SUB: Fluid Mechanics & Fluid Power Engg. Subject Code:BME 308 5th Semester,BTech(MS) Mechanical Engg. Dept VSSUT Burla
SCOPE OF FLUID MECHANICS Knowledge and understanding of the basic principles and concepts of fluid mechanics are essential to analyze any system in which a fluid is the working medium. The design of almost all means transportation requires application of fluid Mechanics. Air craft for subsonic and supersonic flight, ground effect machines, hovercraft, vertical takeoff and landing requiring minimum runway length, surface ships, submarines and automobiles requires the knowledge of fluid mechanics. In recent years automobile industries have given more importance to aerodynamic design. The collapse of the Tacoma Narrows Bridge in 1940 is evidence of the possible consequences of neglecting the basic principles fluid mechanics. The design of all types of fluid machinery including pumps, fans, blowers, compressors and turbines clearly require knowledge of basic principles fluid mechanics. Other applications include design of lubricating systems, heating and ventilating of private homes, large office buildings, shopping malls and design of pipeline systems. The list of applications of principles of fluid mechanics may include many more. The main point is that the fluid mechanics subject is not studied for pure academic interest but requires considerable academic interest.
CHAPTER -1 Definition of a fluid:Fluid mechanics deals with the behaviour of fluids at rest and in motion. It is logical to begin with a definition of fluid. Fluid is a substance that deforms continuously under the application of shear (tangential) stress no matter how small the stress may be. Alternatively, we may define a fluid as a substance that cannot sustain a shear stress when at rest. A solid deforms when a shear stress is applied , but its deformation doesn’t continue to increase with time. Fig 1.1(a) shows and 1.1(b) shows the deformation the deformation of solid and fluid under the action of constant shear force. The deformation in case of solid doesn’t increase with time i.e t1 t 2 ....... tn . From solid mechanics we know that the deformation is directly proportional to applied shear stress ( τ = F/A ),provided the elastic limit of the material is not exceeded. To repeat the experiment with a fluid between the plates , lets us use a dye marker to outline a fluid element. When the shear force ‘F’ , is applied to the upper plate , the deformation of the fluid element continues to increase as long as the force is applied , i.e t 2 t1 . Fluid as a continuum :Fluids are composed of molecules. However, in most engineering applications we are interested in average or macroscopic effect of many molecules. It is the macroscopic effect that we ordinarily perceive and measure. We thus treat a fluid as infinitely divisible substance , i.e continuum and do not concern ourselves with the behaviour of individual molecules. The concept of continuum is the basis of classical fluid mechanics .The continuum assumption is valid under normal conditions .However it breaks down whenever the mean free path of the molecules becomes the same order of magnitude as the smallest significant characteristic dimension of the problem
.In the problems such as rarefied gas flow (as encountered in flights into the upper reaches of the atmosphere ) , we must abandon the concept of a continuum in favour of microscopic and statistical point of view. As a consequence of the continuum assumption, each fluid property is assumed to have a definite value at every point in the space .Thus fluid properties such as density , temperature , velocity and so on are considered to be continuous functions of position and time . Consider a region of fluid as shown in fig 1.5. We are interested in determining the density at the point ‘c’, whose coordinates are , . Thus the mean density V would be given by ρ= and . In general, this will not be the value of the density at point ‘c’ . To determine the density at point ‘c’, we must select a small volume , , surrounding point ‘c’ and determine the ratio and allowing the volume to shrink continuously in size. Assuming that volume is initially relatively larger (but still small compared with volume , V) a typical plot might appear as shown in fig 1.5 (b) . When becomes so small that it contains only a small number of molecules , it becomes impossible to fix a definite value for ; the value will vary erratically as molecules cross into and out of the volume. Thus there is a lower limiting value of designated , ꞌ . The density at a point is thus defined as ρ= ꞌ Since point ‘c’ was arbitrary , the density at any other point in the fluid could be determined in a like manner. If density determinations were made simultaneously at an infinite number of points in the fluid ,