Fluid_Kinematics_I_2022_Notes

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Oct 30, 2023

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Class Objectives Fluid Kinematics I: Position and Velocity of Fluid Motions • Types of fluid Flows • Descriptions • Visualization tools

Fluid Kinematics Fluid motions involve position , velocity , acceleratin of fluid . position , velocity , acceleration and (Text: Chapter 1-4, Chapter 4-1 and 4-2)

(1) Types of Fluid Flows Density variation  Dimension (degree of freedom) ~ incompressible / compressible flows ~ one /two /three - dimensional flows i u V    Temporal variation ~ steady 0    t V 0    t V  Spatial variation ~ uniform 0    x V 0    x V Friction/Viscosity ~ ideal 0   0   j v   k w   / unsteady flows / non-uniform flows / real fluid flows const   const     (See Chapter 1-4)

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Real fluid has viscosity that causes the flow stagnant at the bottom.  No Slip effect  Flow types friction Ideal fluid

• Dimension • Space • Time • Friction 1D 2D 3D Uniform Non-uniform Unsteady Ideal Fluid Laminar Turbulent Unsteady Real Fluid • Flow type Non-uniform Unsteady Real Fluid Inviscid

Describes the field (velocity, acceleration, concentration, etc.) as functions of position and time . Describes a defined particle (position, velocity, acceleration, concentration, etc.) as a function of time . (B) Eulerian approach (2) Descriptions of Fluid Motions (A) Lagrangian approach C(t) C(x,y,z,t) C(x,y,z,t) ~ motions of a moving particle ~ motions at a fixed points C(t) Lagrangian Eulerian (See Chapter 4-1)

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Streamline A line that is _______to the instantaneous velocity field ~ has the direction of the velocity vector at each point ~ does not have flow across the streamline ~ is based upon the _________ description (3) Tools to Visualize Flow Patterns tangent Eulerian dx dy z u v w d   ~ Text Example 4.4 (Math) (See Chapter 4-2)

Pathline A line traced out by a given particle as it flows over time ~ is a trajectory of a particle path _________ ~ is based upon the __________ description. over time Lagrangian a given particle dx dt u  dy dt v  dz dt w  t = 0 t = t 1 ~ Example 4.5 (Math)

Pathlines produced by white tracer particles suspended in water and captured by time-exposure photography; as waves pass horizontally, each particle moves in an elliptical path during one wave period. dx dt u 

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Streakline A line consists of ______________in a flow that has _________ passed through a _________ point ~ is commonly seen in a tracer injected continuously into a flow ~ reveres back to an original or prescribed source all particles previously common Origin

Timeline An ___________ consisting of previously marked adjacent particles follows flow motions evolution line

At t=0 , a plant releases a dye streak at point A in a lake. (a) Sketch a streamline when t=2 sec and t=8 sec. (b) Sketch the pathline for the particle released from point A at t=2 sec A Streakline at t = 10 sec B Assume flow speed is constant and uniform over 10 sec but there is a wind direction change at t =5 sec. At t=10 sec , the streakline is shown in the sketch.

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