CHAPTER 1

Is the science of the

mechanics of liquids and

gases,

and is based on the same

fundamental principles

that are employed in the

mechanics of solids.

Mechanics of fluids is defined

as the science that deals with

the behaviour of fluids at rest

or in motion.

INTRODUCTION Statics/Dynamics

Thermodynamics

Fluid Mechanics

CATEGORIES OF FLUID MECHANICS

Hydrodynamics study of fluids that are practically incompresible

Hydraulics deals with liquid flows in pipes and open channels

Gas Dynamics deals with the flow of fluids that undergo significant density changes, such as flow of gases through nozzles at high speeds.

Aerodynmics deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automobiles at high or low speeds.

Pressure the normal force acting on fluid at rest.

liquid

Free surface

gases

No-slip condition fluid in direct contact with a solid sticks to the surface due to viscous effects, and there is no slip.

Plate

Uniform Approach velocity

Zero Velocity at the surface

Boundary layer

Flow separation

Boundary Layer

Curve surface

CLASSIFICATION OF FLUID FLOWS

Frictional effect significant

VISCOUS FLOW REGION

INVISCID FLOW REGION

INVISCID FLOW REGION

PLATE

CLASSIFICATION OF FLUID FLOWS

External Flow the flow of unbounded fluid over a surface such as plate.

Internal Flow if the flow is completely bounded by solid surfaces, i,e pipe

Incompressible Flow if the density remains nearly constant throughout. The volume of every surface of fluid remains unchanged over the course of its motion. densities of liquids are essentially constant, and thus flow of liquids is incompressible.

When analyzing high speed gas flow (i.e. Rockets , spacecraft) the speed is often expressed as

Mach Number (Ma) = --- = ------------------- V c

Speed of flow Speed of sound

speed of sound = 346 m/s in air at room temperature at sea level.

A flow is

Sonic when Ma = 1

Subsonic when Ma < 1

Supersonic when Ma > 1

Hypersonic when Ma >> 1

When modeling gas flow as incompressible depends on the Mach number

Gas flow can be approximated as incompressible if the density changes are about 5% usually at Ma < 0.3.

Compressibility effects of can be neglected at speed under 100 m/s.

Laminar Flow the highly ordered fluid motion characterized by smooth layers of fluid.

Turbulent Flow the highly disordered fluid motion that typically occurs at high velocity and characterized by velocity fluctuations.

Laminar Flow flow that alternates between being laminar and turbulent.

Forced Flows flow is initiated by external means such as pipe.

Natural Flows fluid motion due to natural means such as buoyancy effect Steady Flows implies no change at a point with time. The opposite is unsteady.

Uniform implies no change with location over a specified region.

Transient used for developing flow Periodic the kind of unsteady flow in which the flow oscillates about steady mean.

One-, Two-, and Three-Dimensional Flows

z

r

Developing velocity Profile, V(r, z)

Fully developed Velocity profile, V(r)