UI ME 5160 - Lecture Notes (28 pages)

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Lecture Notes



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Lecture Notes

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Lecture Notes


Pages:
28
School:
University of Iowa
Course:
Me 5160 - Intermediate Mechanics of Fluids
Intermediate Mechanics of Fluids Documents

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058 0160 Professor Fred Stern Fall 2009 Chapter 1 1 058 160 Intermediate Mechanics of Fluids Class Notes Fall 2007 Prepared by Professor Fred Stern Typed by Derek Schnabel Fall 2004 Nobuaki Sakamoto Fall 2006 Hamid Sadat Hosseini Fall 2006 Maysam Mousaviraad Fall 2006 Corrected by Jun Shao Fall 2004 Mani Kandasamy Fall 2005 Tao Xing Hyun Se Yoon Fall 2006 Hamid Sadat Hosseini Fall 2007 Hamid Sadat Hosseini Fall 2009 058 0160 Professor Fred Stern Chapter 1 2 Fall 2007 Chapter 1 Introduction Definition of a fluid A fluid cannot resist an applied shear stress and remain at rest whereas a non fluid i e solid can Solids resist shear by static deformation up to an elastic limit of the material after which they undergo fracture Fluids deform continuously undergo motion when subjected to shear stress Consider a fluid between two parallel plates with the lower one fixed and the upper moving at speed U which is an example of Couette flow i e wall shear driven flows y V u y u U h u y x u 0 1 D flow velocity profile 058 0160 Professor Fred Stern Chapter 1 3 Fall 2007 No slip condition Length scale of molecular mean free path length scale of fluid motion therefore macroscopically there is no relative motion or temperature between the solid and fluid in contact Knudsen number Kn 1 Exceptions are rarefied gases and gas liquid contact line Newtonian fluids Rate of Strain u uy dy dt y y u uydy dy dy u d tan 1 uydt x x u dt Fluid element with sides parallel to the coordinate axes at time t 0 tan d u y dydt dy Fluid element deformation at time t dt d u y dt 058 0160 Professor Fred Stern Chapter 1 4 Fall 2007 du dy rate of strain velocity gradient For 3D flow rate of strain is a second order symmetric tensor u u 1 eij i j ji 2 xj xi Diagonal terms are elongation contraction in x y z and off diagonal terms are shear in x y x z and y z Liquids vs Gases Liquids Gases Closely spaced with large Widely spaced with small intermolecular cohesive intermolecular cohesive forces forces Retain



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