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INTRODUCTION • Mechanics is a physical science that deals with both stationary and moving bodies under the influence of forces. • The branch of mechanics that deals with bodies at rest is called statics, while the branch that deals with bodies in motion is called dynamics. • The subcategory fluid mechanics is defined as the science that deals with the behaviour of fluids at rest (fluid statics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries. • Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity
Fluid mechanics itself is also divided into several categories. The study of the motion of fluids that are practically incompressible (such as liquids, especially water, and gases at low speeds) is usually referred to as hydrodynamics. • A subcategory of hydrodynamics is hydraulics, which deals with liquid flows in pipes and open channels. • Gas dynamics deals with the flow of fluids that undergo significant density changes, such as the flow of gases through nozzles at high speeds. The category aerodynamics deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automobiles at high or low speeds. • Some other specialized categories such as meteorology, oceanography, and hydrology deal with naturally occurring flows.
What Is a Fluid?: Fluids vrs Solids • A substance in the liquid or gas phase is referred to as a fluid. • Distinction between a solid and a fluid is made on the basis of the substance’s ability to resist an applied shear (or tangential) stress that tends to change its shape. • A solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of shear stress, no matter how small. • In solids stress is proportional to strain, but in fluids stress is proportional to strain rate. • When a constant shear force is applied, a solid eventually stops deforming, at some fixed strain angle, whereas a fluid never stops deforming and approaches a certain rate of strain.
Stress in Fluids • Stress is defined as force per unit area and is determined by dividing the force by the area upon which it acts. • The normal component of the force acting on a surface per unit area is called the normal stress, and the tangential component of a force acting on a surface per unit area is called shear stress (Fig. 1.1). • In a fluid at rest, the normal stress is called pressure. The supporting walls of a fluid eliminate shear stress, and thus a fluid at rest is at a state of zero shear stress.
Distinction between liquids and gases • In a liquid, chunks of molecules can move relative to each other, but the volume remains relatively constant because of the strong cohesive forces between the molecules. • liquids take the shape of their containers and it forms a free surface in a larger container in a gravitational field. • A gas expands until it encounters the walls of the container and fills the entire available space. • This is because the gas molecules are widely spaced, and the cohesive forces between them are very small. • gases cannot form a free surface (fig 1.2)
The arrangement of atoms in different phases: • (a) molecules are at relatively fixed positions in a solid, • (b) groups of molecules move about each other in the liquid phase, and • (c) molecules move about at random in the gas phase
FLUID PROPERTIES Every fluid has certain characteristics by which its physical conditions may be described. We call such characteristics as the fluid properties. • Specific Weight • Mass Density • Viscosity • Vapor Pressure • Surface tension • Capillarity • Bulk Modulus of Elasticity
Properties involving the Mass or Weight of the Fluid Mass Density, r The “mass per unit volume” is mass density. Hence it has units of kilograms per cubic meter. - The mass density of water at 4 oC is 1000 kg/m3 while it is 1.20 kg/m3 for air at 20 oC at standard pressure. Specific Weight, w The gravitational force per unit volume of fluid, or simply “weight per unit volume”. - Water at 4oC has a specific weight of 9.81kN/m3.
Specific Gravity, S • The ratio of specific weight of a given liquid to the specific weight of water at a standard reference temperature (4 oC)is defined as specific gravity, S. • The specific weight of water at atmospheric pressure is 9810 N/m3. • The specific gravity of mercury at 20 oC is
VISCOSITY • What is the definition of “strain”? “Deformation of a physical body under the action of applied forces” • Solid: – shear stress applied is proportional to shear strain (proportionality factor: shear modulus) – Solid material ceases to deform when equilibrium is reached • Liquid: – Shear stress applied is proportional to the time rate of strain (proportionality factor: dynamic (absolute) viscosity) – Liquid continues to deform as long as stress is applied
Example of the effect of viscosity • Think: resistance to flow. • V : fluid velocity • y : distance from solid surface • Rate of strain, dV/dy • μ : dynamic viscosity [N.s/m2] t: shear stress Shear stress: An applied force per unit area needed to produce deformation in a fluid t = μdV/dy Velocity distribution next to a boundary
Shear stress causes shear strain • A Fluid is a substance which deforms continuously, or flows, when subjected to shearing forces. • On the other hand, If a fluid is at rest there are no shearing forces acting. Thus, all forces must be perpendicular to the planes which the are acting. Shearing force, F, acting on a fluid element.
Velocity profiles and effect of viscosity b. Flow between parallel plates a. Velocity profile in uniform flow c. Velocity profile in a pipe.
No Slip condition • If fluid velocity is the same at every point then there is no shear stress produced: the particles have zero relative velocity. This gives rise to a uniform velocity profile • Consider a flow over a plane surface, the velocity at wall is zero due to adhesion between the surface and a thin film of the fluid. (NO SLIP CONDITION) • The velocity will increase as we move further away from the wall, thus resulting in a variable velocity distribution
