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- 2. CHAPTER ONE 1.1 INTRODUCTION TO FLUID 1.2 UNITS AND DIMENSION USED IN ENGINEERING FLUIDS
- 3. INTRODUCTION WHAT IS HYDRAULICS WHAT IS FLUID MECHANICS? •Mechanics of fluids •It’s that branch of engineering science which deals with the behaviour of fluid under the conditions of rest & motion •Greek word “HUDAR” , means – “WATER” •It’s that branch of engineering science deals with water ( at rest or in motion) •Or its that branch of engineering science which is based on experimental observation of water flow.
- 4. FLUID MECHANICS FLUID MECHANICS is a study of the behavior of liquids and gases either at rest (fluid statics) or in motion (fluid dynamics). The analysis is relate continuity of mass and energy with force and momentum. FLUID is a substance which deforms continuously under the action of shearing force (however small it is may be)
- 5. Last Updated:7 September 2022 © LMS SEGi education group 5 WHAT IS FLUID MECHANICS? Fluid – a substance that continually deforms (flows) under applied shear stress Mechanics – science concerned with behaviour of physical bodies when subjected to forces Fluid Mechanics – the science that deals with the behaviour of fluids at rest (fluid statics) or fluids in motion (fluid dynamics), and their subsequent effects on the surrounding environment
- 6. Application Areas of Fluid Mechanics
- 7. IMPORTANT OF FLUID MECHANICS IMPORTANT OF FLUID MECHANICS TO ENGINEER To determine the stability of floating and submerged objects pontoons, ships To determine the hydrostatic forces dams To determine flow and energy losses in pipe To design fluid machines pumps and turbines To determine flow rate, energy dissipation from spillway and flow in open channels such as rivers
- 8. Archimedes (285-212 BC) - buoyancy Blaise Pascal (1623-1662) - hydrostatics Daniel Bernoulli (1700-1782) – energy equation Antonie Chezy (1718-1798) – velocity in channel Henry Darcy (1803-1858) – groundwater flow Jean Poiseuille (1799-1869) – laminar flow Lord Osborn Reynolds (1842-1912) – flow regime Louis Navier (1785-1836), George Stokes (1819-1903) – equations of fluid motion with friction William Froude (1810-1879) – resistance of partially submerged objects Lord Rayleigh (1842-1919) – 1-D flow through constant area duct with heat transfer Sir Horace Lamb (1849-1934) – waves in solids Wilbur & Orville Wright – 1st aeroplane Ludwig Prandtl (1875-1953) – boundary layer Last Updated:7 September 2022 © LMS SEGi education group 8 HISTORY (Cengel & Cimbala, 2006)
- 9. Last Updated:7 September 2022 © LMS SEGi education group 9
- 10. DIFFERENCE BETWEEN SOLID AND FLUID Have preferred shape Hard & not easily deformed Cannot deformed continuously under shear force SOLID Does not have any preferred shape Soft & easily deformed Deformed continuously under shear force FLUID ITEM 1 ITEM 2
- 11. 3 CONDITIONS OF FLUIDS • The study of incompressible fluid under static conditions (hydrostatics) • That dealing with the compressible static gases- aerostatics STATICS • Deals with the – velocities, accelerations and pattern of flow only • Force and energy causing velocities and accelerations are not deal under this head. KINEMATICS • Deal with the relationship between velocities and accelerations of fluid with the FORCES @ ENERGY causing them. DYNAMICS
- 12. CONCEPT OF FLUID In FLUID: -The molecules can move freely but are constrained through a traction force called cohesion. -This force is interchangeable from one molecule to another. For GASES: -It is very weak which enables the gas to disintegrate and move away from its container. -A gas is a fluid that is easily compressed and expands to fill its container. -It fills any vessel in which it is contained. There is thus no free surface. For LIQUIDS: -It is stronger which is sufficient enough to hold the molecule together and can withstand high compression, which is suitable for application as hydraulic fluid such as oil. -On the surface, the cohesion forms a resultant force directed into the liquid region and the combination of cohesion forces between adjacent molecules from a tensioned membrane known as free surface.
- 13. 1.1 FLUID AS CONTINUUM Continuum mechanics and its concept • It is a branch of mechanics that deals with the analysis of the kinematics and mechanical behaviour of materials modelled as a continuum. (eg. solids and fluids), (eg. liquids and gases) • A continuum concept assumes that the substance of the body is distributed uniformly throughout, and completely fills the space it occupies. • Fluid properties is depends on their molecular structure.However, engineering applications hardly analyses fluids at molecular level. • It is the fluid’s bulk behavior of main concern in engineering applications.
- 14. CONTINUUM CONCEPTS • Atoms are widely spaced in the gas phase. • However, we can disregard the atomic nature of a substance. • View it as a continuous, homogeneous matter with no holes, that is, a continuum. • This allows us to treat properties as smoothly varying quantities. • Continuum is valid as long as size of the system is large in comparison to distance between molecules.
- 15. Fluid as a continuum • A continuous substance where quantities such as velocity and pressure can be taken as constant at any section irrespective of the individual fluid particle velocity.
- 16. PRESSURE Pressure acts perpendicular to the surface and increases at greater depth. area force pressure Pressure is the force per unit area, where the force is perpendicular to the area. A measure of the amount of force exerted on a surface area
- 17. 1.2 UNITS AND DIMENSION USED IN ENGINEERING FLUIDS WHAT IS UNITS? WHAT IS DIMENSION? •Standardized system of measurements used to describe the magnitude of the dimension •A properties that can be measured •Measurable properties used to describe a body/system •The standard element, in terms of which these dimensions can be described quantitatively & assigned numerical values.
- 18. VARIOUS SYSTEM OF UNIT Parameter SI UNITS c.g.s system of unit Imperial units ( British Gravitational system; English Units) Length Meters (m) Centimeters (cm) Foot (ft) Mass kilogram(kg) Gramme (g) Pound ( Ib) Time Seconds (s) Seconds (s) Seconds (s) Temperature Kelvin (K) Degree Fahrenheit ( oF) • The primary quantities which are also referred to as basic dimensions, such as L for length, T for time, M for mass and F for force. • Student also expected to be familiar with the various systems of units used in engineering. These systems include : As any quantity can be expressed in whatever way you like it is sometimes easy to become confused as to what exactly or how much is being referred to. This is particularly true in the field of fluid mechanics.
- 19. DERIVED UNIT
- 21. 1. DENSITY Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space Density of a material is defined by the amount of matter per unit volume. Density of material may be referred to in many ways.
- 22. 1.1 MASS DENSITY, Definition Density of a fluid, , is defined as the mass per unit volume • It is denoted by the Greek symbol, . == V m3 kgm-3 kg m water= 1000 kgm-3 air =1.23 kgm-3
- 23. 1.2 SPECIFIC WEIGHT, Definition Specific weight of a fluid, , is defined as the weight of the fluid per unit volume . Force exerted by gravity, g, upon unit volume of substance = w V = g Units: N/m3 = the density of the material (kgm-3) g = acceleration due to gravity (ms-2) Water = 9.81 X 103 N/m3
- 24. 1.3 RELATIVE DENSITY @ SPECIFIC GRAVITY, SG Definition A ratio of the specific weight of a substance to the specific weight of water at standard temperature (4C) and atmospheric pressure. Units: dimensionless C w s C w s SG 4 @ 4 @ Unit is none, since ratio is a pure number. SG is a dimensionless quantity
- 25. 2. SPECIFIC VOLUME, V Definition The reciprocal of the mass density i.e. the volume per unit mass or the inverse of density Units: m3/kg v = 1/ = V/m
- 27. 3.1 DYNAMIC VISCOSITY, µ Definition Dynamic viscosity, µ , is defined as the Shear force per unit area (shear stress, ) needed to drag a layer of fluid with a unit velocity past another layer at a unit distance away from it in the fluid Measure of internal friction of fluid particles •Molecular cohesiveness •Resistance fluid has to shear (or flow) Units: Water: Air:
- 28. 3.2 KINEMATIC VISCOSITY, ν Definition It defined as the ratio of dynamic viscosity to mass density v μ = dynamic viscosity ρ= mass density • Will be found to be important in cases in which significant viscous and gravitational forces exist. Typical values: Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s; Units: m2/s or stokes (10,000 St = 1m2s-1)
- 29. NEWTON LAW OF VISCOSITY When fluid moves, it generates shearing stress If no movement between the moving fluid particles no shear stresses developed Fluid particles which in contact with solid boundaries will adhere to these boundaries will have same velocities as the solid boundaries Movement of a fluid over solid boundary can be visualized as layers of a fluid moving one above the other. The velocity of fluid layers increases as the distance from the solid boundary increases y v Flowing passing over a solid boundary
- 30. TEMPERATURE VS VISCOSITY (LIQUID AND GASES) Liquids Gases Viscosity Temperature • Viscosity is caused by the cohesive forces between the molecules in liquids and by the molecular collisions in gases, ant it varies greatly with temperature. • The viscosity of liquid decreases with temperature, whereas the viscosity of gases increases with temperature. • This is because in a liquid the molecules possess more energy at higher temperature and they can oppose the large cohesive intermolecular forces more strongly. • As a result, the energized liquid molecules can move more freely. • In gases, the intermolecular activities are negligible and the gas molecules at high temperature move randomly at higher velocity.
- 31. VISCOSITY IN GASES & LIQUIDS Viscosity in gases • Due to intermolecular collision between randomly moving particles • For gas, temperature , amount of intermolecular collision , viscosity Viscosity in liquid • Due to intermolecular collision between liquid particles • For liquid, temperature , intermolecular collision is weakened, viscosity
- 32. NEWTON LAW OF VISCOSITY = shear stress (tau) = viscosity of fluid du/dy = shear rate, rate of strain or velocity gradient dy du (1.1) • The viscosity is a function only of the condition of the fluid, particularly its temperature. • The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .
- 33. NEWTONIAN & NON NEWTONIAN FLUID Fluid Newton’s law of viscosity Newtonian fluids obey refer Example: Air, Water, Oil, Gasoline, Alcohol, Kerosene, Benzene, Glycerine Fluid Newton’s law of viscosity Non Newtonian fluids not obey refer
- 34. NON NEWTONIAN FLUID *The slope of a curve at a point is the apparent viscosity of the fluid at that point
- 35. 1.4 VAPOUR PRESSURE, SURFACE TENSION, AND CAPILLARITY At the end of this topic student should: •Be able to define the fluid parameters.(CO1-PO1) •Be able to apply surface tension and capillarity in solving fluid engineering problem.(CO1-PO1) •Be able to use the Newton’s law of viscosity which are the relationship of shear stress and velocity gradient in solving fluid engineering problems (CO1-PO3)
- 36. 4. SURFACE TENSION, σ Surface tension • defined as the force acting a unit length of a line drawn in the liquid surface Surface tension • Surface tension tend to reduce the surface area of a body of liquid • The internal pressure within the droplet, p and the surface tension forces, must be in equilibrium. p
- 37. Surface tension • Taking vertical equilibrium of the forces acting on the droplet • The magnitude of surface tension forces are very small compared to other forces • Normally are neglected 2 2 r p r r p 2 2 pr Units : N/m
- 38. 5. VAPOR PRESSURE, Pv Vapor pressure • defined as the pressure at which a liquid turns to vapour • the pressure exerted by its vapor in phase equilibrium with its liquid at a given temperature • The molecules which moves above the surface of the liquid exert pressure in the confined surface Vapor pressure Pvapour = P saturation Units: N/m2 or Pascal
- 39. 6. CAPILLARITY When a liquid comes into contact with a solid surface: - Adhesion forces: forces between solid and liquid - Cohesion forces: forces within liquid If cohesive forces > adhesive forces, the meniscus in a glass tube will take a shape as in figure (a) and (b). Figure (a) and (b)
- 40. Capillary effect is the rise or fall of a liquid in a small- diameter tube gd h cos 4 gr h cos 2 d h cos 4 @ @ Units= m @ mm where h = height of capillary rise (or depression) = surface tension = wetting (contact) angle = specific weight of liquid r = radius of tube