Unit 1 CE8394 FMM
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This document provides an introduction to fluid mechanics and fluid properties. It discusses: 1) Fluid mechanics is the study of fluids at rest and in motion, and is divided into fluid statics and fluid dynamics (kinematics and kinetics). 2) Key fluid properties include density, specific weight, specific volume, viscosity, compressibility, and surface tension. Equations for calculating these properties are presented. 3) Types of fluids include ideal, real, Newtonian, non-Newtonian, and plastic fluids. Types of flow include steady, unsteady, uniform, non-uniform, compressible, and incompressible flow.
Unit 1 CE8394 FMM
- 1. UNIT 1 INTRODUCTION CE6451 FLUID MECHANICS & MACHINERY Prepared by S. Muthu Natarajan M.E., (Ph.D.), Assistant Professor Kamaraj College of Engineering and Technology Madurai
- 2. INTRODUCTION TO FLUID MECHANICS • Fluid mechanics is the branch of science which deals with the behaviour of fluids at rest and in motion • Fluid mechanics is classified as Fluid statics Fluid dynamics is classified as a. Fluid kinematics b. Fluid kinetics
- 3. PROPERTIES OF FLUIDS • Density or Mass density (ρ) : It is defined as the ration of the mass of the fluid to the volume of the fluid 𝜌 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑 𝜌 of water = 1000 kgm /m3 units : kgm /m3 • Specific weight or weight density (w) : It is defined as the weight of the fluid volume of the fluid w= 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 ×𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 w = 𝜌 ×g units : N/m3 w of water = 9810 N/m3
- 4. PROPERTIES OF FLUIDS • Specific volume : It is defined as the reciprocal of density of the fluid specific volume = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 Units : m3/ kgm • Specific gravity (S): It is defined as the ratio of the density of the liquid to the density of water (OR) it is defined as the ratio of the weight density of the liquid to the weight density of water. S = 𝜌 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 𝜌 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 (OR) 𝑤 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 𝑤 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
- 5. PROPERTIES OF FLUIDS • Viscosity : It is defined as the property of the fluid which offers resistance to the movement of one layer of the fluid over another adjacent layer of the fluid. • Newtons law of viscosity (µ) : It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the co-efficient of viscosity. Mathematically τ = 𝜇 𝑑𝑢 𝑑𝑦 Units of dynamic viscosity = Ns/m2 , poise 1 poise = 0.1 Ns/m2 • Kinematic viscosity (ϒ) ϒ= 𝜇 𝜌 It is defined as the ratio of dynamic viscosity of the fluid to the density of the fluid. Units of kinematic viscosity = m2 /s , stokes I stoke = 1 cm2/s
- 6. PROPERTIES OF FLUIDS • Compressibility and Bulk modulus : Compressibility is defined as the reciprocal of bulk modulus. Bulk modulus (K) is defined as the ratio of compressive stress to volumetric strain K = 𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒇 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 −𝒅𝒗/𝒗 Surface Tension (σ) = Surface tension is defined as the force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible fluids such that the contact surface behaves like a membrane under tension. Units : N/m For liquid droplet h= 𝟒𝝈 𝒅 For soap bubble h= 𝟖𝝈 𝒅 Capillarity : It is defined as the phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid. The rise of the liquid surface is capillary rise while the fall in the liquid surface is known as capillary depression For capillary rise h= 𝟒𝝈 𝝆𝒈𝒅 For capillary depression h= 𝟒𝝈𝒄𝒐𝒔𝜽 𝝆𝒈𝒅 Where θ = angle of contact between liquid and glass tube.
- 7. TYPES OF FLUIDS • Ideal fluid : A fluid which is incompressible and is having no viscosity is known as ideal fluid. Ideal fluid is an imaginary fluid • Real fluid : A fluid which possess viscosity is known as real fluid. All fluids in practice are known as real fluid • Newtonian fluids : a real fluid in which the shear stress is directly proportional to the rate of shear strain is called as Newtonian fluid • Non – Newtonian fluid : a real fluid in which the shear stress is not proportional to the rate of shear strain is known as non Newtonian fluid • Ideal plastic fluid : A fluid in which shear stress is more than the yield value and shear stress is proportional to the rate of shear strain is known as ideal plastic fluid
- 8. TYPES OF FLOW • Steady flow : a steady flow is a flow in which the fluid characteristics like pressure, density, etc does not vary with respect to time • Un steady flow : a unsteady flow is a flow in which the fluid characteristics like pressure, density, etc vary with respect to time • Uniform flow : A flow in which the velocity at any given time does not change with respect to distance • Non uniform flow : A flow in which the velocity at any given time change with respect to distance • Compressible flow : The flow in which the density of the fluid changes from point to point ρ≠ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, • Incompressible flow : The flow in which the density of the fluid do not change from point to point ρ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- 9. RATE OF FLOW (OR) DISCHARGE • It is defined as the quantity of a fluid flowing per second through a section of a pipe or a channel. For an incompressible fluid the rate of flow or discharge is expressed as the volume of the fluid flowing across the section per second. • For incompressible fluids (Q) = A × V Where A = Cross sectional area of the pipe V = average velocity of fluid across the section
- 10. CONTINUITY EQUATION • The equation is based on the law of conservation of mass • It states that for a fluid flowing through the pipe at all the cross section the quantity of the fluid per second is a constant. • Consider two cross sections of a pipe as shown in the fig Let V1 be the velocity at cross section 1-1 Let V2 be the velocity at cross section 2-2 Let A1 be the velocity at cross section 1-1 Let A2 be the velocity at cross section 2-2 According to the law of conservation of mass Rate of flow at section 1-1 = Rate of flow at section 2-2 𝝆 𝟏 𝑨 𝟏 𝑽 𝟏 = 𝝆 𝟐 𝑨 𝟐 𝑽 𝟐 this is the general expression for both compressible and incompressible fluids For incompressible fluid the above equation is 𝑨 𝟏 𝑽 𝟏 = 𝑨 𝟐 𝑽 𝟐 because density is constant 1 1 2 2
- 11. BERNOULLIS THEOREM • It states that in a steady, ideal flow of an incompressible fluid the total energy at any point of the fluid is constant. The total energy consists of pressure energy, kinetic energy and datum energy. Thus mathematically bernoullis equation is written as 𝒑 𝝆𝒈 + 𝒗 𝟐 𝟐𝒈 + 𝒛 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒑 𝝆𝒈 = Pressure energy 𝒗 𝟐 𝟐𝒈 = Kinetic energy Z = datum energy • Assumptions of Bernoulli's equation : 1. The fluid is ideal 2. The flow is steady 3. The flow is incompressible 4. The flow is irrotational
- 12. DERIVATION OF EULERS AND BERNOULLIS EQUATION
- 13. APPLICATIONS OF BERNOULLIS EQUATION • Venturimeter • Orificemeter • Pitot tube Venturimeter : The venturimeter is a device which is used to measure the rate of flow through a closed pipe It consists of 3 parts (a) A short converging part (b) Throat (c) Diverging part Theoretical discharge Cd = 𝑸 𝒂𝒄𝒕𝒖𝒂𝒍 𝑸 𝑻𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍 a1 = area of the pipe a2 = area of the throat h= x 𝒔 𝒎 𝒔 𝒇 − 𝟏 𝒔 𝒎 = specific gravity of manometric fluid for mercury = 13.6 𝒔 𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫 for water = 1
- 14. ORIFICEMETER • It is a device used for measuring the rate of flow of a fluid through a pipe. It consists of a flat circular plate which has a circular sharp edged hole called as orifice which is concentric to the pipe
- 15. DISCHARGE OF ORIFICEMETER • Let a1 = area of the pipe a0 = area of the orifice • Actual discharge h= x 𝒔 𝒎 𝒔 𝒇 − 𝟏 𝒔 𝒎 = specific gravity of manometric fluid for mercury = 13.6 𝒔 𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫 for water = 1
- 16. PITOT TUBE
- 17. PITOT TUBE