CORNELL CEE 331 - Fluid Kinematics (13 pages)

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Fluid Kinematics



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Fluid Kinematics

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Pages:
13
School:
Cornell University
Course:
Cee 331 - Fluid Mechanics
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Fluid Kinematics Fluid Mechanics January 14 2019 Monroe L Weber Shirk School of Civil and Environmental Engineering Fluid Flow Concepts and Reynolds Transport Theorem Descriptions of fluid motion fluid flows temporal and spatial classifications Analysis Approaches Lagrangian vs Eulerian Moving from a system to a control volume Reynolds Transport Theorem Descriptions of Fluid Motion streamline Defined instantaneously has the direction of the velocity vector at each point no flow across the streamline steady flow streamlines are fixed in space unsteady flow streamlines move pathline Defined as particle moves over time path of a particle same as streamline for steady flow streakline Draw Streamlines tracer injected continuously into a flow same as pathline and streamline for steady flow Unsteady demo Descriptors of Fluid Flows Laminar flow fluid moves along smooth paths viscosity damps any tendency to swirl or mix Turbulent flow fluid moves in very irregular paths efficient mixing velocity at a point fluctuates Temporal Spatial Classifications Steady unsteady Changing in time Uniform nonuniform Changing in space Can turbulent flow be steady If averaged over a suitable time Analysis Approaches Lagrangian system approach mass position velocity Describes a defined acceleration pressure temperature etc as functions of time Track the location of a migrating bird Eulerian field velocity acceleration Describes the flow pressure temperature etc as functions of position and time Count the birds passing a particular location If you were going to study water flowing in a pipeline which approach would you use Eulerian The Dilemma The laws of physics in their simplest forms describe systems the Lagrangian approach Conservation of Mass Momentum Energy It is impossible to keep track of the system in many fluids problems The laws of physics must still hold in a Eulerian world We need some tools to bridge the gap Reynolds Transport Theorem A moving system flows through the fixed control volume The moving system transports extensive properties across the control volume surfaces We need a bookkeeping method to keep track of the properties that are being transported into and out of the control volume Control Volume Conservation Equation B Total amount of some property in the system b Amount of the property per unit mass DBsys Dt r bdV r bV n dA t cv cs Rate of increase of the property in the system Rate of increase of the property in the control volume Rate of efflux of the property across the control volume boundary Summary Reynolds Transport Theorem can be applied to a control volume of finite size We don t need to know the flow details within the control volume We do need to know what is happening at the control surfaces Conservation of mass for all species Newton s 2nd law of motion momentum F ma First law of thermodynamics energy Control Volume Conservation Equation DBsys r bdV r bV n dA Dt t cv cs 0 1 0 1 0 1 1 0 0 0 0 0 Mt St Helens Application of Reynold s Transport Theorem Chemical with concentration Cin enters reactor with flow rate Q and exits with concentration C Chemical decays at rate kC What is b What is B C CV What is b C equation What is left side of kCV What is Q V n dA cs1 DBsys Dt r bdV r bV n dA t cv cs CV kCV Q C Cin t


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