Ch En 374 Review Sheet Final Exam

II. Fundamentals & Differential Theory

A. Lectures 14-15: Fluid Kinematics

Things you should know Calculations you should be able to do

• Identify whether a flow is 1D, 2D, 3D and/or • Plot a velocity field. axisymmetric • Find a vorticity given the velocity • The difference between a Lagrangian and Eulerian reference frame • Determine if a flow field is irrotational.

• Meaning of the three basic modes of kine- • Find the streamfunction and plot stream- matic motion: translation, rotation and de- lines given the velocity formation • Find the velocity given the streamfunction. • Definition and physical meaning of stream- • Calculate the local acceleration, convective lines and streaklines acceleration, and/or the material derivative • Definition and physical meaning of vorticity and irrotational flow • Use a shell balance to write a differential mass balance • Difference between local acceleration and the material derivative • Find a missing velocity component using the continuity equation • What the continuity equation is (compress- ible and incompressible), and what it means • Determine if a flow field satisfies conserva- physically tion of mass.

B. Lectures 15-16: Fluid Dynamics (Navier-Stokes)

Things you should know Calculations you should be able to do

• Definition and physical meaning of the rate- • Given the velocity, calculate components of-strain tensor and how it relates to defor- of the rate-of-strain and Newtonian viscous mation stress tensors. • What the stress tensor means physically, in- • Given a rate-of-strain tensor and a direction, cluding the difference between a normal and calculate the deformation. a shear stress • Calculate the total stress from the viscous • Relationship between total stress tensor, stress and pressure. pressure, viscous stress tensor • Given a stress tensor, find the force vector • Surface forces versus body forces on a surface. • Newton’s law of viscosity (tensor version): what it is, what it means physically • Given 3 of the 4 expressions (vx, vy, vz, P ), find the 4th using the NS equation • What the Cauchy momentum equation is and what the terms mean physically • Identify the correct BCs for a NS problem from a physical description of the problem • Assumptions needed for the Navier-Stokes equation • Boundary conditions for NS: no-slip, no- penetration Ch En 374 Review Sheet Final Exam

C. Lectures 18-21: Unidirectional Flow, Creeping/Invicid Flow

Things you should know Calculations you should be able to do

• Examples of unidirectional flow: Couette • Simplify the NS equation using assumptions flow (simple shear), Poiseuille flow (pipe with physical names (e.g. steady, fully de- flow) veloped, unidirectional) • What common assumptions (e.g. steady, 2D or axisymmetric, fully-developed, unidirec- • Solve unidirectional flow problems (e.g. tional) mean physically. Couette & Poiseuille flow) using NS

• Qualitative features of the velocity profile of • Find the average velocity, wall shear stress pipe flow for a power-law fluid and/or the friction factor for pipe flow • How the power-law Reynolds number is de- • Solve unidirectional flow problems for a fined power-law fluid • Non-dimensionalization of Navier-Stokes (high and low Re) • Simplify the drag force formula in cartesian coordinates • What Stokes equation and Euler’s equation mean and physical situations when they ap- • Given pressure and velocity fields for a creep- ply ing/inviscid flow and a simplified drag force • The connection between inviscid flow & ir- formula, calculate the form/friction/total rotational flow drag force and/or the drag coefficient.

D. Lectures 22-24: Advanced Flow Concepts

Things you should know Calculations you should be able to do

• D’Alembert’s paradox and resolution • Use the Von-K´arm´an–Pohlhausen solution • What the Boundary Layer equations are and to find a boundary layer thickness and drag when they apply force/drag coefficient.

• Qualitative features of the boundary layer • Given an average velocity profile for turbu- velocity profile lent pipe flow, calculate the friction factor. • Concept of average velocity profiles and why • Run and interpret a CFD code we need them in turbulent flow • Calculate discrete derivatives using finite dif- • The concept of eddy diffusivity and how it ferences applies to turbulent flow • Use CFD data and discretized derivatives to • How the velocity profile of turbulent flow calculate a drag force. compares to laminar flow • What CFD is and why it is useful • What the pressure Poisson equation is