...Fundamentals of Fluid Mechanics Fluid mechanics is the study of fluids and the forces on them. (Fluids include liquids, gases, and plasmas.) Fluid mechanics can be divided into fluid kinematics, the study of fluid motion, and fluid dynamics, the study of the effect of forces on fluid motion, which can further be divided into fluid statics, the study of fluids at rest, and fluid kinetics, the study of fluids in motion. Fluid mechanics is very important to engineers when observing flow in pipes, viscous effects of fluids, and the forces that act on a fluid. As a student, I am suppose to demonstrate an adequate understanding of many properties involved fluid mechanics. Some learning outcomes that must be accomplished by taking this class are: * Demonstrate understanding of fluid mechanics fundamentals, fluid and flow properties such as compressibility, viscosity, buoyancy, hydrostatic pressure and forces on surfaces * Apply Bernoulli equation to solve problems in fluid mechanics * Solve fluid mechanics problem using control volume analysis using conservation of mass, energy equation and irreversible flow * Use differential analysis of fluid flow, potential flow theory, viscous flow, Navier Stokes equations to solve problems * Perform modeling and similitude using Buckingham Pi theorem, correlation of experimental data. * Analyze flow in pipes to determine laminar and turbulent flow behaviors. * Apply energy and momentum equations to determine...
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...This is page i Printer: Opaque this A Mathematical Introduction to Fluid Mechanics Alexandre Chorin Department of Mathematics University of California, Berkeley Berkeley, California 94720-3840, USA Jerrold E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, California 91125, USA ii iii A Mathematical Introduction to Fluid Mechanics iv Library of Congress Cataloging in Publication Data Chorin, Alexandre A Mathematical Introduction to Fluid Mechanics, Third Edition (Texts in Applied Mathematics) Bibliography: in frontmatter Includes. 1. Fluid dynamics (Mathematics) 2. Dynamics (Mathematics) I. Marsden, Jerrold E. II. Title. III. Series. ISBN 0-387 97300-1 American Mathematics Society (MOS) Subject Classification (1980): 76-01, 76C05, 76D05, 76N05, 76N15 Copyright 1992 by Springer-Verlag Publishing Company, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-Verlag Publishing Company, Inc., 175 Fifth Avenue, New York, N.Y. 10010. Typesetting and illustrations prepared by June Meyermann, Gregory Kubota, and Wendy McKay The cover illustration shows a computer simulation of a shock diffraction by a pair of cylinders, by John Bell, Phillip Colella, William Crutchfield, Richard Pember, and Michael Welcome...
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...Variation of Pressure vertically in a fluid under gravity P_2 A P_1 Force due to P_1 on area A acting up = P_1 A Force due P_2 on area A acting down = P_2 A Force due to the weight of the element =mg= ρA(z_2- z_1 )g Since the fluid is at rest, there can be no shear forces and hence no vertical forces on the side of element due to surrounding fluid. Considering upward as positive, sum of all forces = 0, We have P_1 A-P_2 A - ρA(z_2- z_1 )g=0 Or P_2- P_1= - ρ(z_2- z_1 )g So, under the influence of gravity , pressure decreases with the increase height. Equality of Pressure at the same level in a static fluid Since the fluid is at rest, there are no horizontal shear stresses on the sides of the element. For static equilibrium the sum of horizontal forces must be zero, P_1 A=P_2 A P_1=P_2 Therefore the pressure at any two points at the same level in a body of fluid at rest will be the same If the (x,y) is the horizontal plane then ∂p/∂x=0 and ∂p/∂y=0 Variation of pressure due to gravity from point to point in a static fluid Since the element is in equilibrium, the resultant of the forces in any direction should be zero Resolving forces in the axial direction, pA-(p+δp)A-ρgAδs cosθ=0 δp=-ρgδs cosθ Putting above equation in differential form, dp/ds=-ρgcos θ Special...
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...the earth is roughly 7000˚C. The two reasons why the earth is hot is when the earth was formed, the interior was heated rapidly due to the gravitational forces being converted into heat and radioactive isotopes within the earth liberate heat as they continue to decay. Our ability to drill into the earth is restricted to the upper few kilometers of the earth’s crust. We must look for a location where the earth’s interior heat is brought within our reach. This is most common at plate boundaries. Direct heating systems are designed to supply hot water only with no electricity generation. Borehole drilled to depth of 1800 meters beneath the city of Southampton, UK. Near the bottom of the hole is water at 70˚C. The fluid contains dissolved salts. The fluid is more accurately described as Brine. The Brine is pressurized and so rises unaided to within 100 m of the surface. A turbine pumps the Brine up to the surface through a heat exchanger that transfers heat to clean...
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...Pascal's law or the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure variations (initial differences) remain the same. The law was established by French mathematician, Blaise Pascal. This principle is stated mathematically as: * P=pg( h) * P is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;ρ is the fluid density (in kilograms per cubic meter in the SI system);g is acceleration due to gravity (normally using the sea level acceleration due to Earth's gravity, in SI in metres per second squared); * h is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column * Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. * A container, as shown below, contains a fluid. There is an increase in pressure as the length of the column of liquid increases, due to the increased mass of the fluid above. * For example, in the figure below, P3 would be the highest value of the three pressure readings, because it has the highest level of fluid above it. * If the above container...
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...Instructions – Parts List Parts Manufactured by Paint Preparation System Spray Guns INTENDED USE: 3M–Graco spray gun systems are intended for use only by trained and professional tradesmen, and used solely for the purpose of spray application of liquid coating materials. They must be used only in areas which are compatible with the material being sprayed, in strict compliance with applicable local and national regulations. HVLP, Compliant, and Airspray 100 psi (0.7 MPa, 7 bar) Maximum Working Air Pressure 29 psi (200 kPa, 2.0 bar) Maximum Compliant Inbound Air Pressure (HVLP and Compliant) U.S. Patent Pending Read warnings and instructions. Table of Contents Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Warnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Selection Charts . . . . . . . . . . . . . . . . . . . . . . . . 4 Typical Installation . . . . . . . . . . . . . . . . . . . . . . . 5 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Daily Gun Care, Flushing, and Cleaning . . . 13 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . 16 Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Accessories . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Dimensions . . . . . . . . . . . . . . . . . . . . . ...
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...1. What is the dry adiabatic lapse rate (give a number with units)? The cooling and warming of unsaturated air of 10C every 1000 meters or about 5.5F for every 1000 feet. The rate of change of any meteorological factor with altitude, esp atmospheric temperature, which usually decreases at a rate of 0.6°C per 100 metres (environmental lapse rate). Unsaturated air loses about 1°C per 100 m (dry adiabatic lapse rate), whereas saturated air loses an average 0.5°C per 100 m (saturated adiabatic lapse rate) 2. Is the moist adiabatic rate greater than or less than the dry adiabatic lapse rate? Less .During saturated ascent, the release of latent heat via condensation partly offsets the conversion of thermal energy into work as parcels expand, reducing the cooling rate of the parcel to less than the dry adiabatic lapse rate (that observed for unsaturated parcels.) The saturated adiabatic lapse rate is 6 degrees per 1,000 meters. The dry adiabatic rate is 10 degrees per 1,000 meters. When a mass of saturated air rises in the atmosphere adiabatically,its temperature falls with height at a rate which is considerably less than the dry adiabatic lapse rate on account of continuous addition of the latent heat of condensation that accompanies the adiabatic cooling of saturated air and the consequent separating out of excess water vapour in the form of drops of liquid water. 3. A parcel of air becomes cooler than its environment if lifted. Is this a stable or unstable condition?...
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...Q1. Briefly describe how the physical properties of materials used to produce tablets influence flow ability. Construct a chart of the flow studies and comment on the results. There are a variety of properties that will affect the flow ability of a tablet, some of these factors will include physical properties such as particle size and the amount of fine particles. The size of the particles can be a significant factor in influencing the overall flow ability, as when the particles become too small (below 50 m), there will be no flow as the cohesive forces between the particles will be greater than the driving force. There will also be no flow for particles that are too large (above 1200 m), as the resistance force will be greater than the gravitational forces, also, too large of a particle can clog the orifice, causing an intermittent flow, thus cannot give an accurate flow rate1. The impact of granule size is demonstrated in Figure 1 as the flow rate will increase up to approximately 215 m, and will then decrease after this. Therefore, demonstrating that the flow rate will increase due to optimal particle size until the particle size causes interactions such as friction and inter-particle cohesive forces, which will reduce flow rate. The percentage of fine particles will also influence the flow rate as increasing the percentage of fines until a certain point will increase the flow rate due to their ability to increase the bulk density of the powder by filling up the void space...
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...------------------------------------------------- Old School: Smoothbore Nozzles in the Fire Service ------------------------------------------------- The City of ______ Fire Department is in current discussion of using either smooth bore nozzle versus combination nozzles in commercial structures. This conversation has been a topic within the fire service since the introduction of the fog/combination nozzles in the 1960’s. Although there are positives to both pieces of equipment, I believe that the department needs to make a decision on which nozzle to use for a standard operating procedure and safety purposes. To better understand the background of the contrasting views, we must look at how the fire service has developed around these two nozzles. The original nozzle was the smooth bore, partly because of its simple design-no moving parts or springs, just a piece of metal that allows water to take shape when it leaves. When Dr. Charles Oyston obtained a patent on a spray nozzle in 1863, the debate slowly emerged. The U.S. Navy introduced the fog nozzle to thousand of men during World War II. Lloyd Layman, commander of the Coast Guard Fire School, discovered the indirect application of fog technique. It was taught at great length, since shipboard fires are very easily compartmentalized and a flammable liquid was the combustible. This fire condition was efficiently and safely extinguished with ease with the indirect fog attack method. According to Layman, the rules for...
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...FLUID DYNAMICS In physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. Fluid dynamics is "the branch of applied science that is concerned with the movement of liquids and gases," according to the American Heritage Dictionary. Fluid dynamics is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them. (The other branch is fluid statics, which deals with fluids at rest.) Scientists across several fields study fluid dynamics. Fluid dynamics provides methods for studying the evolution of stars, ocean currents, weather patterns, plate tectonics and even blood circulation. Some important technological applications of fluid dynamics include rocket engines, wind turbines, oil pipelines and air conditioning systems. FLOW The movement of liquids and gases is generally referred to as "flow," a concept that describes how fluids behave and how they interact with their surrounding environment — for example, water moving through a channel or pipe, or over a surface. Flow can be either steady or unsteady. In his lecture notes, "Lectures in Elementary Fluid Dynamics" (University of Kentucky, 2009) J. M. McDonough, a professor of engineering at the University of Kentucky, writes, "If all properties of a flow are independent of time, then the flow is steady; otherwise, it is unsteady." That is, steady flows do not change over time. An example of...
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...LAMINAR AND TURBULENT FLOW We can observe the nature of the flow of a fluid by injecting a fine filament of dye into the stream of flow and taking note of what happens to this filament. It was found in experiments that at low velocities the dye filament remained intact and that the filaments made parallel lines in the stream of flow. This is known as Laminar flow (or viscous or streamline). If the velocity of flow is gradually increased, the dye filament is eventually broken up and spread over the cross section of the pipe. This is turbulent flow, in which the particles of fluid are not moving in parallel lines but are moving across the general direction of flow. If a fluid particle in a stream is disturbed, its inertia will tend to move it in a new direction, however the viscous forces from the surrounding fluid will tend to move it in the general direction of flow. If the shear forces are large enough to overcome any deviation, then we have viscous or laminar flow. However, if the shear forces are relatively weaker, and not sufficient to overcome the inertia of the particles, then we have turbulent flow. [pic] Therefore it is the ratio of the inertia to the viscous forces which determines whether flow will be laminar or turbulent. The ratio of the inertia forces to the viscour forces is given by: [pic] c l (Reynolds Number) μ Therefore, it is the Reynolds number which determines whether a flow will be laminar or turbulent. As Kinematic Viscosity...
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...CVEN 3100: Fluid Mechanics Fluid Properties: Review Questions 1. What is the definition of a fluid? A substance that deforms continuously when acted on by a shearing stress of any magnitude. 2. Normal force per unit area in a fluid is called what? Pressure 3. True or False: - Static fluids are not subjected to shear force at any time. T 4. True or False: - Normal forces can occur in a fluid whether it is static or Moving T 5. What is the relation between absolute pressure and gage pressure? Absolute pressure can be found from the gage pressure by adding the value of the atmospheric pressure. 6. What formula is used to calculate density of gases? Identify the parameters in the formula p/RT 7. Define specific weight. What is relation to density? Weight per unit volume. Multiply by gravity 8. Because of viscosity, what happens when a fluid tries to flow? It resists and does not flow quick 9. What is kinematic viscosity? The ratio of absolute viscosity to density 10. State the Newton’s law of viscosity and express it mathematically. Change in velocity over distance which velocity changes. Du/dy 11. What is the purpose of lubricating metal hinges? 12. Why does viscosity of liquids decrease with temperature? Molecules are spread further apart 13. Why does viscosity of gases increase with temperature? Molecular activity increases 14. What is an ideal fluid? A fluid that lacks...
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...3.4 Coolant Piping System The cooling water piping system was modelled by applying fluid dynamic principles. Figure 3.4 – Schematic of system 3.4.1 Coolant Piping, Fittings, Valves, and Surge Tank The resulting pressures are determined by using the modified Bernoulli’s equation, Equation (16). The dimensionless factors are used to determine the head losses within the piping system. The dimensionless friction factors used to develop the model, for 90 degree bends, 45 degree bends, valves, and the TCV are shown in Table 3.1. Table 3.2 – Dimensionless Friction Factors K90 K45 Kvalve KTCV 0.2 0.14 6.0 8.0 Along with the fitting friction factors, the friction factor due to the pipe roughness must be considered. The...
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...shall begin by studying incompressible flow problems. Of course all fluids are, to some extent, compressible but under steady flow conditions we may assume that the effects of changes in fluid density are small. In fact, it is the velocity of the fluid that dictates whether changes in density are significant and must be accounted for. In Chapter 6 we shall quantify the velocity limit, below which may assume that the fluid is incompressible; however, the majority of fluid flow problems that you are likely to encounter may be assumed to be incompressible. We shall focus in this chapter on incompressible flow, and on problems in which the fluid is bounded by a surface (we shall call this internal flow); the next chapter will focus on unbounded (or external) fluid flow problems. Both chapters will study real fluid flows and do this by taking into account the effects of viscosity. To do this we must examine how fluids interact with boundaries and here the concept of zero fluid velocity on a surface (boundary) is important. Once we have an understanding of how real fluid flows behave – and see how difficult it is to analyses turbulent flows –then in Chapters 4 and 5 we shall turn our attention to modelling techniques useful for examining simple fluid flow problems commonly found in engineering. Accordingly, this chapter will look at laminar and turbulent bounded fluid flows. We shall focus on pipe flow as this represents a classic example...
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...[12]. Originally the equation was used for describing hydraulic transient of flowing liquid inside a pipe restricted by sudden blockage or closure of valve. In S4 test, the conditions are contrariwise, the pressurized fluid is suddenly released due to the propagating crack. This makes the fluid ahead of the crack to back-flow axially triggering a set of expansion wave/decompression wave [3].Due to the similarity, the equation for compression wave speed measurement in water hammer can be used for determining the speed of decompression wave. As in the experimental set-up, the water is confined in a pipe, the decompression speed (Cw) has the following relationship [10]. (1) Where ρ is the density of the pressurized medium, K is the bulk modulus of elasticity of the pressurized medium inside the pipe, Di is the inner pipe diameter, t is the pipe wall thickness E is the modulus of elasticity of the pipe material....
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