VVR 120 Fluid Mechanics 1. Introduction, fluid properties (1.1, and handouts) • Introduction, general information • Course overview • Fluids as a continuum • Density • Compressibility • Viscosity Exercises: A1 VVR 120 Fluid Mechanics Applications of fluid mechanics • Societal supply of safe energy and water by gas and fluids in pipes and channels • Energy production (oil, hydropower, nuclear energy, natural gas) • Environmental engineering and water treatment (channels, basins, filtering) • Industrial process technology (relationship temperature, pressure, and energy) • Protection against climate extremes/catastrophes (flooding, harbours, wind forces) • Biomedical engineering • Ecological evolution of species (predator-prey) VVR 120 Fluid Mechanics Major ”Fluid mechanics” employers • SWECO • Thyréns • WSPgroup • Skanska • Eon, VA SYD • Community offices • Governmental, Naturvårdsverket VVR 120 Fluid Mechanics Fluid mechanics • Fluid properties (2) • Hydrostatics (3) • Basic equations (6) • Pipe flow (5) • Flow around submerged bodies (1) • Channel flow (3) • Repetition (2) VVR 120 Fluid Mechanics FLUID AS A CONTINUUM • A fluid is considered to be a continuum in which there are no holes or voids velocity, pressure, and temperature fields are continuous. • Validity criteria: Smallest length scale in a flow >> average spacing between molecules composing the fluid. VVR 120 Fluid Mechanics VVR 120 Fluid Mechanics DENSITY () Mass/ unit volume (kg/m3) Density decreases normally with increasing temperature water = (T,S,p) i.e., dependent on - Temperature - Salt content ( 1000 + 0.741S, S in per mille; S = 3.5% in ocean = 1026 kg/m3) - Pressure (but only a small variability) VVR 120 Fluid Mechanics OTHER DEFINITIONS • Weight = mass gravity acceleration (W = mg, [N = kgm/s2]) (Eqn. 1.4) • Weight density (or specific weight)= density gravity acceleration (w = g, [N/m3 = kg/(m2s2)]) (Eqn. 1.6) (Note w = γ in exercises) • Specific volume = reciprocal of density ( = 1/, [m3/kg]) • Relative density (or specific gravity), s, is the density normalized with the density of water at a specific temperature and pressure (normally 4C and atmospheric pressure): s = R.d. = /water (often = /1000) (Eqn. 1.7) • Power P [W = J/s = kgm2/s3 = Nm/s]; P = T ω (T = torque, ω = angular velocity [rad/s, 360o = 2rad]; V = ω r (V = velocity, r = radius) VVR 120 Fluid Mechanics Example – density. The specific weight of water at ordinary temperature and pressure is 9.81 kN/m3. The specific gravity of mercury is 13.56. Compute the density of water and the specific weight and density of mercury. VVR 120 Fluid Mechanics COMPRESSIBILITY • All fluids can be compressed by application of pressure elastic energy being stored • Modulus of elasticity describes the compressibility properties of the fluid and is defined on the basis of volume VVR 120 Fluid Mechanics • Modulus of elasticity: E=-dp/(dV/V1) [Pa] • For liquids, region of engineering interest is when V/V1 1 V p V E 9 • Ewater ~ 210 Pa (function of temperature) VVR 120 Fluid Mechanics A1 What pressure must be applied to water to reduce its volume 1 % ? VVR 120 Fluid Mechanics Example – compressibility. At a depth of 8 km in the ocean the pressure is 81.8 MPa. Assume that the specific weight of sea water at the surface is 10.05 kN/m3 and that the average volume modulus of elasticity is 2.34*109 N/m2 for the pressure range. A) What will be the change in specific volume between that at the surface and at that depth? B) What will be the specific volume at that depth? C) What will be the specific weight at that depth VVR 120 Fluid Mechanics IDEAL FLUID A fluid in which there is no friction REAL FLUID A fluid in which shearing forces always exist whenever motion takes place due to the fluid’s inner friction – viscosity. VVR 120 Fluid Mechanics VISCOSITY • Viscosity is a measure of a fluid’s “inner friction” or resistance to shear stress. • It arises from the interaction and cohesion of fluid molecules. • All fluids posses viscosity, but to a varying degree. For instance, syrup has a considerably higher viscosity than water. VVR 120 Fluid Mechanics DEFINITION OF DYNAMIC VISCOSITY - y Shearing of thin fluid film between two plates. The upper plate has an area A. • Experiments have shown that for a large number of fluids: F ~ AV/h (if V and h not too large) • Linear velocity profile V/h = dv/dy VVR 120 Fluid Mechanics • Introduction of the proportionality constant , named dynamic viscosity, gives Newton’s viscosity law shear force: F V dv 2 (Eqn. 4.1-4.2) N/m A h dy [Pas or kg/ms] • = / [m2/s] - Kinematic viscosity • No-slip condition – water particles adjacent to solid boundary has zero velocity (observational fact) VVR 120 Fluid Mechanics μ (Pa·s) VVR 120 Fluid Mechanics Implication of viscosity: a fluid cannot sustain a shear stress without deformation VVR 120 Fluid Mechanics Implications of Newton’s law: • , independent of pressure (in contrast to solids) • no velocity gradient no shear stress Restriction of Newton’s law: • law only valid if the fluid flow is laminar in which viscous action is strong VVR 120 Fluid Mechanics • Laminar flow: smooth, orderly motion in which fluid elements appears to slide over each other in layers (little exchange between layers). • Turbulent flow: random or chaotic motion of individual fluid particles, and rapid mixing and exchange of these particles through the flow Turbulent flow is most common in nature. VVR 120 Fluid Mechanics Newtonian – non-Newtonian fluids Examples non-Newtonian fluids: Plastics, blood, suspensions, paints, foods Shear vs. rate of strain re- lations for non-Newtonian fluids: Bingham plastic du , i dy i n>1: Shear-thickening fluid, n<1: Shear-thinning fluid du n ( ) dy VVR 120 Fluid Mechanics Example – density. The specific weight of water at ordinary temperature and pressure is 9.81 kN/m3. The specific gravity of mercury is 13.56. Compute the density of water and the specific weight and density of mercury. VVR 120 Fluid Mechanics A1 What pressure must be applied to water to reduce its volume 1 % ? VVR 120 Fluid Mechanics Example – compressibility. At a depth of 8 km in the ocean the pressure is 81.8 MPa. Assume that the specific weight of sea water at the surface is 10.05 kN/m3 and that the average volume modulus of elasticity is 2.34*109 N/m2 for the pressure range. A) What will be the change in specific volume between that at the surface and at that depth? B) What will be the specific volume at that depth? C) What will be the specific weight at that depth.