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Introduction to Fluid Mechanics

Introduction to Fluid Mechanics. Fluid Mechanics is concerned with the behavior of fluids at rest and in motion Distinction between solids and fluids : According to our experience: A solid is “hard” and not easily deformed. A fluid is “soft” and deforms easily.

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Introduction to Fluid Mechanics

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  1. Introduction to Fluid Mechanics • Fluid Mechanics is concerned with the behavior of fluids at rest and in motion • Distinction between solids and fluids: • According to our experience: A solid is “hard” and not easily deformed. A fluid is “soft” and deforms easily. • Fluid is a substance that alters its shape in response to any force however small, that tends to flow or to conform to the outline of its container, and that includes gases and liquids and mixtures of solids and liquids capable of flow. • A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. Chee 223

  2. Course Organization Textbook: deNevers “Fluid Mechanics for Chemical Engineers” • Introduction (Chapter 1) / Dimensions, Units Fluid statics: Fluid is at rest Fluid mechanics Fluid dynamics: Fluid is moving • Fluid statics (Chapter 2): Pressure, measurement of pressure, hydrostatic forces, buoyancy • Fluid dynamics (Chapters 3-5, 7): Mass, energy and momentum balances • Applications in Engineering (Chapters 6, 9, 11, 12): Flow in pipes, turbomachines, flow over immersed bodies, flow through porous media • Dimensional analysis and modeling (Chapter 13) Chee 223

  3. Introduction Chee 223

  4. Dimensions and Units In fluid mechanics we must describe various fluid characteristics in terms of certain basic quantities such as length, time and mass • A dimension is the measure by which a physical variable is expressed qualitatively, i.e. length is a dimension associated with distance, width, height, displacement. • Basic dimensions: Length, L (or primary quantities) Time, T Mass, M Temperature, Q • We can derive any secondary quantity from the primary quantities i.e. Force = (mass) x (acceleration) : F = M L T-2 • A unit is a particular way of attaching a number to the qualitative dimension: Systems of units can vary from country to country, but dimensions do not Chee 223

  5. Dimensions and Units • Conversion factors are available in the textbook inside of front cover. Chee 223

  6. Units of Force: Newton’s Law F=m.g • SI system: Base dimensions are Length, Time, Mass, Temperature • A Newton is the force which when applied to a mass of 1 kg produces an acceleration of 1 m/s2. • Newton is a derived unit: 1N = (1Kg).(1m/s2) • BG system: Base dimensions are Length, Force, Time, Temperature • A slug is the mass which produces an acceleration of 1 ft/s2 when a force of 1lb is applied on it: • Slug is a derived unit: 1slug=(1lb) (s2)/(ft) • EE system: Base dimensions are Length, Time, Mass, Force and Temperature • The pound-force (lbf) is defined as the force which accelerates 1pound-mass (lbm), 32.174 ft/s2. Chee 223

  7. Units of Force – EE system To make Newton’s law dimensionally consistent we must include a dimensional proportionality constant: where Chee 223

  8. Example: Newton’s Law • An astronaut weighs 730N in Houston, TX, where the local acceleration of gravity is g=9.792 m/s2. What is the mass of the astronaut? What is his weight on the moon, where g=1.67 m/s2? • Redo the same problem in EE units. In EE units the astronaut weighs 164.1lbf, gHouston=32.13 ft/s2 and gmoon=5.48 ft/s2. Chee 223

  9. Dimensional Homogeneity • All theoretically derived equations are dimensionally homogeneous: dimensions of the left side of the equation must be the same as those on the right side. • Some empirical formulas used in engineering practice are not dimensionally homogeneous • All equations must use consistent units: each term must have the same units. Answers will be incorrect if the units in the equation are not consistent. Always chose the system of units prior to solving the problem Chee 223

  10. Properties of Fluids • Fundamental approach: Study the behavior of individual molecules when trying to describe the behavior of fluids • Engineering approach: Characterization of the behavior by considering the average, or macroscopic, value of the quantity of interest, where the average is evaluated over a small volume containing a large number of molecules • Treat the fluid as a CONTINUUM: Assume that all the fluid characteristics vary continuously throughout the fluid Chee 223

  11. Measures of Fluid Mass and Weight • Density of a fluid, r (rho), is the amount of mass per unit volume of a substance: r = m / V • For liquids, weak function of temperature and pressure • For gases: strong function of T and P from ideal gas law: r = P M/RT where R= universal gas constant, M=mol. weight R= 8.314 J/(g-mole K)=0.08314 (liter bar)/(g-mole K)= 0.08206 (liter atm)/(g-mole K)=1.987 (cal)/(g-mole K)= 10.73 (psia ft3)/(lb-mole °R)=0.7302 (atm ft3)/(lb-mole °R) (1.1) Chee 223

  12. Measures of Fluid Mass and Weight • Specific volume: u = 1 / r • Specific weight is the amount of weight per unit volume of a substance: g = w / V = r g • Specific Gravity (independent of system of units) Chee 223

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