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Question 1 - 20 marks (a) A tiny aerosol particle of density P, and characteristic diameter D, falls in air of density e and viscosity u (Figure Q1a). If the particle is small enough, the creeping flow approximation is valid, and the terminal settling speed of the particle V depends only on D., H, gravitational constant 9, and the density different (P.-). Use dimensional analysis to generate a relationship for V as a function of the independent variables. . Pp tor Figure Qla (20 marks) 0.1 0,09 Lamisar Transitional Turbulent flow flow flow 0.08 Fully rough turbulent flow levels off) 0.07 0.05 0.04 0.03 EM211/BEM2033 Fluid Mechanics 0.06 0,05 0.02 0.015 0.04 0.01 0.008 0.006 Laminar flow. = 64/Re 0.03 Darcy friction factor, 0.004 Relative roughness, s/D 0.025 Appendix 1 0.002 Smooth pipes 0.02 0.001 Roughnesse 0.0008 Material 0.0006 ft 0.015 Glass, plastic 0.0004 0 Concrete 0.003 0.03 09.9 Woodstave 00016 05 0.0002 Rubber, smoothed DO033 001 Copper or brass tubing ID=0 0.000005 0.0015 Castin 0. 0.0001 0.26 0.01 Galvanized iron 0.0005 0.15 0.00005 Wought iron 0.0015 0.046 0.009 Stainless steel e/D=0.000005 0.0007 0.002 Commercial steel 0045 e/D=0.000001 0.008 LLLL 0.00001 103 2109) 3 4 5 6 8 104 2(105) 3 4 5 6 8 105 2105 3 4 5 6 8 106 2(105) 3 4 5 6 8 107 2010 )3 4 5 6 8 109 Reynolds number, Re 0.00015 Test 2 (Jan-Apr 2022)