

Section 7: Similarity and Dimensional Analysis  
7.1  Euler's equation for inviscid motion: a relationship between fluid acceleration (convective and temporal) and pressure distribution  
7.2  Concepts for describing fluid flows: streamlines, particle paths, and streaklines.  
7.3  Euler's equation for steady flow expressed in streamline coordinates: the pressurevelocity relation along the streamline direction, and the pressure gradient normal to streamlines when streamlines have curvature. Comments on the "inviscid” flow approximation and the boundary conditions that are appropriate for velocity and pressure in such flows.  
7.4  Incompressible flow examples involving both Bernoulli's integral and the effects of streamline curvature. Classroom demonstrations of the Bernoulli effect and the streamline curvature effect (the latter being the origin of lift on airfoils).  
7.5  Bernoulli's integral for two types of steady, isentropic, compressible flows: (a) perfect gases and (b) liquids with constant compressibility. Isentropic expansion of a gas into a vacuum. A criterion for "incompressible flow.  
Reading  
A. A. Sonin, "The Physical Basis of Dimensional Analysis" (Read atleast Sections 1 and 3) Fay, Chapter 10 

Problem Set Section 7 

Problem 7.2  
Problem 7.3  
Problem 7.5  
Problem 7.9  
Problem 7.11  
Problem 7.14  
Problem 7.16  
Problem 7.18  