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 Fluid Mechanics5 Faces of Fluid Mechanics Archimedes (C BC) Newton ( ) Leibniz ( ) Euler ( ) Navier ( ) Stokes ( ) Reynolds ( ) Prandtl ( ) Bernoulli ( ) Taylor ( )

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 Fluid Solid Shear Stress 

Classes of Fluids – Liquids: Close packed, strong cohesive forces, retains volume, has free surface Liquids and gasses – What’s the difference? Liquid Free Surface Gas Expands –Gasses: Widely spaced, weak cohesive forces, free to expand

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 – length – time – mass – force – temperature L T M MLT -2 

Dimensions and Units QuantitySymbolDimensions VelocityV LT -1 AccelerationaLT -2 AreaA L 2 Volume  L 3 DischargeQ L 3 T -1 Pressurep ML -1 T -2 Gravityg LT -2 TemperatureT’  Mass concentrationC ML -3

Dimensions and Units QuantitySymbolDimensions Density  ML -3 Specific Weight  ML -2 T -2 Dynamic viscosity  ML -1 T -1 Kinematic viscosity L 2 T -1 Surface tension  MT -2 Bulk mod of elasticityE ML -1 T -2 These are _______ properties! fluid How many independent properties? _____ 4

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.

Density Mass per unit volume 20 o C, 1 atm) – Water  water = 1000 kg/m 3 – Mercury  Hg = 13,500 kg/m 3 – Air  air = 1.22 kg/m 3 Densities of gasses increase with pressure Densities of liquids are nearly constant (incompressible) for constant temperature Specific volume = 1/density

Specific Weight Weight per unit volume 20 o C, 1 atm)  water = (998 kg/m 3 )(9.807 m 2 /s) = 9790 N/m 3 [= 62.4 lbf/ft 3 ]  air = (1.205 kg/m 3 )(9.807 m 2 /s) = 11.8 N/m 3 [= lbf/ft 3 ]

Specific Gravity Ratio of fluid density to density at STP 20 o C, 1 atm) –WaterSG water = 1 –MercurySG Hg = 13.6 –AirSG air = 1

Ideal Gas Law Equation of state R n = universal gas constant M= molecular weight of the gas