Fluid Mechanics: CIV 142 Course Overview

• The presentation covers Fluid Mechanics, course code CIV 142, held at the Civil Engineering Department of the Faculty of Engineering at Sphinx University, for first-year Civil Engineering students.

Course Grades

• Final Exam is worth 40 points.
• Oral Exam & Lab Report contribute 20 points.
• Mid-term Exam is valued at 20 points.
• Class work, including quizzes, sheets, and attendance, accounts for 20 points.
• Total points for the course amount to 100.

Text Books

• Fundamentals of Fluid Mechanics, 4th Edition, by Bruce R. Munson, Donald F. Young, and Theodore H. Okiishi, published by John Wiley & Sons in 2002.
• Fluid Mechanics, 5th Edition, by F. M. White, McGraw-Hill, 2003.
• Engineering Fluid Mechanics, 9th Edition, by Crowe, Elger, and Roberson, 2009, published by John Wiley & Sons.
• Schaum's 2500 Solved Problems in Fluid Mechanics by J.B. Evett & Cheng Liu.

Aim of the Course

• Importance in hydraulics and civil engineering applications.
• Understanding basic concepts of fluid mechanics: mass conservation laws, energy conservation laws, and momentum conservation laws.
• Knowledge of applications to hydraulics and civil engineering problems, including basics of other subjects and design applications.

Chapter 1: Fluids and Their Properties

• Includes introduction, definition of Fluid, Units and dimensions, Physical properties of liquid, and solved examples.

Introduction

• Hydraulics, derived from the Greek word 'Hudour' (meaning water), is the branch of engineering science dealing with water at rest or in motion, based on experimental observation of water flow.
• Fluid Mechanics is the branch of engineering science dealing with the behavior of fluid under rest and motion.
• Fluid mechanics has 3 parts: statics, kinematics and dynamics.
• Statics studies incompressible fluids under static conditions, called hydrostatics, and compressible static gases, termed aerostatics.
• Kinematics deals with velocities, accelerations, and flow patterns, excluding forces or energy causing velocity and acceleration.
• Dynamics involves the relations between velocities, accelerations of fluid, and the forces or energy causing them.

Definition of Fluid

• A fluid is any substance that continuously deforms under the action of shearing forces
• Fluids flow under their own weight and assume the shape of their container.
• A gas is a fluid that is easily compressed.
• A liquid is a fluid that resists compression.
• Solids resist shape change when loaded due to strong intermolecular forces
• Fluids flow with even slight loads due to very weak intermolecular attraction forces
• Liquids are nearly incompressible and form a free surface.
• Water, oil, mercury, gasoline, and alcohol are examples of liquids.
• Gases are relatively easy to compress and completely fill any vessel.
• Air, helium, hydrogen, and steam are examples of gases.

Dimensions and Units

• Physical quantities can be represented by basic physical dimensions such as Mass [M], length [L], time [T] (mass system) and Force [F], length [L], time [T] (force system).
• A unit expresses how much of the physical quantity is present.
• Unit systems include the International System, French System, and British System of Units.
• Conversions: 1 ft = 12 inches = 30.48 cm, 1 inch = 2.54 cm, 1 mile = 5280 ft, 1 mile = 1.6 km, 1 lb = 453.6 gm, 1 slug = 32.2 lbm, 1 Kgf = 9.81 N, and 1 N = 10^5 dyne.

Physical Properties of Liquid

• Includes: Density, specific weight, specific gravity, specific volume, compressibility & elasticity, viscosity, cohesion & adhesion, and surface tension & capillarity.

Density

• Density (p) is the mass per unit volume (kg/m³).
• Density depends on temperature and atmospheric pressure or static imposed head.
• At standard conditions of 20°C and 101.325 kPa, the density of water = 998.2kg/m3 and air = 1.2kg/m3.
• ρ = m/V, where ρ is density, m is mass, and V is volume.
• Fluid densities decrease with temperature.
• The flow of constant density fluids is incompressible
• Flow of fluids with significant density variations is compressible
• Gas flows are often treated as incompressible if there are no large pressure fluctuations.

Specific Weight

• Specific weight (y), sometimes referred to as unit weight, is the weight of fluid per unit volume.
• γ = ρg, where γ is specific weight, ρ is density, and g is acceleration due to gravity.

Specific Gravity

• Specific gravity is a dimensionless quantity defined as the ratio of the density of a substance to the density of a given reference material.
• Specific gravity of Mercury (Hg) is 13.6
• Specific gravity of water is 1.
• S.G = (γLiquid / γWater) = (ρLiquid / ρWater)

Specific Volume

• Specific volume is volume divided by mass or the reciprocal of density: Vs = V/m = 1/ρ.

Compressibility & Elasticity

• Compressibility is the relative change in fluid volume per unit external pressure change: B = - (ΔV/Vo) / ΔP, where Vo = original volume, ΔV = volume change, and ΔP = pressure change.
• Bulk Modulus of Elasticity is the measure of the decrease in volume with an increase in pressure that is the reciprocal of compressibility coefficient: E = - ΔP / (ΔV/Vo).

Viscosity

• Viscosity measures a fluid's resistance to deformation or movement of its parts relative to one another, indicating opposition to flow.
• Viscosity considered as internal friction within a fluid, which opposes velocity differences.
• Laminar motion shear stress is proportional to the velocity gradient: τ ∝ du/dy and τ = μ(du/dy)
• μ: coefficient of viscosity (dynamic viscosity) or absolute viscosity
• du / dy: rate of shear stress, shear deformation rate or velocity gradient.
• S.I. Unit of Viscosity: N.s/m²
• M.K.S. Unit of Viscosity: kgf . sec/m2
• C.G.S. Units of Viscosity: (dyne . s/cm2) = poise.
• Kinematic viscosity is the ratio of dynamic viscosity to the density of fluid.
• ν = μ/ρ,
• Where v is the kinematic viscosity.
• S.I. and M.K.S Units of Kinematic Viscosity: m²/s
• C.G.S. Unit of Kinematic Viscosity: (cm²/s) = stocke.

Cohesion and Adhesion

• Cohesion is the attraction force when similar substances or molecules face each other, forming water droplets.
• Adhesion happens between dissimilar molecules or substances and is generally the attraction force between water molecules and vessel walls, causing liquid spread.

Surface Tension & Capillarity

• Surface tension results from cohesion between particles at the surface, quantified as force per unit length.
• Capillary action occurs due to water molecules' attraction between forces of cohesion and adhesion where water molecules bond each other strongly due to forces of cohesion and adhesion where water molecules are attracted and stick to other substances.
• h = (2 σ cos α) / (γ r)
• Where σ is the surface tension, γ is the specific weight of the liquid, and α is the angle of contact.

Solved Examples

• Examples with calculating specific weight, density, specific volume and specific gravity.
• Examples of finding the bulk modulus of liquids.
• Examples for finding viscosity of fluids.
• Examples with area sliding down the inclined.
• Examples with tubes immersed in a liquid with a coefficient of surface tension.