B-2 Physics: Fluid Dynamics PDF

Module: B-2 Physics Topic 2.2.4 Fluid Dynamics  INTRODUCTION On completion of this topic you should be able to: 2.2.4.1 Describe specific gravity and density in relationship to fluids. 2.2.4.2 Describe the following in relati...

Module: B-2 Physics Topic 2.2.4 Fluid Dynamics  INTRODUCTION On completion of this topic you should be able to: 2.2.4.1 Describe specific gravity and density in relationship to fluids. 2.2.4.2 Describe the following in relationship to fluids: viscosity - fluid resistance effects of streamlining effects of compressibility 2.2.4.2 Describe the following types of pressure: static dynamic total 2.2.4.2 State Bernoulli’s Theorem and describe the operation of a venturi. 30-03-2024 Slide No. 2  PHYSICAL NATURE OF MATTER Solid, Liquid and Gas are known as the three physical states of matter or material. Characteristics of Matter Solid Liquid Gas Definite Shape Indefinite Shape Indefinite Shape - Independent of the container - takes the shape of the container - takes the shape of the container Define Volume Define Volume Indefinite Volume Not easily compressible Not easily compressible Compressible - little free space between particles - little free space between particles - lots of free space between particles Does not flow easily Flows easily Flows easily - particles cannot move past one - particles can move past one another - particles can move past one another another 30-03-2024 Slide No. 3  DENSITY Density of a substance is its weight per unit volume. Usually expressed in pounds per cubic foot (lb⁄ft³) or in grams per cubic centimetre (g⁄cm³). The density of solids and liquids varies with temperature:  A standard temperature of 4°C is used when measuring the density of each matter. The density of a gas varies with temperature and pressure:  The density of a gas increases in direct proportion to the pressure exerted on it  Standard conditions at 0°C for temperature and a pressure of 76 cm (29.92 inch) of Mercury (Hg) are used for the measurement of the densities of gases. 30-03-2024 Slide No. 4  SPECIFIC GRAVITY (S.G.) When comparing the densities: The standard for liquids and solids is water at 4°C The standard for gases is air at 0°C Specific gravity for liquids and solids is calculated by comparing the weight of a definite volume of substance with the weight of an equal volume of water. Specific gravity is not expressed in units, but as a pure number. The specific gravity of common substances. 30-03-2024 Slide No. 5  SPECIFIC GRAVITY (S.G.) A device called a hydrometer is used to measure the specific gravity of liquids. This device has a tubular- shaped glass float contained in a larger glass tube. 30-03-2024 Slide No. 6  VISCOSITY IN LIQUIDS Viscosity, one of the most important properties of hydraulic fluids, is a measure of a fluid’s resistance to flow. A liquid, such as gasoline, which flows easily has a low viscosity; and a liquid, such as tar, which flows slowly has a high viscosity. The viscosity of a liquid is affected by changes in temperature and pressure: As the temperature of a liquid increases its viscosity decreases If the pressure on the liquid is very high its viscosity will increase. A liquid that is too thin (too low viscosity) will allow rapid wearing of moving parts while a liquid that is too thick will give a bigger internal friction resistance. 30-03-2024 Slide No. 7  VISCOSITY IN GASES The term viscosity also applies to gases. The viscosity of air is a consideration in aerodynamics. When the temperature of a gas rises, it becomes more viscous. Viscosity in gases is independent of pressure under normal conditions. 30-03-2024 Slide No. 8  VISCOSITY INDEX The viscosity index (V.I.) of an oil is a number that indicates the effect of temperature changes on the viscosity of the oil: A high V.I. indicates small oil viscosity changes with temperature:  A fluid with a high V.I. can be expected to undergo very little change in viscosity with temperature extremes and to have a stable viscosity. A low V.I. indicates high viscosity changes with temperature:  A fluid with a low V.I. can be expected to undergo a significant change in viscosity as the temperature fluctuates. Failure to use an oil with the proper viscosity index may result in poor lubrication and equipment failure. For hydraulic oils used in aircraft, a high viscosity index is expected since the aircraft is exposed to a wide range of operating temperatures. 30-03-2024 Slide No. 9  STREAMLINING MAGNITUDE OF AIR RESISTANCE OR ‘DRAG’. All three objects have the same cross-sectional area. A flat shape fights air flow and causes more drag or resistance. A curved shape allows air to flow smoothly around it. The shaping of an object, such as an aircraft body or wing, to reduce the amount of drag or resistance air, due to viscosity, to motion through a stream of air. This is called streamlining. STREAMLINES 30-03-2024 Slide No. 10  EFFECT OF STREAMLINING STREAMLINES Streamlining reduces the amount of resistance and increases lift. To produce less resistance for subsonic streamlining: The front of the object should be well rounded The body should gradually curve back from the midsection to a tapered rear section. 30-03-2024 Slide No. 11  COMPRESSIBILITY The terms “Compressibility” and “Incompressibility” describe the ability of molecules in a fluid to be compacted or compressed (made more dense) and their ability to bounce back to their original density. An incompressible fluid cannot be compressed and has relatively constant density throughout. Liquid is considered as incompressible. A gaseous fluid such as air can be either compressible or incompressible. 30-03-2024 Slide No. 12  EFFECTS OF COMPRESSIBILITY Compressibility is an important factor in aerodynamics. Generally, at low speeds, the compressibility of the fluid (the air) is not significant in relation to aircraft design: The motion of the aircraft travelling through the air at such speed does not affect the density of the air. However, at high speeds, some of the energy of the quickly moving aircraft goes into compressing the air and changing air density. The airflow is now compressible. 30-03-2024 Slide No. 13  STATIC, DYNAMIC AND TOTAL PRESSURE When an aircraft flies, it travels through a fluid (air) which has a certain atmospheric pressure due to the weight of the atmosphere - static pressure (Ps). The aircraft also has forward, dynamic, motion which means that it is striking air molecules at a rate proportional to its speed - dynamic pressure (usually denoted by q, or Q). The sum of the static and dynamic pressure is the total pressure (Pt or sometimes P0), also known as the total pitot pressure, stagnation pressure of the fluid. A pitot tube in aircraft is commonly a pressure measurement instrument used to measure fluid flow velocity. 30-03-2024 Slide No. 14  STATIC, DYNAMIC AND TOTAL PRESSURE Static pressure is the actual pressure of the fluid, which is associated not with its motion but with its state. In aircraft, static pressure is open to the atmosphere. Dynamic Pressure is parallel to the flow of air and expressed as: q = ½rV² Where r is the fluid density and V is the fluid velocity. 30-03-2024 Slide No. 15  STATIC, DYNAMIC AND TOTAL PRESSURE Static pressure is used to calculate aircraft altitude. 30-03-2024 Slide No. 16  MEASURING DYNAMIC PRESSURE Sealed capsule Case Total pressure is fed to the inside of the sealed capsule. As the static pressure varies in the case, the sealed capsule expands or contracts. This is equivalent to: ½rV2 = Pt – Ps A suitable link can moves an indicator as required. q = ½ rV² is then used to calculate airspeed in flight: 30-03-2024 Slide No. 17  BERNOULLI’S PRINCIPLE The Swiss mathematician and physicist Daniel Bernoulli developed a principle that explains the relationship between potential and kinetic energy in a fluid. All matter contains potential energy and/or kinetic energy: In a fluid the potential energy is that caused by the pressure of the fluid while the kinetic energy is that caused by the fluid’s movement Although the energy cannot be created or destroyed, it is possible to exchange potential energy for kinetic energy or vice versa. 30-03-2024 Slide No. 18  BERNOULLI’S PRINCIPLE A P B C Q “Venturi,” or “Venturi tube”, is a tube constructed in which the cross-sectional area gradually decreases to a minimum diameter in its center section. Where the cross-sectional area is decreasing, the passageway is referred to as a converging duct. As the passageway starts to spread out, it is referred to as a diverging duct. Bernoulli’s principle, as illustrated by the venturi, states that the static pressure of a fluid (liquid or gas) decreases at points where the velocity of the fluid increases, provided no energy is added to nor taken away from the fluid. 30-03-2024 Slide No. 19  BERNOULLI’S PRINCIPLE A P B C Q At points A and C, the liquid moves at low velocity, producing a high static pressure. As the tube narrows in the center, it must contain the same volume of fluid as the two end areas. As the fluid approaches the constriction at point B, the liquid moves at a higher velocity, producing a lower pressure than that at points A and C. 30-03-2024 Slide No. 20  BERNOULLI'S THEOREM EQUATION Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation. There are different forms of the Bernoulli equation for different types of flow. One common Bernoulli's equation which appears in many physics, fluid mechanics, and airplane textbooks: Static Pressure + Dynamic Pressure = Total Pressure = Constant 30-03-2024 Slide No. 21  VENTURI EFFECT A1 > A2, V1 < V2, thus, P1 > P2 The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. The fluid velocity must increase through the constriction to satisfy the equation of continuity, while its pressure must decrease due to conservation of energy. Using Bernoulli's equation for a incompressible flow (Density ρ is constant), the relationship of the pressure P of a fluid to its velocity V is given by: 30-03-2024 Slide No. 22  VENTURI EFFECT Venturis are found in many applications. The piston forces air through the venturi (yellow) and the pressure at the throat drops. Atmospheric pressure in the round container (reservoir) is now greater, and the liquid (red) travels up the tube, joins the airstream, and is sprayed. 30-03-2024 Slide No. 23  VENTURI EFFECT An extension of Bernoulli’s Theorem is the basis of how some of the lift is generated by aircraft wings, propellers and helicopter rotor blades. The top of the wing roughly approximates to half of a venturi. The air passing over the top surface of the wing moves at a higher velocity. The higher velocity causes a decreased pressure, and the pressure difference between upper and lower wing surfaces contributes to the force known as ‘lift’. Note: The ‘leading edges’ of wings experience total pressure, not dynamic pressure only. 30-03-2024 Slide No. 24  CONCLUSION Now that you have completed this topic, you should be able to: 2.2.4.1 Describe specific gravity and density in relationship to fluids. 2.2.4.2 Describe the following in relationship to fluids: viscosity - fluid resistance effects of streamlining effects of compressibility. 2.2.4.2 Describe the following types of pressure: static dynamic total. 2.2.4.2 State Bernoulli’s Theorem and describe the operation of a venturi. 30-03-2024 Slide No. 25  This concludes: Module: B-2 Physics Topic 2.2.4 Fluid Dynamics