Chaper 3 Elementary Fluid Dynamics The Bernoulli Equation3章基本流体动力学伯努利方程.docVIP

CHAPTER 3. Elementary Fluid Dynamics - Understanding the physics of fluid in motion - Derivation of the Bernoulli equation from Newton’s second law ( Basic Assumptions of fluid stream, unless a specific comment 1st assumption: Inviscid fluid (Zero viscosity = Zero shearing stress) ( No force by wall of container and boundary ( Applied force = Only Gravity + Pressure force ( Newton’s Second Law of Motion of a Fluid Particle (Net pressure force) + (Gravity) = (Fluid mass) ( (Acceleration) 2nd assumption: Steady flow (?) ( No Change of flowing feature with time at a given location ( Every successive particle passing though the same point : Same path (called streamline) Same velocity (tangential to the streamline) ( Additional Basic Terms in Analysis of Fluid Motion ( Streamline (Path of a fluid particle) - Position of a particle = where : Initial position, : Velocity of particle - No streamlines intersecting each other ( Two Components in Streamline Coordinates (See the figure) 1. Tangential coordinate: : Moving distance along streamline, : Related to Particle’s speed 2. Normal coordinate: : Local radius of curvature of streamline : Related to Shape of the streamline ( Two Accelerations of a fluid particle along s and n coordinates 1. Streamwise acceleration (( Change of the speed) using the Chain rule 2. Normal acceleration (( Change of the direction) (: Centrifugal acceleration) Q. What generate these as and an? (Pressure force and Gravity) Part 1. Newton’s second law along a streamline ( direction) Consider a small fluid particle of size as shown Newton’s second law in direction along direction = Gravity force + Net Pressure force where : Volume of a fluid particle = (i) Gravity force along direction (ii) Pressure force along direction Let p: Pressure at the center of : Average pressures at Left face (Decrease