Turbulent Friction Factors Of Non-Newtonian Fluids - Research Paper Example

Turbulent Friction Factors Of Non-Newtonian Fluids Background The theory of the hydrodynamics of viscous fluids is based on a law governing the relationship between two components that of stress in a given fluid and of the strain-velocity. Hence making its applicability limited to Newtonian fluids. This paper will show the general relations between these two components and derivation of laws obeyed by visco-inelastic fluid, which is also incompressible in a steady, and laminar flow. It is also going to show how these equations of motion and the existing boundary conditions are obtained with known relationships Two applicability of these laminar flow will be summarized. The discussion touches on: the torsional motion of mass of a fluid in a cylinder, the motion is produced by a forces put on its ends, also the flow of a mass of fluid confined between coaxial cylinders rotating with dissimilar angular velocities.it is mandatory for normal tractions to be applied to the flat surfaces of the fluid, together with the azimuthal tractions got from this classical theory, for the stated motion. In the second case, the analogous results can be got or calculated immediately. Assuming there is no centrifugal forces, these results should still apply, and so it causes a qualitative variance between the distinct case of classical hydrodynamics and the behavior of fluids in general. (Kostic and Hartnett 345) Sir Isaac Newton is recognized throughout the science world as the one famous for coming up with numerous scientific theories in physics and mathematics. He was able to describe in details how ‘standard’ fluids behave, Newton noted that the behavior is that of a uniform flow. Therefore, this flow behavior known as viscosity only varies with changes in their pressure or temperature. A good example is when water freezes and turns ice at 0˚C or become a gas at 100˚C. Within this range of temperature change, water would behave like a ‘normal’ fluid having constant or uniform viscosity. Naturally, liquids assumes the shape of the container they in. this is referred to as Newtonian fluids. However, some fluids do not obey this particular rule. Therefore, they are called non-Newtonian fluids in fluid mechanics. (Schechter 445) Normally the trigger of a hydro- pistol is pulled to squirt out water. In order for this to happen faster, the must be force increased considerably. This indicates that fluids naturally will resist flow. This what newton referred to as viscosity. It can be demonstrated by using a simple model developed by Newton to show relationship between how hard the trigger is pulled and how fast is the squirting of the liquid out from the pistol. Imagine the flowing liquid is like as a series of layers of liquid particles sliding against and past one other. The resistance to flow is caused by the frictions between the layers of the liquid. The speed of sliding of these layers can be increased may be as twice as fast as the initial one, the fluid must be made to overcome the resisting force which is also twice as much. Newton therefore explained that the slower these layers slide over each other, the lesser resistance. If there were, no variance between this speed the resistance would not be there. This behavior can be seen in Fluids such as water and gasoline and they are grouped as Newtonian fluids. Other fluids like blood, yogurt, pie fillings, ketchup, gravy, mud, and cornstarch paste do not exhibit this behavior. That is why they are called non-Newtonian fluids. For these fluids, doubling the speed of the layers sliding past each other is not proportional to force of the resistance. In some fluids such as snow or mud, there is no flow until there is a lot of pushing hard, before the substance starts to flow like any liquid normally available. This is what causes For any fluid to flow there must two components at play, these are stress and strain. The stress is known to be the force applied to a given body. Its effect on the other hand is termed as strain. Imagine a person holding a metal horizontally and hammering from the cross-sectional side. The applied force on the metal produces stress to that specific area. This result into an effect causing deformation on this metal is called strain. Like in solids, Newtonian fluids will not resist much of this stress; hence, there will not be any signs of strain in them. Imagine hitting water with a hammer, the liquid never show any sign of resistance much to the amount of stress applied giving no signs of strain. Non-Newtonian fluids vary their flow or viscosity when put under this stress. If the force is applied here, the stress can make them very thick to an extent of showing a sign of a solid like behavior, or otherwise causing them to be runnier than before. Removal of the stress will result into them reverting to their former state. A good example in getting some tomato sauce quirt out of the bottle. Although it is can appear like there are some inside there, but when it is turned the bottle upside down, no tomato sauce flows out. The best way to remove it is by trying to shake or sometimes hit the bottle. This makes the tomato sauce to turn into liquid enabling it to easily squirt a little out. This means, the sauce’s viscosity reduces, making flow with ease at the applied stress. Other examples are Oobleck, which is made by mixing water, and corn flour this liquid is very runny after stress application on it by hitting a bowlful with a hammer, then it quickly behaves like a solid. It will not splash everywhere, instead the particles latch together. It can be rolled into a solid ball in the hand, as soon as moving it is stops, no, sooner than it reverts to liquid. Therefore, this substance resistance to flow or viscosity rises with increased stress. There exist different categories of non-Newtonian fluids. it also worth to note that not all non-Newtonian Fluids would show the same behavior when this kind of stress is applied on them while others become more solid, some more fluid like. Then non-Newtonian fluids reactions depends on two factors the amount of stress and the duration of time, that stress is applied. Applicability section: non-Newtonian fluids The behavior of non-Newtonian fluids has very significant implications: If a certain clay is used to build a house is built and something like an earthquake generates some stress on clay material after causing a sudden movement on the wall, this solid clay eventually can converted into a flowing liquid. Body armour worn by soldiers is made to behave like a liquid so that solider can move with ease, on the other hand it turns into a solid when hit from stress. Fluid mechanics is a branch of continuum mechanics that focuses on the study of fluids; it can be further small areas of study namely fluid static and fluid dynamics. Fluid statics focuses on fluids at rest, while fluid dynamics mainly deals with fluids in motion. Parts of fluids consist of tiny molecules that are in constant collision with each other. This suggests that fluids are continuous in nature. This provide the fact that properties of fluids such as pressure, density, velocity and temperature are assumed to be infinitely small points, and are to vary continuously at every point of the fluid. A small change in vertical water velocity would provide shear forces that are arranged parallel to the floor. These forces acting on the floor of a channel produces shear stress, which rolls out bed load motion.  The stresses curry a magnitude, which is a function of water surface slant, channel flow, and geometry. It has a moment of force where the directive forces known as shear forces tends to work against restrictive forces popularly called inertia friction is also referred to as the moment of incipient motion this will produce a shear stress known as the critical shear stress (t). (Schurz 170) A shear stress (), is the component or a constituent of stress coplanar with the cross section any given material. It is also taken as an amount of force of friction from a fluid acting directly on an object along that fluid’s path. Focusing on open channel flow, this force is the one that is responsible for dragging the water against the floor of that channel. Shear stress is built up from the force vector component, which tend to be parallel to the cross section. Alongside the shear stress is a normal stress which is otherwise generated from the force vector component vertical or antiparallel to the under lying material cross section at the point of action. Equations of shear stress is given by Where: is equal to shear stress. Is equal to the force being applied; is the cross-sectional area of material this area must be parallel to this vector force. On further simplification Shear stress described by the following equations Where: Is the Shear Stress measured in (N/m2,   ). g is the weight Density of the fluid given in (N/m3). D is the given mean water depth in (m). Sw is the water Surface slope in (m/m) Pure shear stress in relation any given pure shear strain, has a symbol of, is illustrated as follows Where represents the shear modulus of the material. In full Expressed as Young's modulus while is Poisson's ratio. Beam shear is also known as the internal shear stress of a parallel beam Where V gives the total shear force at that point; Q stands for moment of the area; t stands for the material thickness orthogonal to the shear. I stands for the Moment of Inertia of the entire cross sectional area. This is the Jourawski formula. (Astarita 225) Semi-monocoque shear is a Shear stress that is found within a semi-monocoque configuration. It is be evaluated by conceptualizing the cross-section area of the structure as a set of stringers bearing solely its axial loads and webs. Taking the ratio of the shear flow and the thickness of a given part of the semi-monocoque structure so that this will produces the shear stress. Hence, the maximum shear stress is given within either the web of maximum shear flow or least thickness. In engineering a constructions underground can be paralyzed due to this kind of shear. The whole weight of a dam or dike may results in to collapse of the subsoil, just like in a small landslide. The maximum shear stress is shown as follows: Where U stands for change in kinetic energy. G represent the shear modulus.V is the volume of rod; and so Stands for the mass moment of inertia. Is the angular speed. One of the biggest application areas of non-Newtonian fluids is the measurement by shear stress sensors Diverging fringe or simply shear stress sensor: This sensor was demonstrated by A. A. Naqwi and W. C. Reynolds. They showed that this idea could be developed further and be used to measure shear stress at the edges of the wind flow called the wall shear stress. Suppose this sensor could be used directly to obtain the measurement of the gradient of the velocity profile at the wall, times the dynamic viscosity, this would eventually yield the shear stress. The production of interference pattern by passing a beam of light through some two parallel holes or slits forms a system of linearly diverging fringes that look like they are to be generated from the plane of these two tiny slits. As the fringes allow a particle in a fluid to pass through them, a receiver would detect the reflection of these fringe patterns. The velocity and height of that particle can be deduced instantly as the signal is processed, together with using the known fringe angle. This value measured of wall velocity gradient is autonomous of the fluid properties and hence, does not need calibration. Other area includes recent developments in the micro-optic fabrication. These technologies brought about the use of integrated diffractive optical element also to make diverging fringe shear stress sensors accurately usable all fluids. The use of Micro-pillar shear-stress sensor technique is that of slim wall-mounted micro-pillars. They are made of the stretchy polymer, which curve in response to the applying some drag forces in the proximity of the wall. The sensor in that way is one of the indirect measurement principles relying on the correlation between near-wall velocity gradients and the fundamental l wall-shear stress. Shear thinning fluid is a further example of the reverse. It helps in development a pseudo plastic fluid or a shear thinning fluid, which a form of a wall paint. If anyone would like to see the paint flow easily, off from the brush at the time of use on the wall surface being painted, and not to be dripping in excess. It is good to note that all available thixotropic fluids are tremendously shear thinning, but are expressively time dependent, however the informal "shear thinning" fluids respond immediately to changes in shear rate. Consequently, to avoid any confusion, the shear thinning is classified more as pseudo plastic. (Schechter 170) Works Cited Astarita, G. "The Engineering Reality of the Yield Stress." Astarita, G. The Engineering Reality of the Yield Stress. J. Rheol., 1990. 275. Kostic and Hartnett . "Predicting turbulent friction factors of non- Newtonian fluids in noncircular ducts." Kostic, M. and Hartnett , J.P. ,. Int. Comm. Heat Mass Transf., 1984. Schechter, R.S. "On the steady flow of a non-Newtonian fluid in cylinder ducts." On the steady flow of a non-Newtonian fluid in cylinder ducts. AIChE J, 1961. 445. Schurz, J. "The yield stress - an empirical reality." The yield stress - an empirical reality. Rheo.Acta, 1990. 170. Read More