stationary layer with zero velocity pressure, p 1 pressure, p 2 figure 41 fluid flow through a pipe a streamline is an imaginary line in a fluid, the tangent to which gives the direction of the flow velocity at that position, as shown in figure 42, where the distance between two streamlines is an. In recent years fluid mechanics is truly a hightech discipline and many exciting areas have been developed like the aerodynamics of multistorey buildings, fluid mechanics of atmosphere, sports, and micro fluids. V v eulerian control volume lagrangian control volume fixed in space moving with fluid. Conservation of mass this is a fundamental principle, stating that for any closed volume fixed in space, the rate of increase of mass within the volume is equal to the net rate at which fluid enters across the surface of the volume. Fluid is a substance that deforms continuously under the application of shear tangential stress no matter how small the stress may be.
Fluid mechanicscontrol volume analysis wikibooks, open. Mechanics me 305 fluid mechanics i part 1 fundamental. This first volume of two aims to help prepare students of fluid mechanics for their examinations by presenting a clear explanation of theory and application in the form of solutions to typical examination and assignment type questions. Fluid mechanics deals with the behaviour of fluids at rest and in motion. For a continuum fluid, the answer is to construct one of the two following models. Study guide chapter 3 control volume relations for fluid. Consider a steady, incompressible boundary layer with thickness. Created to emulate the instructors officehour environment, masteringengineering provides students with wronganswer specific feedback and hints as they work through tutorial homework problems. A fluid dynamic system can be analyzed using a control volume, which is an imaginary surface enclosing a volume of interest. In fluid mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. Use your fluid mechanics book to find the expression for. The surface enclosing the control volume is referred to as the control surface.
The main objective is to introduce a variety of classical experimental and. Marsden control and dynamical systems, 10781 california institute of technology pasadena, california 91125, usa. Consider the flow over a smooth flat plate of a newtonian fluid, with no pressure gradient in the flow direction. The prediction error between the plant output and the neural network output is used as the neural. In an inertial frame of reference, it is a volume fixed in space or moving with constant velocity through which. Properties of fluids specific gravity, specific weight, viscosity, compressibility, vapour pressure and gas laws capillarity and surface tension. The experiments here are designed to demonstrate the applications of the basic fluid mechanics principles and to provide a more intuitive and physical understanding of the theory. Motion of a fluid element fluid kinematics in a general flow field, fluid motion can be decomposed into the following 4 components 1 translation 2 linear deformation 3 rotation 4 angular deformation movie.
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