Fluid Mechanics (DE-1102) Course Outline PDF

# Fluid Mechanics (DE-1102) ## Course Outline ### Module 1: Introduction to fluid mechanics - Units and dimensions, Properties of fluids. ### Module 2: Static pressure of liquids - Static pressure of liquids: Hydraulic pressure, absolute and gauge pressure. - Pressure head of a liquid, Pressure on...

# Fluid Mechanics (DE-1102) ## Course Outline ### Module 1: Introduction to fluid mechanics - Units and dimensions, Properties of fluids. ### Module 2: Static pressure of liquids - Static pressure of liquids: Hydraulic pressure, absolute and gauge pressure. - Pressure head of a liquid, Pressure on vertical rectangular surfaces. - Compressible and non-compressible fluids. Surface tension, capillarity. ### Module 3: Pressure measuring devices - Simple manometer, piezometer, U tube manometer. - Micro manometer, Inclined manometer. - Differential manometer. - Mechanical gauges ### Module 4: Floating bodies - Archimedes principle, stability of floating bodies. - Equilibrium of floating bodies. Metacentric height. ### Module 5: Fluid flow - Classification, steady uniform and non uniform flow, Laminar and turbulent. - Continuity equation. - Bernolli's theorem. - Application of Bernolli's theorem. ### Module 6: Flow through pipes - Loss of head (a). Major head loss. - Loss of head (b). Minor head loss. - Problems on head loss. - Determination of pipe diameter, determination of discharge, friction factor, critical velocity. ### Module 7: Flow through orifices, mouthpieces, notches and weirs - Orifices, vena contracta, Hydraulic coefficients. - Discharge losses, Time for emptying a tank. - Loss of head due to contraction, enlargement at entrance and exit of pipe. - External and internal Mouthpieces - Types of notches, rectangular and triangular notches. Rectangular weirs. ### Module 8: Measuring Instruments - Venturimeters, pitot tube. - Rota meter, Water level point gauge, hook gauge. ### Module 9: Dimensional analysis - Buckinghams theorem application to fluid flow phenomena. - Froude Number, Reynolds number, Weber number. - Hydraulic similitude. ### Module 10: Pumps - Classification. - Reciprocating pump. - Centrifugal pump, Pressure variation, work done, efficiency. - Types of chambers, selection and sizing. ## Introduction - Fluid is a substance which will continuously deform or flow whenever a shear stress is applied to it. e.g. water, milk, steam, gas, etc. It can't preserved its shape unless it is restricted into a particular form depending upon the shape of its surroundings. - **Fluid Mechanics** is the study of fluids either in motion (fluid dynamics) or at rest (fluid statics). Gases and liquids (e.g. air, water) come under the category of fluid. - One of the areas of modern fluid mechanics is Computational Fluid Mechanics which deals with numerical solutions using computers. Fluid mechanics comprises of the following subjects: - **Fluid Statics:** Study of fluids under rest. - **Fluid Kinematics:** Study of fluids under motion (velocities, acceleration). - **Fluid Dynamics:** Study of fluids under motion (velocities, acceleration with the forces or energy causing them). ## Classification of Fluids - **Ideal Fluid:** Ideal fluid is one which has no property other than density. Such fluids have no viscosity, no surface tension and are incompressible. When such fluid flows, no resistance is encountered. Ideal fluid is imaginary fluid as all the fluids have some viscosity. - **Real Fluid:** The fluids which have viscosity, surface tension in addition to density. All the fluids have these properties whether large or small. ## Why to study fluid mechanics? - Dairy plants handle various types of fluids such as milk, water, air, refrigerants, steam etc. It is very important to learn the behaviour of fluid under various conditions in order to design the system for handling of such fluids in dairy plants. Fluid mechanics is a branch of Engineering Science, the knowledge of which is needed in the design of: - Water supply and treatment system. - Pumps used for handling of different fluids. - Ships, submarines, aeroplanes, Automobiles. - Storage tanks (milk silo, tankers, feed tanks, balance tanks etc.). - Piping systems for various utilities, pipefitting & valves, flow meters etc. - CIP systems for optimum performance. - Heat transfer behaviour in processing equipments. ## Units and Dimensions - Solution to numerical and engineering problems becomes meaningless without units. A unit of measurement is a definite magnitude of a physical quantity. The different systems of unit are: - **SI system:** It is the International System of Units (abbreviated SI from the French *Le Système International d'Unités*). - **C.G.S. system:** It is a system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time. - **M.K.S. system:** It is a metric system of physical units based on meter as the unit of length, kilogram as a unit of mass, and second as a unit of time. ## Commonly used units in SI, CGS and MKS: | Dimension | CGS units | MKS units | Si units | |---|---|---|---| | Length (L) | Centimeter (cm) | meter (m) | meter (m) | | Mass (M) | Gram (g) | kilogram (kgm) |kilogram (kg) | | Time (T) | Second (sec) | Second (sec) | Second (s) | | Force (F) | Dyne (Dyn) | Kilogram (kgf) | Newton (N) (=kg m/s²) | | Temperature (°C) | Ranking (OR) | Celsius (°C) | Kelvin (K) | | Fahrenheit (°F) | Celsius (°C) | Celsius (°C) | ## Unit prefixes in SI | Factor | Prefix | Symbol | |---|---|---| | 10⁹ | Giga | G | | 10⁶ | Mega | M | | 10³ | Kilo | k | | 1 | | | | 10⁻² | Centi | c | | 10⁻³ | Milli | m | | 10⁻⁶ | Micro | µ | | 10⁻⁹ | Nano | n | ## Quantities, dimensions and units | Quantity | Dimensions (MLT) | Preferred units (Si) | |---|---|---| | Length (L) | L | m | | Time (T) | T | s | | Mass (M) | M | kg | | Area (A) | L² | m² | | Volume (Vol) | L³ | m³ | | Velocity (V) | LT⁻¹ | m/s | | Acceleration (a) | LT⁻² | m/s² | | Discharge (Q) | L³T⁻¹ | m³/s | | Kinematic viscosity (u) | L²T⁻¹ | m²/s | | Weight/Force (F) | MLT⁻² | N | | Pressure (p) | ML⁻¹T⁻² | Pa (N/m²) | | Shear stress (τ) | ML⁻¹T⁻² | Pa (N/m²) | | Mass Density (ρ) | ML⁻³ | kg/m³ | | Specific weight (γ) | MLT⁻² | N/m³ | | Energy/Work/Heat (E) | MLT⁻² | J | | Power (P) | MLT⁻³ | W | | Dynamic viscosity (µ) | ML⁻¹T⁻¹ | Ns/m² | ## Some important units and conversions - Dyne = g cm/s² and 1 dyne = 10⁵ N - 1 pound = 0.453 kg - Pressure: 1 atm = 101.325 kPa, 1 bar = 10⁵ Pa - 1 m = 3.28 ft - 1 m = 100 cm - 1 feet = 30.5 cm - 1 feet = 12 inch - 1 inch = 2.54 cm - 1 km = 0.621 miles - 1 ha = 2.47 acre - 1 acre = 4,046.85 m² - 1 litre = 0.264 gallon - °C = (5/9)X (F°-32) ## Properties of fluids ### Mass density (ρ) - Mass of fluid per unit volume. - Mass density = Mass/Volume - Unit: kg/m³ - Dimension: ML⁻³ - The density of liquids vary slightly with variation of temperature while that of gases changes with variation of pressure and temperature. - ρ of water = 1000 kg/m³ at 4°C. ### Weight Density (Specific Weight) - Weight of fluid per unit volume - w=(Weight of fluid)/(Volume of fluid) - w=(mass of fluid×Acceleration due to gravity)/(volume of fluid) - w=(mass of fluid)/(volume of fluid)xg - ω = ρ.g - Unit: MKS kgf/m³ - SI→ N/m³ - Dimensions → ML⁻²T⁻² - The specific weight of for water is 1000 kgf/m³ in MKS units and 9.81×1000 N/m³ in SI units. ## Specific Gravity - Ratio of density of any substance to the density of pure water at 4°C. - Sp. Gravity = Density of any substance/ density of pure water at 4°C. - Dimensions: M⁰L⁰T⁰ - Unitless - Specific gravity of milk is 1.028 to 1.032. ## Viscosity - Viscosity, µ, is the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to shear deformation. - Different fluids deform at different rates under the same shear stress. The ease with which a fluid pours is an indication of its viscosity. Fluid with a high viscosity such as syrup deforms more slowly than fluid with a low viscosity such as water. The viscosity is also known as dynamic viscosity. - Units: N.s/m² or kg/m/s - Typical values: - Water = 1.14x10⁻³ kg/m/s; Air = 1.78x10⁻⁵kg/m/s ## Shear stress in moving fluid - If fluid is in motion, shear stress are developed if the particles of the fluid move relative to each other. Adjacent particles have different velocities, causing the shape of the fluid to become distorted. - On the other hand, the velocity of the fluid is the same at every point, no shear stress will be produced, the fluid particles are at rest relative to each other. ## 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] - τ: shear stress - **Shear stress:** An applied force per unit area needed to produce deformation in a fluid τ = μ d'V/dy ## VISCOSITY - **Would it be easier to walk through a 1-m pool of water or oil?** - **Water** - **Why?** - Less friction in the water. - Water moves out of your way at a quick rate when you apply a shear stress (i.e., walk through it). - Oil moves out of your way more slowly when you apply the same shear stress ## Compressibility - Compressibility is a measure of how much a fluid’s volume changes when subjected to a change in pressure or external force. It is also known as isothermal compressibility or coefficient of compressibility. - Compressibility is defined as the change in volume per unit change in pressure. For example, if the pressure is increased, the volume decreases. - It is reciprocal of the bulk modulus of elasticity, K which is defined as the ratio of compressive stress to volumetric strain. K= change in pressure / volumetric strain K=-ΔP/ΔV/V ## Newtonian Vs Non-Newtonian fluid - A Newtonian fluid is a fluid whose viscosity is not affected by shear rate. This means that flow speeds or shear rates do not change the viscosity. Examples of Newtonian fluids include air, water, kerosene, gasoline, and other oil-based liquids. - Non-Newtonian fluids are fluids that do not follow Newton's law of viscosity. They have variable viscosity that depends on stress. When a non-Newtonian fluid is under force, its viscosity can change to become more liquid or more solid. For example, ketchup becomes runnier when shaken. - Other Examples: Salt solutions, Blood, Paint, Toothpaste, Starch solutions ## Kinematic Viscosity - Many fluid mechanics equations contain the variables of: - Viscosity, µ - Density, ρ - So, to simplify these equations, sometimes we use kinematic viscosity (v) | Terminology | | |---|---| | Viscosity, µ | ν=Ns/m² | | Density, ρ | ρkg/m³ | | Kinematic Viscosity, ν | ν=m²/s | ## Surface Tension - Liquids possess the properties of cohesion and adhesion due to molecular attraction. - Due to the property of cohesion, liquids can resist small tensile forces at the interface between the liquid and air, known as surface tension, σ. - Surface tension is defined as force per unit length, and its unit is N/m. - FOL - F, surface tension force [N] - σ, surface tension [N/m] - L = length over which the surface tension acts [m] ## Capillarity - Capillarity is a phenomenon of rise or fall of a liquid surface in a small tube (capillary) relative to the adjacent general level of liquid when tube is held vertically in the liquid. - Liquid rise in tubes if they wet a surface (adhesion>cohesion), such as water, and fall in tubes that do not wet (cohesion> adhesion), such as mercury. - Capillarity is important when using tubes smaller than 10 mm. - For tube larger than 12 mm capillarity effects are negligible. ## Capillary Rise (h) - h= (2σ x cos θ)/ (ρxgxr) - h = (4σ cose)/ (ρg d) - Where. - h = Capillary rise or fall - σ = Surface tension - ρ = Density - g = gravitational acceleration - d = diameter of capillary - θ = Angle of contact between liquid and glass tube