Chapter_1_Fluid_Properties.ppt
- 1. 1 FLUID MECHANICS AND EQUIPMENTS (CHE 241) CHAPTER 1 FLUID PROPERTIES
- 2. 2 OBJECTIVE To acquire fundamental concepts of fluid properties LEARNING OUTCOMES At the end of this chapter, student should be able to: i. Define fluid ii. State the differences between solid and fluid iii. Calculate common fluid properties when appropriate information are given. iv. Define Newton’s Law of viscosity; relationship between shear stress and rate of shear strain
- 3. 3 1.1 FLUIDS • We normally recognize 3 states of matter : Solid, Liquid and Gas. • Although differ in many respects, liquids and gases have common characteristics in which they are differ from solids. • Liquid and gas are fluids: in contrast to solids, they (fluid) lack the ability to resist deformation. Because a fluid cannot resist the deformation force, it moves, it flows under the action of the force. Its shape will change continuously as long as the force is applied. • A solid can resist a deformation force while at rest, this force may cause some displacement but the solid does not continue to move indefinitely FLUID Deforming continuously for as long as the force applied Flow under the action of such forces Unable to retain any unsupported shape
- 4. What is a fluid? • A fluid is a substance in the gaseous or liquid form • Distinction between solid and fluid? – Solid: can resist an applied shear by deforming. Stress is proportional to strain – Fluid: deforms continuously under applied shear. Stress is proportional to strain rate F A F V A h Solid Fluid 1.1 FLUIDS
- 5. • Stress is defined as the force per unit area. • Normal component: normal stress – In a fluid at rest, the normal stress is called pressure • Tangential component: shear stress 1.1 FLUIDS
- 6. • A liquid takes the shape of the container it is in and forms a free surface in the presence of gravity • A gas expands until it encounters the walls of the container and fills the entire available space. Gases cannot form a free surface • Gas and vapor are often used as synonymous words 1.1 FLUIDS
- 7. solid liquid gas 1.1 FLUIDS
- 8. No-slip condition • No-slip condition: A fluid in direct contact with a solid ``sticks'‘ to the surface due to viscous effects • Responsible for generation of wall shear stress w, • surface drag D= ∫w dA, and the development of the boundary layer • The fluid property responsible for the no-slip condition is viscosity
- 9. 9 1.1 FLUIDS • Deforming is caused by shearing forces, i.e. forces such as F (refer Figure 1.1), which act tangentially to the surfaces to which they are applied and causes the material originally occupying the space ABCD to deform AB’C’D. F D A B’ B C’ C y x E ø Figure 1.1: Deformation caused by shearing forces We can then say: A fluid is a substance which deforms continuously, or flows, when subjected to shearing forces. On the other hand, this definition means the very important point that: If a fluid is at rest, there are no shearing forces acting. All forces must be perpendicular to the planes which they are acting.
- 10. 10 1.2 SHEAR STRESS IN A MOVING FLUID • Shear stresses are developed when the fluid is in motion. If the particles of the fluid move relative to each other so they have different velocities, causing the original shape of fluid to become distorted. • If the velocity of fluid is the same at every point, no shear stresses will be produced, since the fluid particles are at rest relative to each other. • If ABCD (refer Figure 1.1) represents an element in a fluid with thickness s perpendicular to the diagram, the force F will act over an area A equal to BC x s. • The force per unit area, F/A is the shear stress τ and the deformation, measured by angle ø (the shear strain), will be proportional to the shear stress. • The shear strain ø will continue to increase with time and the fluid will flow. • The rate of shear strain (or shear strain per unit time) is directly proportional to the shear stress.
- 11. 11 • Suppose that in time t, a particle at E (refer Figure 1.1) moves through a distance x. • If E is a distance y from AD then, for a small angles, • Revise that shear stress is proportional to shear strain, then E at particle the of velocity the is t / x u where y u y ) t / x ( yt x strain shear of Rate y x , strain Shear u constant x y 1.2 SHEAR STRESS IN A MOVING FLUID Equation 1.1
- 12. 12 • The term u/y is the change of velocity with y and may be written in differential form du/dy. • The constant of proportionality is known as the dynamic viscosity μ of the fluid. Substitute to Equation 1.1, Equation 1.2 is Newton’s law of viscosity du τ=μ dy 1.2 SHEAR STRESS IN A MOVING FLUID Equation 1.2
- 13. 13 • Fluids obeying Newton’s law of viscosity and for which μ has a constant value are known as Newtonian fluids. • Most common fluids fall into this category, for which shear stress is linearly related to velocity gradient (refer Figure 1.2) 1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS Figure 1.2: Variation of shear stress with velocity gradient Rate of shear strain, du/dy
- 14. 14 • Fluids which do not obey obeying Newton’s law of viscosity are known as non-Newtonian fluids and fall into one or the following groups. 1. Plastic: Shear stress must reach a certain minimum before flow commences. Thereafter, shear stress increases with the rate of shear according to the relationship in Equation 1.3, where A, B and n are constants. If n=1, the material is known as Bingham plastic, e.g. sewage sludge. 2. Pseudo-plastic: Dynamic viscosity decreases as the rate of shear increases, e.g. colloidial substances like clay, milk and cement. 1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS 1.3 n A B Equation du dy
- 15. 15 1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS 3. Dilatant substances: Dynamic viscosity increases as the rate of shear increase, e.g. quicksand. 4. Thixotropic substances: Dynamic viscosity decreases with the time for which shearing force is applied, e.g. Thixotropic jelly paints. 5. Rheopectic substances: Dynamic viscosity increases with the time for which shearing force is applied. 6. Viscoelastic materials: Behave similar to Newtonian fluids but if there is a sudden large change in shear stress, they behave like plastic. • The above is a classification of actual fluids. • There is also one more - which is not real, it does not exist - known as the ideal fluid. This is a fluid which is assumed to have no viscosity (τ = 0). This is a useful concept when theoretical solutions are being considered - it does help achieve some practically useful solutions in analyzing some of the problems arising in fluid mechanics.
- 16. 16 1.4 DENSITY The density of a substance is that quantity of matter contained in unit volume of the substance. It can be expressed in three different ways. 1.4.1 MASS DENSITY • Mass density ρ is defined as the mass of substance per unit volume. • Units: kilogram per cubic meter (kgm-3) • Dimensions: ML-3 • Typical values at p=1.013 x 105 Nm-2, T=288.15 K, mass density of water is 1000 kgm-3 and air is 1.23 kgm-3.
- 17. 17 1.4 DENSITY 1.4.2 SPECIFIC WEIGHT • Specific weight w is defined as the weight per unit volume. • Since weight is dependent on gravitational attraction, the specific weight will vary from point to point, according to the local value of gravitational acceleration g. • The relationship between w and ρ can be deduced from Newton’s second law where, Weight per unit volume = Mass per unit volume x g ω = ρg • Units: newtons per cubic meter (Nm-3) • Dimensions: ML-2T-2 • Typical values for water is 9.81 x 103 Nm-3 and air is 12.07 Nm-3.
- 18. 18 1.4 DENSITY 1.4.3 RELATIVE DENSITY • Relative density or specific gravity (SG) σ is defined as the ratio of the mass density of a substance to some standard mass density. • For solids and liquids, the standard mass density chosen is the maximum density of water (which occur at 4°C at atmospheric pressure). • The relationship between is represented by, C ° 4 at water ce tan subs ρ ρ = σ • For gases, the standard density may be that air or hydrogen at a specified temperature and pressure, but the term is not used frequently. • Units: since relative density is a ratio of two quantities of the same kind, it is a pure number having no units. • Dimensions: as a pure number, its dimension are M0L0T0=1. • Typical values for water is 1.0 and oil is 0.9.
- 19. 19 1.5 VISCOSITY 1.5.1 DYNAMIC VISCOSITY • The coefficient of dynamic viscosity μ can be defined as the shear force per unit area (or shear stress τ) required to drag one layer of fluid with unit velocity past another layer a unit distance away from it in the fluid. • Rearranging Equation 1.2, Time x Lenght Mass or Area Time x Force = Distance Velocity Area Force = dy du τ = μ • Unit: newtons seconds per square meter (Nsm-2) or kilograms per meter per second (kgm-1s-1). But note that the coefficient of viscosity is often measures in poise (P) where 10 P = 1 kgm-1s-1. • Dimension: ML-1T-1 • Typical values for water is 1.14 x 10-3 kgm-1s-1 and air is 1.78 x 10-5 kgm-1s-1.
- 20. 20 1.5 VISCOSITY 1.5.2 KINEMATIC VISCOSITY • The kinematic viscosity, is defined as ratio of dynamic viscosity, μ to mass density, ρ. • Unit: square meters per second (m2s-1) but note that the kinematic viscosity is often measures in stokes (St) where 10 St = 1 m2s-1. • Dimension: L2T-1 • Typical values for water is 1.14 x 10-6 m2s-1 and air is 1.46 x 10-5 m2s-1. ρ μ = ν
- 21. 21 1.6 UNIT AND CONVERSION FACTORS • In the United States most measurements use the English system of units (based on the foot, pound and °F), but most of the world uses the metric (or SI) units (based on the meter, kilogram and °C).
- 22. Tutorial 1. Determine the density, specific gravity, and mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100 kPa and 25oC.