Chapter%201%20Introduction

# Chapter%201%20Introduction - Fluid Mechanics I Introduction...

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Unformatted text preview: Fluid Mechanics I. Introduction 1.1 Definition of Fluids * Fluid is a substance which deforms continuously under the action of an applied shear force. * A portion of fluid has no preferred shape . * In contrast, for an elastic solid , the deformation does not continue forever under an applied force. γ Hence, a solid can resist the applied force and remain at rest while a fluid cannot. Solid has a definite shape which changes only under applied forces. * The distinction between solids and fluids is not completely clear-cut. Take a piece of "Play Doh" and make a ball. If you squeeze it slowly, it will deform continuously; in this sense, it behaves like a fluid. Throw it against a wall ⇒ bounce back. Hit it with a hammer, it will crack. In that sense, the Play Doh behaves like a solid. Whether it behaves like a solid or a fluid depends on the rate at which the force is applied—subject of Non-Newtonian Fluid Mechanics. * There are t wo types of fluids we routinely consider: a) Liquids : state of matter in which the molecules are free to move with respect to one another, but they are constrained or restricted by intermolecular cohesive forces . liquids have a definite volume they will form a free surface in a gravitational field if unconstrained from above g b) Gas : state of matter where the molecules are free to move with respect one another, but they are not constrained by intermolecular forces (i.e. they are subject to collision processes). no definite shape, volume a gas will expand to fill the container a gas tends to possess a much lower bulk modulus / higher compressibility comparing with liquids 1.2 Descriptions of Fluids i. Microscopic description * Fluid is composed of a large number of molecules: air at STP (15 ° C, 101.2 kPa) has 3 x 10 19 molecules in 1 cm 3 . * One needs to apply the principles of quantum mechanics to study the motion of atoms and molecules. * On the molecular scale, a physical quantity (such as density ρ , velocity v , & acceleration a ) is highly nonuniform in space because of a. large inter-molecular spacing comparing with molecular size; b. discontinuous distribution of molecular mass within a molecule; c. random molecular motions . * Typical scale of molecular motion can be estimated based on the mean free path λ of molecules. At room temperature, λ ~1.5 ν / ( γ RT) 1/2 = 0.653 x 10-5 cm = 0.065 μ m . ii. Macroscopic description; continuum hypothesis • L = typical dimension of flow field. e.g.. chord length of an airfoil, pipe diameter, wavelength… • In many practical fluid flows, L / λ »1. ⇒ a. # of molecules ∝ ( L / λ ) 3 ⇒ a large number of collections of molecules even in a small portion of the fluid....
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Chapter%201%20Introduction - Fluid Mechanics I Introduction...

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