lab1_Exercise_Note - 57:020 Mechanics of Fluids &...

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-1- 57:020 Mechanics of Fluids & Transfer Processes Exercise Notes for Fluid Property TM Measurement of Density and Kinematic Viscosity Marian Muste, Surajeet Ghosh, Stuart Breczinski, and Fred Stern 1. Purpose The purpose of this investigation is to provide Hands-on experience using a table-top facility and simple measurement systems to obtain fluid property measurements (density and kinematic viscosity), comparing results with manufacturer values, and implementing standard EFD uncertainty analysis. Additionally, this laboratory will provide an introduction to camera settings and flow visualization for the ePIV system with a circular cylinder model. 2. Experimental Design 2.1 Part 1: For Determination of Fluid Properties Common methods used for determining viscosity include the rotating-concentric-cylinder method (Engler viscosimeter) and the capillary-flow method (Saybolt viscosimeter). In the present experiment we will measure the kinematic viscosity through its effect on a falling object in still fluid (figure1). The maximum velocity attained by an object in free fall (terminal velocity) is inversely proportional to the viscosity of the fluid through which it is falling. When terminal velocity is attained, the body experiences no acceleration, and so the forces acting on the body are in equilibrium. Figure 1. Schematic of the experimental setup The forces acting on the body are the gravitational force, g 6 D = mg = F sphere g 3 π ρ (1) the force due to buoyancy, g 6 D = F fluid b 3 (2) and the drag force, the resistance of the fluid to the motion of the body, which is similar to friction. For Re << 1 ( Re is the Reynolds number, defined as Re = VD / ν ), the drag force on a sphere is described by the Stokes expression, D V 3 = F fluid d ν (3) where, D is the sphere diameter, fluid is the density of the fluid, sphere is the density of the falling sphere, is the kinematic viscosity of the fluid, V is the velocity of the sphere through the fluid (in this case, the terminal velocity), and g is the acceleration due to gravity (White 1994). Once terminal velocity is achieved, a summation of the vertical forces must balance. This gives: λ 18 t 1) - / ( g D = fluid sphere 2 / ) ( (4) where t is the time taken for the sphere to fall the vertical distance λ . Using equation (4) for two different materials, Teflon and steel spheres, the following relationship for the F F F λ V Sphere falling at terminal velocity b d g
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-2- density of the fluid is obtained, where subscripts s and t refer to the steel and Teflon spheres, respectively. ) /( ) ( 2 t D - t D t D - t D = s 2 s t t s s 2 s t t 2 t fluid ρ (5) In this experiment, we will drop spheres (Steel and Teflon), each set of spheres having a different density and diameter, through a long transparent cylinder filled with glycerin (Figure 1). Two horizontal lines are marked on the vertical cylinder. The sphere will reach terminal velocity before entering this region, and will fall between these two lines at constant velocity. We will measure the time required for the sphere to fall through the distance λ . The measurement system includes:
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This note was uploaded on 12/08/2011 for the course MECHANICS 57:020 taught by Professor Fredrickstern during the Fall '10 term at University of Iowa.

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lab1_Exercise_Note - 57:020 Mechanics of Fluids &amp;...

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