In order to use this principle to calculate deflections for beams, we need to be able to express the total potential energy of the system. Computational fluid dynamics of incompressible flow. How do you use potential energy to find velocity answers. Learn for free, pay a small fee for exam and get a certificate. If a velocity potential exists, it is simpler to describe the motion by means of the potential rather than the vector velocity, since the former is a single scalar function whereas the latter is a set of three scalar functions. In other words, the velocity potential is a function whose gradient is equal to the velocity vector. Derive the governing equations for 2d and axisymmetric potential flow 3. Jul 18, 2018 fluid mechanics part 17 velocity potential function and stream function duration. The velocity is everywhere normal to the surfaces of constant velocity potential.
The stream function of a flow is given by the expression, y 2x2 y2. Now we will go ahead to understand the basic concept of velocity potential function and stream function, in the field of fluid mechanics, with the help of this post. Introduce the velocity potential and the stream function 2. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The functions given satisfy the continuity equation equ. In terms of gravity, the potential energy, u, is the mass of an object times the. The stream function is defined for incompressible divergencefree flows in two dimensions as well as in three dimensions with axisymmetry. It is a vector function of position and time with components, and. The flow velocity components can be expressed as the derivatives of the scalar stream function. A velocity potential is a scalar potential used in potential flow theory. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero.
One might have guessed that the flow lines would be more crowded together around the midsection of the sphere, reflecting a greater velocity insteadand as will be shown later in this chapter, that is indeed the case at much higher reynolds numbers. The quantity in parentheses is at most a function of time. In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function. Also the rotational vector written as omega is given by curl of velocity vector only if the curl o.
Aa200 ch 10 elements of potential flow stanford university. This section is concerned with an important class of flow problems in which the vorticity is everywhere zero, and for such problems the navierstokes equation may be greatly simplified. One of the most important fluid variables is the velocity field. Twodimensional potential flow and the stream function. It was introduced by josephlouis lagrange in 1788 it is used in continuum mechanics, when a continuum occupies a simplyconnected region and is irrotational. The kinematic viscosity of water at typical ocean temperatures is 1e. Made by faculty at the university of colorado boulder, department of chemical and biological engineering. Deformation and conservation of mass of fluid a element lecture 5. In general, we cannot guarantee the existance of such a function. Note that, using the potential or stream function, we can confirm that the velocity field resulting from these functions has no radial component and only a circumferential velocity component. The average velocity field of heleshaw flow is an physical analog for.
Chakraborty,department of mechanical engineering,iit kharagpur. There are a lot of different laws that governs the physical aspects and it is important to be familiar with the same to gain a clear understanding of the thought process. We conclude that, for twodimensional, irrotational, incompressible flow, the velocity potential and the stream function both satisfy laplaces equation. If a fluid is incompressible and has zero viscosity an ideal fluid its. The circulation can be found mathematically as thec line integral of the tangential component of velocity taken about a closed curve, c, in the flow field. Electromagnetic theory online course video lectures by iit bombay. As we have seen, a twodimensional velocity field in which the flow is everywhere parallel to the plane, and there is no variation along the direction, takes the form 5. Therefore, the gradient of any given equipotential line denotes slope, or the x and y components of velocity. Vorticity, stream function, bernoullis equation youtube. Deflections using energy methods purdue university. This pretty much summarise the entire fairy tale about the potential in any area of physics where they come into play. Equipotential lines, when graphed, resemble contour lines on a map which specifies altitude. This suggests that the real and imaginary parts of a wellbehaved function of the complex variable can be interpreted as the velocity potential and stream function, respectively, of some twodimensional, irrotational, incompressible. General solution of the incompressible, potential flow.
Java video tutorials video tutorials, lessons from. Introduction to fluid mechanics and fluid engineering by prof. The stream function can be used to plot streamlines, which represent the trajectories of particles in a. Velocity potential article about velocity potential by. As energy is a conservative force, the total energy of a system is the potential energy plus the kinetic energy. Finding potential functions c marc conrad november 6, 2007 1 introduction given a vector. Envelope of the velocity potential for several values of the source speed and the closest sourcetoreceiver distance. Full text of fluid mechanics nptel internet archive. Show that these functions represent a possible case of an irrotational flow. As a result, u can be represented as the gradient of a scalar function. Nptel, online courses and certification, learn for free. Plot of velocity as a function of radius from the vortex center.
Further the laplace equation is linear and is easily solved by many available standard techniques, of course, subject to boundary conditions at the boundaries. The rst is naturally associated with con guration space, extended by time, while the latter is the natural description for working in phase space. Velocity potential an overview sciencedirect topics. Electromagnetic theory online course video lectures by iit.
Chapter 2 lagranges and hamiltons equations in this chapter, we consider two reformulations of newtonian mechanics, the lagrangian and the hamiltonian formalism. Physics mainly deals with the study of matter and the movement of the same through different medium. Why does a velocity potential function exist only for an. Write and explain the fundamental equations of potential flow theory 2. Cauchyriemann relations complex velocity potential equations are identical to equations. Stokes law, the bernoulli equation, turbulence, boundary layers, flow separation introduction 1 so far we have been able to cover a lot of ground with a minimum of material on fluid flow. List and explain the assumptions behind the classical equations of fluid dynamics topicsoutline. Nptel iit kharagpur video lecture study material online. To find the velocity potential mathematics stack exchange. The given relation for an irrotational flow is known as which one of the following.
Compactness of meromorphic functions in the spherical metric, spherical derivative, normality, theorems of martyzalcmanmontelpicardroydenschottky mathematics dr. Fluid mechanics module 3 potential and stream function. Finding potential functions department of mathematics. Velocity potential definition is the scalar quantity whose negative gradient equals the velocity in the case of irrotational flow of a fluid. Existence of velocity potential implies that a fluid is in continuum b fluid is irrotational c fluid is ideal d fluid is compressible 3. A flow governed by this equation is called a potential flow. Fluid mechanics part 17 velocity potential function and stream function duration. A velocity potential is a scalar function whose gradient is equal to the velocity of the fluid at that point. Mcdonough departments of mechanical engineering and mathematics university of kentucky c 1991, 2003, 2007. Thus the average velocity field in a heleshaw flow is irrotational.
And angular velocity of a flow is defined as, math. Velocity potentials and stream functions as we have seen. Suppose a mass m is located at the origin of a coordinate system and that mass m move according to keplers first law of planetary motion. Jan 22, 2018 velocity potential function watch more videos at. Aerospace engineering principles of fluid dynamics nptel. Let us consider that v is the resultant velocity of a fluid particle at a point in a flow filed.
Aug 26, 2017 potential flow is same as irrotational flow. Relationship between stream function and velocity potential. Then the radius vector from mass m to mass m sweeps out equal areas in equal times. In contrast, velocities encountered in ocean waves are on the order of 10ms, with. In addition to the determination of the stream function and velocity potential, it is observed that for a doublet. Java video tutorials, j2ee video tutorials, j2ee video lectures, java video lectures, java tutorial videos, java video tutorial torrent, java tutorial video tutorials, java tutorial video free download, core java tutorial video torrent, java tutorial vide. If you are not able to download lectures due to bandwidth constraints, you can obtain the courses in dvds by paying a nominal fee to cover the cost of storage media and distribution.
Streamlines, velocity potential for a doublet nptel. Feb 05, 2016 the best way to download any youtube playlist is via youtubedl command prompt utility. The fluid velocity v is assumed to be composed by the waveinduced velocity, obtained by nablaphi, where phi is a velocity potential, plus a horizontal current u u. Lecture notes on classical mechanics a work in progress daniel arovas department of physics university of california, san diego may 8, 20. Nptel material is available for free on nptel website. Example equilibrium stationary extremum potential energy note. At the core of the potential vortex the velocity blows up to. Velocity potential can be graphed, where lines of equivalent velocity potential denote equipotential lines. An internet book on fluid dynamics velocity potential irrotational. An example problem relating the velocity potential and the stream function.
Nptel provides elearning through online web and video courses various streams. On the other hand the field potential is somehow provided all good assumptions equivalent to the field with no further physical. It is necessary to bring out the similarities and differences between them. Let us assume that u, v and w are the components of the resultant velocity v in x. If the fluid is incompressible, the average velocity field is also solenoidal can can be expressed as the curl of a vector potential or the stream function. Velocity potential california institute of technology. Physics 5153 classical mechanics velocity dependent. Lectures in computational fluid dynamics of incompressible flow. Nptel courses in engineering, science, management, humanities and social sciences.
A potential flow is characterized by a velocity field that is the gradient of a scalar function, the velocity potential. This velocity field is irrotational, because the curl of a gradient is identically zero. Times new roman arial narrow arial monotype sorts symbol fm. Equation of continuity for 1 d, 2 d, and 3 d flows stream and velocity potential functions, flow net analysis. Mod01 lec42 potential flow past immersed bodies youtube. The notion of a velocity potential in threedimensions arises when the flow is irrotational. The velocity components in a twodimensional velocity field for an incompressible fluid are expressed as 3 2 2 3 3 2 2 3 x v xy y x x y y u. Velocity potential definition of velocity potential by. Nonlinear evaluation of the kinematics of directional field wavesrealistliku lainevalja uksiklainete kinemaatiliste parameetrite arvutamine veepinna. Note that in terms of velocity potential expression for circulationeqn. Likewise, knowledge of the potential function in any point of the space allows to derive back the field, equivalently again, provided the correct assumptions on connectivity of the regions to hold. Gutierrez physics 5153 classical mechanics velocity dependent potentials 1 introduction we have so far only considered forces and therefore potentials, that are dependent only on the. These are flows in which the fluid particles do not rotate, their angular velocity is zero. We notice that velocity potential and stream function are connected with velocity components.
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