Environmental Engineering CWR 3201 Fluid Mechanics,
Florida International University, Department of Civil andEnvironmental EngineeringCWR 3201 Fluid Mechanics, Fall 2018Fluid Properties1Arturo S. Leon, Ph.D., P.E., D.WRE
1.1 INTRODUCTIONUnderstanding fluid mechanics is needed for: Biomechanics - To understand the flow of blood and cerebral fluid. Meteorology and Ocean Engineering - To understand the motion of air movementsand ocean currents. Chemical Engineering - To design different kinds of chemical-processing equipment. Aeronautical Engineering - To maximize lift, minimize drag on aircraft, and to designfan-jet engines. Mechanical Engineering - To design pumps, turbines, internal combustion engines. Civil Engineering - To design irrigation canals, water distribution systems, floodcontrol systems, etc.2
Motivation for Fluid PropertiesCFD Simulations of Rigid Bodies Falling Under Gravityhttps://www.youtube.com/watch?v LKdii-Y8NQgRoad Erosionhttps://www.youtube.com/watch?v tacW yUArPg3
1.2 DIMENSIONS, UNITS, AND PHYSICAL QUANTITIESFundamental Dimensions - Nine quantities that can express all other quantities.4
1.2 DIMENSIONS, UNITS, AND PHYSICAL QUANTITIESIn general, for the study of mechanics of fluids, four fundamental dimensions are used:Length (L), mass (M), time (T) and temperature ( ) orLength (L), force (F), time (T) and temperature ( )Example: Dimensions of Force in MLTThere are two primary systems of units: English units5 Système International units (SI)
Derived Quantities Combinations of fundamentalquantities to form differentparameters.6
1.2 DIMENSIONS, UNITS, AND PHYSICAL QUANTITIES7
Example 1.1 (textbook): A mass of 100 kg is acted on by a400-N force acting vertically upward and a 600-N force actingupward at a 45o angle. Calculate the vertical component of theacceleration. The rollers are frictionless.8
1.3 CONTINUUM VIEW OF GASES AND LIQUIDS Substances can be both liquids or gases. Liquids - matter in which molecules are relatively free to change their positions withrespect to each other. The molecules are restricted by cohesive forces so as to maintain arelatively fixed volume. Gas – matter in which molecules are unrestricted by cohesive forces. Gas has neitherdefinite shape nor volume. 9A force ΔF that acts on an area ΔA can bebroken into tangential (Ft) and normal (Fn)components.Stress - Force divided by the area uponwhich it acts.
1.3 CONTINUUM VIEW OF GASES AND LIQUIDS Stress Vector - The force vector divided by the area. Normal Stress - Normal component of force divided bythe area. Shear Stress (t) - Tangential force divided by the area.(defined as shown below)10
1.3 CONTINUUM VIEW OF GASES AND LIQUIDS Assume that fluids act as a continuum: A continuous distribution of a liquid or gas throughout a region of interest Density is used to find out if the continuum assumption is appropriate. Δm: Incremental massΔV: Incremental volume Standard Atmospheric Conditions Pressure: 101.3 kPa (14.7 psi, 1.013 bars, 760 mm Hg) Temperature: 15 C (59 F) Density of air: 1.23 kg/m3 (0.00238 slug/ft3) Density of water: 1000 kg/m3 (1.94 slug/ft3)11
1.4 PRESSURE AND TEMPERATURE SCALES The pressure, p, can be defined as:ΔFn: Incremental normalcompressive forceΔA: Incremental areaUnits: N/m2 or Pa Absolute Pressure: Zero is reached for an ideal vacuum. Gage Pressure: Pressure relative to the local atmospheric pressure.12
1.4 PRESSURE AND TEMPERATURE SCALES Temperature scales (Celsius and Fahrenheit scales)Celsius to KelvinFahrenheit to Rankine13
1.5 FLUID PROPERTIES Specific Weight, : Weight per unit volume Units: N/m3 or lb/ft31.5.1 Density and Specific Weightg: Local gravity Specific Gravity, S: Ratio of density of a substance to the density of water at 4 C. Units: Dimensionless14
1.5 FLUID PROPERTIES1.5.1 Density and Specific Weight15
1.5 FLUID PROPERTIES Viscosity, μ: Measure of the resistance of a fluid to gradual deformations by shearstress. Accounts for energy losses in the transport of fluids in ducts or pipes1.5.2 Viscosity Plays a role in the generation of turbulence Units: N.s/m2 or lb-s/ft216
1.5 FLUID PROPERTIES Newtonian fluid: A fluid in which the shear stress is directly proportional to thevelocity gradient. e.g., Air, water, and oil Non-Newtonian fluid: A fluid 1.5.2in whichthe shear stress is NOT directlyViscosity - Newtonian fluidproportional to the velocity gradient. e.g., slurries17
1.5 FLUID PROPERTIES No-slip Condition: Causes fluid to adhere to the surface (due toviscosity)1.5.2 Viscosity - Non-Newtonian fluid kinematic viscosity dynamic viscosity/density Units of kinematic viscosity: m2/s or ft2/s18
Example: P.1.45. For two 0.2-m long rotating concentric cylinders, the velocitydistribution is given by u(r) 0.4/r -1000r m/s, where r is in m. If the diameters of thecylinders are 2 cm and 4 cm, respectively, calculate the fluid viscosity if the torque onSurface Tensionthe inner cylinder is measured to be1.5.40.0026N-m.19
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1.5.3 Compressibility Can be described using the Bulk modulus of elasticity, B. This is the ratio of the change in pressure to relative change in density. Same units as pressure. For gases: Significant changes in density ( 4%) - Compressible. Small density changes (under 3%) - Incompressible. The speed of sound in a liquid can be found using the Bulk modulus of elasticityand density, as shown above.21
Example: P.1.54. Two engineers wish to estimate the distance across a lake. Onepounds two rocks together under water on one side of the lake and the othersubmerges his head and hears a small sound 0.62 s later, as indicated by a very1.5.4 Surface Tensionaccurate stopwatch. What is the distancebetween the two engineers?22
1.5.4 Surface TensionVideo: /fluid-dynamics/v/surface-tension-and-adhesion Results from the attractive forces between molecules. Hence seen only in liquids at an interface (liquid-gas). Forces between molecules in a liquid bulk are equal in all directions. No net force is exerted on them. At an interface, the molecules exert a force that has a resultant force. Holds a drop of water on a rod and limits its size.23
1.5.4 Surface Tension Unit: Force per unit length, N/m or lb/ft. Force results from the length (of fluid in contact with a solid) multiplied by the surface tension. A droplet has one surface. A bubble is a thin film of liquid with an inside and an outside surface.24Pressure in the dropletbalances the surfacetension around thecircumference.Pressure in the bubble isbalanced by the surfacetension forces on the twocircumferences.
1.5 FLUID PROPERTIES1.5.4 Surface Tension As seen before, the internal pressure in a bubble is twice as large as that in adroplet of a similar size. Liquid rises in a glass capillary tube due tosurface tension. The liquid makes a contact angle β with a glasstube. For most liquids (and water) this angle βis zero. Mercury has an angle greater than 90 .25
1.5 FLUID PROPERTIES1.5.4 Surface Tension h: Capillary rise D: Tube diameter σ: Surface tension26
Example: P.1.62. Mercury makes an angle of 130o ( inFig. 1.10) when in contact with clean glass. What distancewill mercury depress in a vertical 0.8-in diameter glasstube? Use 0.032 lb/ft.h27
Additional Examples:P.1.20. Determine the units on c, k and f(t) in𝑑2𝑦𝑑𝑦𝑚 2 𝑐 𝑘𝑦 𝑓 𝑡𝑑𝑡𝑑𝑡28if m is in Kilograms, y is in meters, and t is in seconds
P.1.26. A particular body weighs 60 lb on earth. Calculate its weight on the moon,where g 5.4 ft/s2.29
P.1.49. Calculate the torque needed to rotate the cone shown in Figure P1.49 at 2000rpm if SAE-30 oil at 40oC fills the gap. Assume a linear velocity profile between thecone and the fixed wall.30
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P.1.66. Find an expression for the maximum vertical force F needed to lift a thin wirering of diameter D slowly from a liquid with surface tension .32
Mechanics of Fluids, 4th Edition33Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition34Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition35Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th EditionExample 1.436Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition37Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition38Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th EditionExample 1.739Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition40Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition41Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition42Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition43Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition44Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition45Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition46Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition47Potter, Wiggert, & Ramandan
Mechanics of Fluids, 4th Edition48Potter, Wiggert, & Ramandan
Typical components ofa pipe system49
General Characteristics of pipe flowPipe flow50Open-channel flow
Laminar or Turbulent Flow?(http://www.youtube.com/watch?v WG-YCpAGgQQ)51
Laminar or Turbulent Flow?Typical dye streaks52
Time dependence of fluid velocity ata point53
Understanding fluid mechanics is needed for: Biomechanics - To understand the flow of blood and cerebral fluid. Meteorology and Ocean Engineering - To understand the motion of air movements and ocean currents. Chemical Engineering - To
CropWat software calculated onion crop water requirement R Onion CWR, tomato crop water requirement, R Tomato CWR and pepper water requirement R Pepper CWR. 42 Figure 6: Average monthly recharge to the ground water for the two scenarios; if there was irrigation since 1997 and if there was no irrigation to the present i.e. 2008.
Watco Companies, LLC CWR Plan Procedures for the Installation, Adjustment, Maintenance and Inspection of CWR as Required by 49 CFR 213.118 . Page 1 . Appendix B - Watco Railroads .Attached Appendix B: Lists individual railroads managed by Watco Transportation Services L.L.C. which have adopted these procedures. .
L M A B CVT Revision: December 2006 2007 Sentra CVT FLUID PFP:KLE50 Checking CVT Fluid UCS005XN FLUID LEVEL CHECK Fluid level should be checked with the fluid warmed up to 50 to 80 C (122 to 176 F). 1. Check for fluid leakage. 2. With the engine warmed up, drive the vehicle to warm up the CVT fluid. When ambient temperature is 20 C (68 F .
Fluid Mechanics Fluid Engineers basic tools Experimental testing Computational Fluid Theoretical estimates Dynamics Fluid Mechanics, SG2214 Fluid Mechanics Definition of fluid F solid F fluid A fluid deforms continuously under the action of a s
Jul 09, 2015 · Tiny-Fogger/Tiny F07, Tiny-Compact/Tiny C07 Tiny-Fluid 42 Tiny FX Tiny-Fluid 42 Tiny S Tiny-Fluid 43 Unique 2.1 Unique-Fluid 43 Viper NT Quick-Fog Fluid 44 Viper NT Regular-Fog Fluid 45 Viper NT Slow-Fog Fluid 46 Martin K-1 Froggy’s Fog K-razy Haze Fluid 47 Magnum 2000 Froggy’s Fog Backwood Bay Fluid 48
Fundamentals of Fluid Mechanics. 1 F. UNDAMENTALS OF . F. LUID . M. ECHANICS . 1.1 A. SSUMPTIONS . 1. Fluid is a continuum 2. Fluid is inviscid 3. Fluid is adiabatic 4. Fluid is a perfect gas 5. Fluid is a constant-density fluid 6. Discontinuities (shocks, waves, vortex sheets) are treated as separate and serve as boundaries for continuous .
Motion of a Fluid ElementMotion of a Fluid Element 1. 1. Fluid Fluid Translation: The element moves from one point to another. 3. 3. Fluid Fluid Rotation: The element rotates about any or all of the x,y,z axes. Fluid Deformation: 4. 4. Angular Deformation:The element's angles between the sides Angular Deformation:The element's angles between the sides
ACCOUNTING 0452/12 Paper 1 October/November 2019 1 hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction .
