elementary fluid mechanics

[...]... to define the concept of a fluid particle In fact, the study of fluid mechanics is normally carried out at scales of about 10−3 mm or larger, whereas the intermolecular scale is 10−6 mm or less At the normal temperature and pressure ch01 November 9, 2006 10:1 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in 1.2 Fluid particle and fields 3 (0◦ C and 760 mmHg), a cube of 1 mm in a... = v, Dt (Sec 12.6.2) D v = ∂t v + (v · ∇)v Dt (1.32) (1.33) ch01 October 31, 2006 21:29 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in Chapter 2 Fluids 2.1 Continuum and transport phenomena The motion of a fluid is studied on the basis of the fundamental principle of mechanics, namely the conservation laws of mass, momentum and energy For a state of matter to which the continuum... continuously distributed Motion of a fluid, i.e flow of a fluid, is considered to be a mass flow involving its continuous deformation Fluid mechanics studies such flows of fluids, i.e motions of material bodies of continuous mass distribution, under fundamental laws of mechanics 1.2 Fluid particle and fields When we consider a fluid flow, it is often useful to use a discrete concept although the fluid itself is... 266 266 267 268 269 270 271 273 273 274 275 fm November 3, 2006 0:37 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in Contents 12 Gauge theory of ideal fluid flows 12.1 Backgrounds of the theory 12.1.1 Gauge invariances 12.1.2 Review of the invariance in quantum mechanics 12.1.3 Brief scenario of gauge principle 12.2 Mechanical... , uy and uy +d˜y and uz and uz +d˜z ˜ ˜ u ˜ ˜ u ˜ ˜ u respectively, is defined by Nf (˜x , uy , uz ) d˜x d˜y d˜z u ˜ ˜ u u u ch01 November 9, 2006 10:1 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in 1.2 Fluid particle and fields 5 taken out from the right side of ∆S Both means that the space on the right side has received the same amount of positive momentum Both terms are combined... 337 337 337 338 340 Solutions 343 References 373 Index 377 fm This page intentionally left blank November 9, 2006 10:1 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in Chapter 1 Flows 1.1 What are flows ? Fluid flows are commonly observed phenomena in this world Giving typical examples, the wind is a flow of the air and the river stream is a flow of water On the... brought to an equilibrium in most circumstances by the exchange This is considered to be due to the molecular structure or 17 ch02 October 31, 2006 21:29 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in 18 Fluids due to random interacting motion of uncountably many molecules The entropy law is a typical one in this regard For conservative quantities, the exchange of variables... air flows in order to get lift for being airborne as well as getting thrust for their forward motion In addition, it is understood that plant 1 ch01 November 9, 2006 2 10:1 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in Flows seeds, or pollen, often use wind for their purposes Every living organism has a certain internal system of physiological circulation In general, it might... 10.2 Turbulence signals 204 206 206 208 209 210 212 213 213 215 219 221 221 223 225 229 229 232 235 239 240 242 fm November 3, 2006 0:37 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in xii Contents 10.3 Energy 10.3.1 10.3.2 10.3.3 10.3.4 10.3.5 spectrum and energy dissipation Energy spectrum Energy dissipation Inertial...November 3, 2006 0:37 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in x 6in x Contents 6.6 Sound waves 6.6.1 One-dimensional flows 6.6.2 Equation of sound wave 6.6.3 Plane waves 6.7 Shock waves 6.8 Problems . 9HE Printed in Singapore. ELEMENTARY FLUID MECHANICS Lakshmi - ElemFluidMechanics.pmd 2/27/2007, 9:38 AM1 November 3, 2006 0:37 WSPC/Book -SPI-B364 Elementary Fluid Mechanics Trim Size for 9in.