Fluid Mechanics and Mechanical Engineering Sections ?Fluid Properties ?Fluid Statics ?Fluid Dynamics ?Aerodynamics Fundamentals ?Summary 1. Fluid Properties A fluid is a substance that deforms continuously under an applied shear stress. . ? Liquids ? water ? Gases ? air The difference between the two is that liquids occupy a definite volume, independent of the volume in which they are contained, whereas gases expand to fill the entire volume of the container in which they are placed. . Viscosity Viscosity is a fluid property that relates the magnitude of fluid shear stresses to the fluid strain rate. . For a Newtonian fluid , τ is the shear stress, μ is a constant called the viscosity (in N·s/m2). Newtonian fluids For a large class of fluids, the coefficient of viscosity(μ) is independent of the velocity gradient. Such fluids are called Newtonian fluids. . Most fluids familiar to us, such as water, air, and oil, behave as Newtonian fluids. However, certain other fluids, such as blood, toothpaste, and paint, are non-Newtonian. . Fluid mechanics is concerned with Newtonian fluids. . Notes: The viscosity is a property of the fluid , largely a function of temperature for most Newtonian fluids. The fluids that we commonly deal with — water and air — possess relatively low viscosities. Consequently, over most of the flow field, the fluid can be treated as nonviscous. . The magnitude of the coefficient depends on the cohesive force between molecules and the momentum interchange between colliding molecules. Temperature Effect The cohesive force is dominant for a liquid, so that as the temperature of a liquid is raised and the cohesive force between molecules decreases, the viscosity also decreases. The momentum interchange is dominant for a gas, and as the temperature of the gas is raised, providing for greater momentum interchange, the viscosity of the gas increases. . Surface Tension Surface tension of a liquid is due to the forces of attraction between like molecules, called cohesion, and those between unlike molecules, called adhesion.. Molecules on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called surface tension. 2. Fluid Statics ? Fluid statics is the branch of fluid mechanics which deals with situations in which there is no relative motion between fluid elements. The fluid can be either at rest or in uniform motion. . In a static fluid, there is no motion of one layer of fluid relative to an adjacent layer, so there are no viscous shear forces. Thus, the only forces we shall consider in a study of fluid statics are pressure forces and gravity. Application : manometer The liquid in the tube will reach an equilibrium position where its weight will be balanced by the difference between the tank pressure and the local atmospheric pressure exerted on the liquid at D. Thus, Automobile Hydraulic Lift Hydraulic Drum Brake Archimedes’ principle The principle of buoyancy: . A submerged body is subject to an upward force FB equal to the weight of the fluid displaced. 3. Fluid Dynamics Laminar flow — fluid moves along smooth paths — viscosity damps any tendency to swirl or mix Turbulent flow —fluid moves in very irregular paths —efficient mixing —velocity at a point fluctuates 3.1 Control Volume Approach Solving problems involving fluids in motion, ? to pick a fixed region in the fluid and watch the fluid as it enters and leaves the region. Conservation laws such as conservation of mass, momentum and energy are applied. We don’t need to know the flow details within the control volume ! Example 1 Suppose we are designing a water-piping system for a building with two apartments and wish to supply water to two faucets, which are connected by a tee configuration, as shown in the figure. We want the velocity of the water to be same when it leaves both faucets. What should be the velocity of the water source? Analysis ?Assume that the mass of the fluid per unit time entering the control volume is equal to the amount leaving. And assume that the water is steady, not trapped in control volume. . ? The density of the water is the same throughout (incompressible fluid) , the diameter of the pipe is the same everywhere. Conservation of mass gives the solution. . 3.2 Fluid Force we assume steady one-dimensional flow, then we may write that the force in the kth direction, Fk , as : where is the mass flowrate and (V2k－V1k) is the difference in the velocity of the fluid from station 1 to station 2 in the kth direction. Example 2 Water with a velocity of 10 m/s strikes a turbine used for power generation and is rotated 60? from the horizontal by the blade, as shown in the figure. The cross section of the inlet water is 0.003 m2. What is the force on a turbine blade shown in the figure? Solution We may assume incompressible flow, so that ρ1=ρ2 , also A1=A2. The water is initially horizontal means that v1y=0. Applying the idea of conservation of mass indicates that : Notice that because A1 = A2, then V1 = V2 . Applying equation to the x direction yields, Substituting the appropriate numbers into this expression gives: The arrow indicates the direction of the x component of the force. Likewise, in the y direction, we have Application : Propeller A propeller consists of several rotating blades attached to a hub that is connected to a shaft. The application of a torque to the propeller shaft causes the ambient fluid ahead of the propeller to move past the blades, imparting to the fluid an exit velocity that is greater than the approach velocity. . Application : Windmill The purpose of a windmill is to extract power from the wind. Due to an increasing shortage of conventional energy sources, the windmill is currently being examined as a potential source of at least some of our electrical power. With the wind itself quite variable, means must be found for wind energy storage to handle electrical demands during periods of low wind velocity. Aerodynamics Fundamentals Aerodynamics is the branch of dynamics that treats the motion of air (and other gaseous fluids) and the resulting forces acting on solids moving relative to such fluid. . Basic Forces for Aircraft Flight Weight — The force due to gravity. Lift — To overcome gravity, you need to create an upward force. That's what an airplane's wings are for. Thrust — To create lift, you need forward motion. That's what an airplane's engines are for — they produce a force called thrust. . Drag — To keep moving, you need to overcome the resistance of the air — a force called drag. Lift Force ?With a certain angle of attack, the upper surface of the airfoil has more curvature than the lower, the air must speed up in order to flow over the surface . . For a moving fluid, an increase in velocity cor-responds to a decrease in pressure, the higher pre-ssure on lower surface essentially pushes the wing up. This force is called the lift. Stall ? Increasing the angle of attack can increase the lift, but it also increases drag so that you have to provide more thrust with the aircraft engines. . At too high an angle of attack, the air will not be able to remain attached to the upper surface of the airfoil, turbulent flow increases the drag dramatically and will stall the aircraft. Sonic Boom Sonic boom is an impulsive noise similar to thunder. It is caused by an object moving faster than sound. An aircraft traveling through the atmosphere continuously produces air-pressure waves similar to the water waves caused by a ship's bow. . When the aircraft exceeds the speed of sound, these pressure waves combine and form shock waves, dropping sonic boom along its flight path. The sonic booms can be sometimes quite loud. For a commercial supersonic transport plane (SST), it can be as loud as 136 decibels. . Concorde Problems : Excessively powerful engine /Sonic boom . Civil Aviation