Transcript unit-1
Mechanics of Fluids I.GNANASEELAN lecturer, department of mechanical Engineering, Parisutham institute of technology and science Mechanics of Fluids SEQUENCE OF CHAPTER 1 Introduction Objective History Definition of a fluid Dimension and units Fluid properties Continuum Concept of system and control volume Introduction • Defined: the science that deals with the forces on fluids and their actions. • Fluids: a substance consisting of particles that change their position relative to each other. • A substance that will continuously deform when shear stress is applied to it. • Solids resist stress, do not easily deform. Objectives Identify the units for the basic quantities of time, length, force and mass. Properly set up equations to ensure consistency of units. Define the basic fluid properties. Identify the relationships between specific weight, specific gravity and density, and solve problems using their relationships. History Faces of Fluid Mechanics Archimedes (C. 287-212 BC) Navier (1785-1836) Newton (1642-1727) Stokes (1819-1903) Leibniz (1646-1716) Reynolds (1842-1912) Fluid Mechanics Bernoulli Euler (1667-1748) (1707-1783) Prandtl Taylor (1875-1953) (1886-1975) 5 Fluid Mechanics • Definition – The study of liquids and gases at rest (statics) and in motion (dynamics) • Engineering applications – – – – – Blood in capillaries Oil in pipelines Groundwater movement Runoff in parking lots Pumps, filters, rivers, etc. States of Matter • Fluids (gasses and liquids) and solids • What’s the difference? – Fluid particles are free to move among themselves and give way (flow) under the slightest tangential (shear) force Shear Stress t Solid Fluid Classes of Fluids • Liquids and gasses – What’s the difference? – Liquids: Close packed, strong cohesive forces, retains volume, has free surface – Gasses: Widely spaced, weak cohesive forces, free to expand Free Surface Expands Liquid Gas Common Fluids • Liquids: – water, oil, mercury, gasoline, alcohol • Gasses: – air, helium, hydrogen, steam • Borderline: – jelly, asphalt, lead, toothpaste, paint, pitch Dimensions and Units • The dimensions have to be the same for each term in an equation • Dimensions of mechanics are L – length T – time M – mass F ma – force – temperature MLT-2 Dimensions and Units Quantity Symbol Velocity V Acceleration a Area A Volume Discharge Q Pressure p Gravity g Temperature T’ Mass concentration C Dimensions LT-1 LT-2 L2 L3 L3T-1 ML-1T-2 LT-2 ML-3 Dimensions and Units Quantity Symbol Dimensions Density Specific Weight Dynamic viscosity Kinematic viscosity Surface tension Bulk mod of elasticity r g m E fluid properties! These are _______ How many independent properties? _____ 4 ML-3 ML-2T-2 ML-1T-1 L2T-1 MT-2 ML-1T-2 Fluid Properties • Density: Mass per unit volume – How large is the volume? • Too small: # molecules changes continuously • Large: # molecules remains almost constant – At these scales, fluid properties (e.g., density) can be thought of as varying continuously in space. r m V V * V lim Density • Mass per unit volume (e.g., @ 20 oC, 1 atm) – Water – Mercury – Air rwater = 1000 kg/m3 rHg = 13,500 kg/m3 rair = 1.22 kg/m3 • Densities of gasses increase with pressure • Densities of liquids are nearly constant (incompressible) for constant temperature • Specific volume = 1/density Specific Weight g rg [ N / m3 ] or [lbf / ft 3 ] • Weight per unit volume (e.g., @ 20 oC, 1 atm) gwater = (998 kg/m3)(9.807 m2/s) = 9790 N/m3 [= 62.4 lbf/ft3] gair = (1.205 kg/m3)(9.807 m2/s) = 11.8 N/m3 [= 0.0752 lbf/ft3] Specific Gravity • Ratio of fluid density to density at STP (e.g., @ 20 oC, 1 atm) SGliquid SGgas – Water – Mercury – Air rliquid r water r gas r air SGwater = 1 SGHg = 13.6 SGair = 1 rliquid 9790 kg / m3 r gas 1.205 kg / m3 Ideal Gas Law • Equation of state pV nRnT p rRT , R Rn / M Rn = universal gas constant M = molecular weight of the gas