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Buddhi N. Hewakandamby A first course in Fluid Mechanics for Engineers Download free ebooks at bookboon.com 2 A first course in Fluid Mechanics for Engineers © 2012 Buddhi N. Hewakandamby & Ventus Publishing ApS ISBN 978-87-403-0069-7 Download free ebooks at bookboon.com 3 A first course in Fluid Mechanics for Engineers Contents Contents A Word … 8 Physics of Fluids 9 Introduction 9 1.1 Nature of fluids 9 1.2 Fluid as a continuum 10 1.3 Properties of fluids 11 1.4 Fluid Mechanics 21 References 22 Fluid Statics 23 Introduction 23 2.1 Pressure 23 2.2 Pressure at a point 24 2.3 Pressure variation in a static fluid 26 2.4 Pressure and head 29 2.6 Use of hydraulic pressure 35 1 2 Download free ebooks at bookboon.com 4 A first course in Fluid Mechanics for Engineers Contents 2.7 Buoyancy 36 2.8 Force on immersed plates 38 References 45 Dimensional analysis 46 Introduction 46 3.1 Dimensional homogeneity 47 3.3 Buckingham’ Pi theorem 48 3.2 Uses of dimensional analysis 53 4 Basics of Fluid Flow 54 Introduction 54 4.1 Velocity field 55 4.2 Control volume and system representation 58 4.3 Continuity of flow 60 4.4 Types of flow 63 4.5 Bernoulli equation 64 4.6 Physical meaning of the Bernoulli equation 66 4.7 Applications of Bernoulli equation 67 4.8 Linear Momentum 81 References 87 3 Download free ebooks at bookboon.com 5 A first course in Fluid Mechanics for Engineers 5 Contents Laminar and Turbulent Flow 88 Introduction 88 5.1 Laminar Flow 90 5.2 Turbulent flows 96 References 102 Viscous Flow in Pipes 103 Introduction 103 6.1 Laminar flow in a circular pipe 103 6.2 Turbulent flow in a pipe 107 6.3 Bernoulli Equation revisited 109 6.4 Losses in pipes 112 6.5 Other head losses in pipes 117 References 119 Pumping of liquids 120 Introduction 120 7.1 Pump classification 121 7.2 Centrifugal pumps 123 7.3 Bernoulli’s equation and system head 127 7.4 System curve 133 6 7 Download free ebooks at bookboon.com 6 A first course in Fluid Mechanics for Engineers Contents 7.5 Net Positive Suction Head (NPSH) 136 7.6 Flow Control 138 7.7 Some remarks on practical issues 142 References 143 Download free ebooks at bookboon.com 7 A Word … When students start an undergraduate course in engineering, they experience a step change in the level of complexity of the materials that had to be learned. Fluid Mechanics is one such module taught in the first year of the engineering undergraduate courses. It is a core module for Chemical, Mechanical and Civil engineers. The concepts may seem difficult and hard to grasp at the first instance but as the knowledge broadens, one may find it fascinating. This book is a collection of lecture notes developed from a series of lectures delivered to first year Chemical Engineers. The target readership is the first year engineering undergraduates but it could be used by anybody who wants to find the joy in learning fluid mechanics. Some of the figures in this document are taken from the World Wide Web. -B Download free ebooks at bookboon.com A first course in Fluid Mechanics for Engineers Physics of Fluids 1 Physics of Fluids Introduction Transport phenomena are one of the cornerstones Chemical Engineering is built upon. The three components that comes under transport phenomena ar e 1. Heat transfer 2. Mass transfer 3. Momentum transfer. Other than conduction and diffusion in solid materials, both heat and mass transfer are influenced by the motion of the medium. In most chemical engineering applications the heat and mass transfer involve fluids. For example, reactors are continuously stirred to induce flow to improve heat transfer as well as mixing. In a heat exchanger, two fluids flow on either side of tubes transferring heat from the process fluid to a service fluid (in cooling). The task chemical engineers are expected to perform is to design, and operate a process that produces a commercially valuable product from the raw materials. In most cases, they are to ensure process fluids be transported from the storage tanks through the process equipment to the product storage in a controlled manner. For these tasks and many other, chemical engineers must have an understanding of Fluid Mechanics. In this section, we briefly discuss the nature of fluids. Basic concepts such as density, viscosity, surface tension and pressure are introduced and discussed in detail. We will examine the cause of these properties using a description at molecular level and further investigate how they would behave at macroscopic scales. 1.1 Nature of fluids The greatest scientist ever, Sir Isaac Newton, provided a definition for fluids based on the observation. In Book II, Section V of the Principia the definition is given as “A fluid is any body whose parts yield to any force impressed on it, by yielding, are easily moved among themselves.” With a modest change to the above, describing the nature of the force, we still use this simple definition. A fluid can be defined as “a substance that deforms continuously under the application of a shear (tangential) stress no matter how small the shear stress may be.” From this definition, it is clear that two states of matter, Liquid and gas, are fluids. Even though solids yield under shear stress, the deformation it undergoes is finite and once the force is released, unlike fluids, it tends to assume its initial shape. Download free ebooks at bookboon.com 9 A first course in Fluid Mechanics for Engineers Physics of Fluids 1.2 Fluid as a continuum Fluids, like any other substance, are made of molecules. Weak cohesive forces keep molecules attracted to each other. However, the molecules are in constant motion. Distance a molecule travel before hitting another is called the mean free path λ. This mean free path is directly proportional to the temperature and inversely proportional to the pressure. If we look at a liquid at microscopic length scale, we would be able to see molecules of the liquid moving in the space bouncing off each other and the container wall. At this length scale, fluids are discontinuous spatially. However, we very seldom work at this length scale when handling fluids. At a larger length scale, for instance when we consider a tiny liquid droplet of about 1 mm radius, it appears as a continuous phase. In this example, the diameter of the droplet is called the characteristic length: the length scale at which we observe the droplet. Assume the characteristic length scale to be L. The ratio between the mean free path and the characteristic length gives a nondimensional quantity called Knudsen number. ߣ ‫ ݊ܭ‬ൌ  (1.1) ‫ܮ‬ Knudsen number gives a feeling about the continuity of a fluid at the length scale of observation. Kn ≤ 0.001 ⇒ L ≥1000λ, fluid can be considered as a continuum. 0.001 ≤ Kn ≤0.1 ⇒100λ ≤ L ≤ 10λ, rarefaction effects start to influences the properties. Around Kn = 0.1, the assumption that a liquid is a continuum starts to break down. Kn > 10 we are looking at molecules at a length scale smaller than their mean free path; the continuum approach breaks down completely. Figure 1.1 shows the variation of mass to volume ratio of a fluid across several orders of magnitude in length scale. Consider a miniscule volume ∆V, say a volume with few angstroms in diameter, that can hold few molecules initially. If we increase this ∆V volume in size (across length scales), the number of molecules it can hold increases. Molecules moves in and out of this hypothetical volume element constantly. At the molecular length scale, the rate of molecular movement has an effect on the density making the value to fluctuate. However, at a rather large length scale, say around Kn = 0.001, oscillations start to converge to a constant value. Above this length scale, the fluid can be treated as a continuous medium showing constant bulk properties. It is this approximation that makes us to treat fluids in the way we present in this book. Download free ebooks at bookboon.com 10