Fluid Mechanics 3502 Day 1, Spring 2018


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1 Instructor Fluid Mechanics 3502 Day 1, Spring 2018 Dr. Michele Guala, Civil Eng. Department UMN Office hours: (Tue ?) CEGE 162 9:3010:30? Tue Thu CEGE phone (612) (Mon,Wed,Fr) SAFL, 2 third ave SE, # 382, Phone (612) Class webpage Syllabus Introduction Fluid Properties Part I
2 Introduction: Fluid Mechanics Storing Moving Using To design and manage these systems we need to know : The STATE of the Fluid  Usually PRESSURE (p ) and VELOCITY (u,v,w) at TEMPERATURE (T) The interaction of the fluid with its surroundings (Force, Torque, Boundary conditions)
3 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress
4 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag
5 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum n For example, For an arbitrary fixed volume in a steady flow field u u(x,t) Net flow out of volume = u nda = 0 A
6 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum Conservation of Mass (Volume) For steady state Red=control volume Q  volume flow rate Sum of Q in = sum of Q out
7 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum mgh 1 mv 2 Conservation of Energy (Bernoulli If losses are neglected, e.g., steady state ) 2 mgh 1 2 mv 2
8 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum Newton's 2 nd Law Review Dynamics Statics Conservation of Momentum What is resistance force F r? Net External Force = rate of change of momentum A(V j F r V c )(V j V c ) F r
9 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum IN2 IN1 h F y OUT2 F x OUT1
10 Four steps necessary to solve Fluid Mechanics problems 1. Knowing Fluid Properties e.g., Density, Specific Weight, Viscosity Response to shear stress 2. Understanding Forces in Fluids and on their boundaries e.g., Pressure force, Surface tension Lift & Drag drag 3. Using Conservation Equations Mass Energy Momentum 4. Using Dimensional Analysis
11 Fluid Properties Part 1 SolidLiquidGas Solid under shear vs Liquid under Shear Specific Weight Compressible vs. NonCompressible Viscosity Newtonian vs. NonNewtonian Fluids Surface Tension Vapor Pressure
12 Fluid Properties Part 1 SolidLiquidGas Solid under shear vs Liquid under Shear Specific Weight Compressible vs. NonCompressible Viscosity Newtonian vs. NonNewtonian Fluids Surface Tension Vapor Pressure
13 Some properties of fluids Solid Fluid Solid liquid gas How to best distinguish between them? Certain properties, and response to container boundaries Mass, density, weight, and the specifics
14 SolidLiquid and Gas response to stationary boundaries Solid Fluid liquid or gas If no force is applied, a solid will always retain its shape Fluid liquid or gas Gas will always change its volume to completely fill its container No Surface Tension. Summary (See Table 1.1) Fluids Liquid will maintain its volume (mostly) but change its shape according to that of the container. Surface Tension can be important. Solid retains shape & volume Liquid retains volume & deforms Gas retains mass, not volume or shape
15 SolidLiquid and Gas response to forces at the boundaries Imagine an elastic solid held between two platesand then applying a shear force to the top plate A solid resists to an applied force, only if it deforms. When the force decays, the solid returns to its initial position. the force per unit area is a shear stress = F/ Area Then imagine a long aquarium and a wooden block floating on the surface let us apply a force to that block. Top layer of fluid moves with velocity of the block A fluid resists to the applied forces only if it flows (Newtonian fluids): the deformation rate, also known as the shear rate, within the fluid, represent a spatial variation of the fluid velocity. Deformation alone does not create a stress opposing to motion (there is no memory of the initial location of fluid parcels, no crystals matrix...). Bottom layer does not move The NO SLIP condition E.g., in a linear elastic solid, resistance is proportional to the amount of deformation (shear or strain). think about a spring variation in displacement dx/dy E.g., in a Newtonian fluid, resistance is proportional to the shear rate. variation in fluid velocity (dx/dt)/dy = dv/dy
16 Dimensions, Units, etc. Length : L meter [m] 1m=3.281 ft Mass : M kilogram [kg] 1kg=2.2 lbm Time : t seconds [s] Temperature: T Kelvin [K] K=(F32)/ gravity g = 9.81 m/s 2 = 32.3 ft/s 2 density water(t) ~1000kg/m 3 = 62.4 lbm/ft 3 density air (T) ~ 1 kg/m 3
17 Continuum Assumption We discuss the fluid behavior as observed in the range of scale typical of classical mechanics This is the macroscopic averaged behavior of a vast number of molecules. We define the fluid density: ρ = M V = M V to be independent of V In the case of water the continuum assumption is valid down to a cube of about L = 104 mm, = 107 m. In air (standard condition) L = 103 mm Note that the non slip condition must apply when the continuum approach is valid Note also that very large value of L may not be satisfactory due to variation in density within the (very large ) Volume continuity is respected only if we account for variation in density as well
18 Dimensions Primary dimension: M L t Secondary dimensions: e.g. F = ma ; [N] = [kg m s 2 ] = Kg m s 2 Important: 1) always provide Eng. solutions with units, e.g. v = 3 m/s 2) always check that equations are dimensionally consistent LHS (left hand side) = RHS e.g. L = L 0 + v t + gt2 3) often describe physical processes in dimensionless groups v L e.g. Reynolds number = ν 4) often present experimental results in dimensionless form e.g. pipe flow U/U c = 0.3 at y/d=0.1 2
19 Some guidelines on proper scientific writing and homework preparation 1) make a sketch and assign variable names and reference system 2) Define the boundary conditions provide initial values of the known variables 3) Briefly state what is the question of the problem and mark the unknown variable (INTRODUCTION) 4) Describe how you want to approach the problem and present the equations you intend to use 5) List the assumptions that are needed to simplify the problem consistently with the above equations (METHOD) 6) Briefly describe each step of your calculation, using both symbolic variables and actual numbers 7) Make sure that units are always consistent in the equations and in the resulting variables 8) When required, provide figures or graphs that support your statements. Make sure that figure axis are defined (variable name and units) and that in the figure caption all the variable names and symbols used in the axis or legend are briefly described in words. (RESULTS) 9) Highlight the final numerical result and, when required, explain in words the outcome of your work/laboratory experimentation (CONCLUSION)
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