IntroductionUnits – International System and the US SystemInternational System (SI – Système International d’ Unitès)US System of UnitsBasic DefinitionsWeight and MassTemperature:Absolute Temperature:PressureDensity (ρ)Specific Weight (γ)Specific GravitySurface TensionViscosityAssignment # 1:1 Introduction Fluid Mechanics / Hydraulic Engineering – Old science! Principles of fluid mechanics and hydraulics applied in many ancient civilizations and their construction • Egyptians • Romans • Inca, Mayan Civilizations (South America) • Asian Civilizations (China, India, Middle East)23 Many of the principles and laws developed/discovered – through extensive experimentation  sometimes its referred to empirical science…4 Why do we want to learn about Hydraulics and Fluid Mechanics – very relevant today! Principles of fluid mechanics and hydraulics relevant to – • Water supply and distribution • Irrigation (channels & dams) • Drainage • Town planning • Pumping water • Mechanical systems (engines, machines) • Aerodynamics (air flow) – designing cars, planes,….5 Units – International System and the US System International System (SI – Système International d’ Unitès) Length = meter (m) Time = seconds (s) Mass = kilogram (kg) Force = Newton (N) = kg m/s2 SI Unit prefixes Prefix SI symbol Factor Giga G 109 Mega M 106 Kilo k 103 Milli m 10-3 Micro µ 10-6 Macro n 10-96 US System of Units Length = foot (ft) Time = seconds (s) Force = pound (lb) Mass = lb-s2/ft or slug We will primarily use SI units in the course, but US system will also be used alternately.7 Basic Definitions Fluids – Liquids or Gas! Gases – compressible Liquids – only slightly compressible Weight and Mass Mass is the property of a body of fluid that is a measure of its inertia or resistance to a change in motion. It is also a measure of the quantity of fluid. Weight is the amount that a body of fluid weighs, that is, the force with which the fluid is attracted toward earth by gravitation. Mass = quantity of the substance Weight = force = object influenced by gravity Weight – Force = mass x acceleration W = mg Where g = 9.81 m/s2 in SI units; 32.2 ft/s2 in US units ****8 Units of mass = kg Units of weight = kg . m/s2 = Newton (N) Temperature: Expressed in either – Fahrenheit (F) or Centigrade (C) Tc = (Tf – 32)/1.8 Water freezes at 0C and boils at 100C Absolute Temperature: In comparison to centigrade and Fahrenheit that were arbitrarily set, absolute temperature corresponds to a physical condition of matter– Absolute zero – where all molecular motion stops! = 0 K Where K is the units of Kelvin Tk = Tc + 273.15 Absolute zero in Centigrade is = -273.15 C9 Pressure Amount of force exerted per unit area p = F/ A Two important principles – Referred to as Pascal’s Law – 1. pressure acts uniformly in all directions on a small volume of fluid 2. In a container, pressure acts perpendicular to the boundary1011 Example Problem 1.2 If the total weight = 500N and the area of the piston = 2500 mm2 What is the pressure on the Fluid????? P = 500 / 2500 = 0.2 N / mm2 = 0.2 N x 106 N/m2 = 0.2 MPa Since Pa = N/m2 Compressibility Refers to the change in volume (V) of a substance that is subjected to a change in pressure on it. Density (ρ) Mass per unit volume of the substance = m/V = (ρ) (rho) SI Units = kg/m3 US units = (lb-s2/ft) / ft3= slug/ft3 *** density of water changes with temperature ! Water is most dense at 4C – why???? Any clues????12 Specific Weight (γ) Weight per unit volume of the substance γ (gamma) = w/V SI units = N/m3 or US units = lb/ft3 Relationship between density and specific weight γ = w/V But, w = mg Therefore, γ = mg/V γ = ρ g Specific Gravity Ratio of density of substance to the density of water Or Ratio of specific weight of substance to the specific weight of water13 Density (ρw) of water at 4 degrees C = 1000 kg/m3 Specific weight (γw) of water at 4 degrees C = 9.81 kN/m3 Surface Tension Property by which droplets of water (or water molecules) adhere to each other and other surfaces • When water molecules stick to each other – cohesion • When they stick to other substance – adhesion • Surface tension varies with temperature – decreases with increase in temperature.14 Surface tension helps this spider walk on water. The force of surface tension balances the spider’s weight, helping it to walk on water. Surface tension affects the top layer of water, causing it to behave like a stretched elastic sheet. It occurs because the attraction between water molecules is not balanced at the liquid surface. Away from the surface, H2O molecules are pulled equally in all directions by neighbors, but those in the top layer are not. Viscosity Property of the fluid that determines its motion15  Highly viscous fluid move slowly  Less viscous fluids move fast Why? – viscosity influences the shear stress of movement Shear stress – force between two planes as they move over each other Figure 2.1 Shear stress (τ) (tau) is proportional to the velocity gradient τ = ή (Δv/Δy) – equation 2.116 The ή (eta) is referred to as dynamic viscosity Units of ή = N.s/m2 = or = kg/m.s ( = 1 Poise) Kinematic viscosity (ν – nu) Ratio of dynamic viscosity to the density of the fluid ν = ή/ρ units of kinematic viscosity = m2/s Viscosity varies with temperature. Lower viscosity under higher temperatures. --- Engine oil !!! Newtonian & Non-Newtonian Fluids Newtonian fluid – when the viscosity is a function only of the fluid (e.g., temperature). The velocity gradient does NOT have an affect on the viscosity Follows equation 2.117 e.g., - water, oil, gasoline, benzene……. Non-Newtonian Fluid – when the velocity gradient has an affect on the viscosity Two major classifications – time independent, time dependent Three types of time independent fluids – • Psuedoplastic Initially apparent viscosity is high and then decreases e.g., blood plasma, latex, syrups, inks…..18 • Dilatant Initially low viscosity followed by higher viscosity e.g., Starch in water, …… • Bingham Also called plug-flow fluids – need some initial level of shear stress before motion starts e.g., - toothpaste, paint, asphalt, etc. You tube videos illustrating Non-Newtonian fluids! -