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Transport Phenomena

Transport Phenomena. Lab 4. Topics to be covered. Transport Phenomena Energy Mass Momentum (fluid) Viscosity and rheology Falling ball viscometers examine the effect of viscosity on object falling through the fluid. Energy Fighter jet cooling Radiators Air conditioners Mass

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Transport Phenomena

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  1. Transport Phenomena Lab 4 Autumn Quarter

  2. Topics to be covered • Transport Phenomena • Energy • Mass • Momentum (fluid) • Viscosity and rheology • Falling ball viscometers • examine the effect of viscosity on object falling through the fluid. Autumn Quarter

  3. Energy Fighter jet cooling Radiators Air conditioners Mass Intracellular transfer Momentum (i.e. fluid) Pumps Airplane flight Water flow Applications all over engineering: Mechanical Chemical Aeronautical Biomedical Civil Industrial Systems Materials Science Transportation applications Autumn Quarter

  4. Flow Direction O2 N2 valve Energy and Mass Transport Mechanisms Energy Transport Difference in temperature is the driving force for heat transfer. Mass Transport Difference in concentration is the driving force for mass transfer. Autumn Quarter

  5. Momentum (Fluid) Transport • Flow types • Turbulent flow • Laminar flow • Velocity Gradient • Viscosity • Reynolds Number Autumn Quarter

  6. If pressure drop is large, flow will be relatively large - fluid motion is chaotic and transfer is with blocks of molecules moving in all directions, causing eddy currents. Flow Direction Momentum transport Mechanisms Difference in pressure is the driving force, causing fluid to flow Turbulent flow (Eddy) Autumn Quarter

  7. Momentum transport Mechanisms Difference in pressure is the driving force, causing fluid to flow If pressure drop is small across the object, fluid motion is smooth and transfer is molecular. That is, momentum transfers from molecule to molecule through the fluid. Fluid flows in layers Laminar flow ( Molecular) Autumn Quarter

  8. Velocity Gradient (dVx/dy) There is a gradient of velocity as you move from the stationary to the moving plate, and the liquid tends to move in layers with successively higher speed In case of fluid through a pipe, the velocity of flow varies from zero at the walls to a maximum along the centerline of the pipe. Autumn Quarter

  9. Viscosity – A fluid flow property • Internal property of a fluid that offers resistance to flow – it is a measure of how easily a fluid can flow. • Results from cohesion and molecular momentum exchange between fluid layers – as flow occurs, these appear as shearing stresses between moving layers. • It can also be viewed as a resistance to shear force, more viscous the fluid is, higher the resistance. Autumn Quarter

  10. Coefficient of Viscosity (μ) Under conditions of laminar flow, the force (F) required to move a plate at constant speed against the resistance of a fluid is proportional to the area of the plate (A) and to the velocity gradient (dVx/dy) perpendicular to the plate. • F = μ A (dVx/dy) (or) • τ= μ (dVx/dy) where, τis shear stress per unit area • Newtons Law of Viscosity Unit (SI): kg m-1 s-1 (preferred) or Pa-s Autumn Quarter

  11. Reynolds Number (Re) • Re is a dimensionless parameter that describes flow and is defined as Re = DVρ/µ • D: Characteristic length scale (such as diameter of a pipe, diameter or length of a body) (m) • V: Characteristic Velocity (m/s) • ρ: Density of fluid (kg/m3) • µ: Viscosity of fluid (kg/ms) • Ratio µ/ρ is called Kinematic Viscosity of fluid, usually expressed in (m2/s) Autumn Quarter

  12. Re and Critical Velocity • At a critical value of Re, flow will change from laminar to turbulent - the flow velocity at which this occurs is called the critical velocity. • Critical Re changes based on application – there are no analytical methods for predicting critical Re available due to complex origins of turbulence. Autumn Quarter

  13. Re and Critical Velocity • For fluid flow through pipes, critical Re  2000 • Re < 2000 for laminar • Re >> 2000 for turbulent • 2000 < Re < 4000 is transition region – laminar or turbulent • Critical Re changes for different flow types: •  1 for object moving in a fluid (this lab) •  1000 for flow between parallel walls •  500 for flow in a wide open channel Autumn Quarter

  14. Falling Sphere Viscometer Vt • Requires a transparent vertical tube filled with test fluid and the object (a sphere). • When object starts to drop (free fall), it accelerates downward till it reaches a maximum velocity – called terminal velocity (Vt). • Terminal velocity affected by • Density, viscosity of the fluid • Shape, size, density of object • Measure terminal velocity. Assume: Sphere attains terminal velocity here Autumn Quarter

  15. Sphere at terminal velocity (Vt) Fd = Fg – Fb Fd Fb Fg Falling Sphere Viscometer • When body attains terminal velocity, body experiences no acceleration – forces acting on the body are in equilibrium. • Magnitude of terminal velocity should result in a low Re – critical Re is about 1. • Gravitational Force (Fg) depends on: • Density of sphere • Radius of sphere • Acceleration due to gravity Autumn Quarter

  16. Fd Fb Fg Falling Sphere Viscometer • Force due to buoyancy (Fb) depends on: • Density of fluid • Radius of sphere • Acceleration due to gravity • Drag force (Fd) is the resistance of the fluid to motion of body given by Stokes law, depends on: • Absolute viscosity of fluid • Terminal Velocity (Vt) • Radius of sphere Fd = Fg – Fb Autumn Quarter

  17. Falling Sphere Viscometer Design should consider: • Terminal velocity of object through fluid Should yield Re << 1 for laminar flow. Start recording after sphere attains terminal velocity. Assume sphere attains terminal velocity here Vt • Wall effects Ratio of diameter of sphere to diameter of cylinder should be as small as possible. • Bottom effects To ensure minimal error, we stop recording before a specific height from the bottom of cylinder. Bottom effect considerations Autumn Quarter

  18. Lab Report Requirements - in pairs • Analysis and discussion of the two fluids at your table plus a third fluid from the lab website • Position/time plots with trendlines • Analysis and discussion of the velocities from each group in the class • Comparison of group data against class • Determination of Reynolds number and viscosity for each fluid Autumn Quarter

  19. Today’s Goals • Collect data using the LabVIEW application • Save at least 6 .csv files – 3 per fluid using the two fluids at your table • Collect 6 sample Vt (3 per fluid) and report to the front, as described at end of procedure: • Open your .csv files and determine Vt by fitting trendlines and calculating total velocity Autumn Quarter

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