Lecture 1 Introduction

Slide 1: 

Introduction One of the first questions we need to explore is, What is a fluid? A fluid is a substance that deforms continuously when acted on by a shearing stress of any magnitude . A fluid is a collection of molecules that are randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of a container. Both liquids and gases are classified as fluids. Fluid mechanics is concerned with understanding, predicting, and controlling the behavior of a fluid . Fluid mechanics is the study of fluids at rest (fluid statics) in motion (fluid dynamics)

Motivation for Studying Fluid Mechanics: 

Motivation for Studying Fluid Mechanics Fluid Mechanics is omnipresent Aerodynamics Bioengineering and biological systems Combustion Energy generation Geology Hydraulics and Hydrology Hydrodynamics Meteorology Ocean and Coastal Engineering Water Resources …numerous other examples … Fluid Mechanics is beautiful

Slide 3: 

Fluid Mechanics is omnipresent

Fluid Mechanics is Beautiful: 

Fluid Mechanics is Beautiful

Slide 8: 

Diagram listing the epochs and scientists contributing to the development of fluid mechanics

The Greatest Minds of Fluid Mechanics: 

The Greatest Minds of Fluid Mechanics Faces of Fluid Mechanics : some of the greatest minds of history have tried to solve the mysteries of fluid mechanics Archimedes Da Vinci Newton Leibniz Euler Bernoulli Navier Stokes Reynolds Prandtl

Slide 10: 

Mathematical Modeling of Physical Problems

How To solve a Problem: 

How To solve a Problem Step Analytical Fluid Dynamics Computational Fluid Dynamics 1 Setup Problem and geometry, identify all dimensions and parameters 2 List all assumptions, approximations, simplifications, boundary conditions 3 Simplify PDE’s Build grid / discretize PDE’s 4 Integrate equations Solve algebraic system of equations including I.C.’s and B.C’s 5 Apply I.C.’s and B.C.’s to solve for constants of integration 6 Verify and plot results Verify and plot results

Slide 12: 

All matter consists of only two states, solid and fluid there are two classes of fluids, liquids and gases The Concept of Solid, Liquid and Gas solid liquid gas

Slide 13: 

Comparison of Solids, Liquids, and Gases

The No-Slip Condition: 

The No-Slip Condition No-slip condition: A fluid in direct contact with a solid “sticks” to the surface due to viscous effects It is due to the viscosity of the fluid Responsible for generation of wall shear stress  w ,, surface drag D= ∫  w dA, and the development of the boundary layer Important boundary condition in formulating initial boundary value problem (IBVP) for analytical and computational fluid dynamics analysis

Boundary Layer: 

Boundary Layer When a fluid stream encounters a solid surface, the fluid velocity assumes a value of zero at the surface. The velocity then varies from zero at the surface to the freestream value sufficiently far from the surface. The region of flow in which the velocity gradients are significant is called the boundary layer. The development of a boundary layer is caused by the no-slip condition.

Classification of Flows: 

Classification of Flows Viscous vs. Inviscid Regions of Flow Internal vs. External Flow Compressible vs. Incompressible Flow Laminar vs. Turbulent Flow Steady vs. Unsteady Flow One-, Two-, and Three-Dimensional Flows

Viscous vs. Inviscid Regions of Flow: 

Viscous vs. Inviscid Regions of Flow Regions where frictional effects are significant are called viscous regions. They are usually close to solid surfaces. Regions where frictional forces are small compared to inertial forces are called inviscid

Internal vs. External Flow: 

Internal vs. External Flow Internal flows are dominated by the influence of viscosity throughout the flow field For external flows, viscous effects are limited to the boundary layer and wake.

Compressible vs. Incompressible Flow: 

Compressible vs. Incompressible Flow A fluid flow during which the density of the fluid remains nearly constant is called incompressible flow . A fluid whose density is practically independent of pressure (such as a liquid) is called an incompressible fluid. The flow of compressible fluid (such as air) is not necessarily compressible since the density of a compressible fluid may still remain constant during flow.

Laminar vs. Turbulent Flow: 

Laminar vs. Turbulent Flow Laminar: highly ordered fluid motion with smooth streamlines. Turbulent: highly disordered fluid motion characterized by velocity fluctuations and eddies. Transitional: a flow that contains both laminar and turbulent regions Reynolds number, is the key parameter in determining whether flow is laminar or turbulent.

Steady vs. Unsteady Flow: 

Steady vs. Unsteady Flow Steady implies no change at a point with time. Unsteady is the opposite of steady. Transient usually describes a starting, or developing flow. Periodic refers to a flow which oscillates about a mean. Unsteady flows may appear steady if “time-averaged”

One-, Two-, and Three-Dimensional Flows: 

One-, Two-, and Three-Dimensional Flows Velocity vector, U(x,y,z,t)= [Ux(x,y,z,t),Uy(x,y,z,t),Uz(x,y,z,t)] Lower dimensional flows reduce complexity of analytical and computational solution Change in coordinate system (cylindrical, spherical, etc.) may facilitate reduction in order. Example: for fully-developed pipe flow, velocity V(r) is a function of radius r and pressure p(z) is a function of distance z along the pipe.

System and Control Volume: 

System and Control Volume A system is defined as a quantity of matter or a region in space chosen for study. A closed system consists of a fixed amount of mass. An open system, or control volume, is a properly selected region in space.

Dimensions and Units: 

Dimensions and Units Any physical quantity can be characterized by dimensions. The magnitudes assigned to dimensions are called units. Primary dimensions include: mass m , length L , time t , and temperature T . Secondary dimensions can be expressed in terms of primary dimensions and include: velocity V , energy E , and volume V . Dimensional homogeneity is a valuable tool in checking for errors. Make sure every term in an equation has the same units. Unity conversion ratios are helpful in converting units.