Air (p = 1.2 kg/m, = 1.8 x 10-5 Pa-s) flows through a 2 m...

 

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Air (p = 1.2 kg/m³, μ = 1.8 x 10-5 Pa-s) flows through a 2 m x 1m flat plate and a sphere. Attached to the plate is a string, and at the end of the string is a 40-cm diameter sphere. The flat plate is cantilevered at the bottom to keep it in place. a.) Determine the maximum speed of air to maintain a laminar boundary layer at the trailing edge of the plate. b.) At this speed, compute the thickness of the boundary layer and shear stress at the trailing edge of the flat plate. c.) Find the total friction drag on the flat plate. d.) If the string is inclined 30° from the horizontal at this speed, what is the weight of the sphere? The coefficient of drag of the sphere can be determined from the graph provided below as a function the Reynolds number. Darcy friction factor, f 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.025 0.02 ●‒‒‒‒‒ Laminar Transitional Turbulent flow flow flow N 0.01 0.009 0.008 Laminar flow 64/Re Material 0.015 Glass, plastic Concrete Wood stave Rubber, smoothed Copper or brass tubing Cast iron Galvanized iron Wrought Iron Stainless steel Commercial steel ft 0 0.003-0.03 0.0016 0.000033 0.000005 0.00085 0.0005 0.00015 0.000007 0.00015 Moody Diagram Roughness, mm 0 0.9-9 05 0.01 0.0015 0.26 015 0.046 0.002 0.045 Fully rough turbulent flow (f levels off) Smooth pipes e/D=0 e/D-0.000005 0.05 0.04 0.03 0.02 0.015 0.01 0.008 0.006 0.004 0.002 0.001 0.0008 0.0006 0.0004 0.0002 0.0001 0.00005 /D-0.000001 --▬▬▬▬▬▬▬▬ 0.00001 103 2(10) 3 4 5 6 8 104 2(10) 3 4 5 6 8 105 2(10) 3 4 5 6 8 10 2(10) 3 4 5 6 8 107 2(10) 3 4 5 6 8 108 Source: Cengel and Cimbala, 2006. Figure A-12. Reynolds number, Re Relative roughness, e/D Air (p = 1.2 kg/m³, μ = 1.8 x 10-5 Pa-s) flows through a 2 m x 1m flat plate and a sphere. Attached to the plate is a string, and at the end of the string is a 40-cm diameter sphere. The flat plate is cantilevered at the bottom to keep it in place. a.) Determine the maximum speed of air to maintain a laminar boundary layer at the trailing edge of the plate. b.) At this speed, compute the thickness of the boundary layer and shear stress at the trailing edge of the flat plate. c.) Find the total friction drag on the flat plate. d.) If the string is inclined 30° from the horizontal at this speed, what is the weight of the sphere? The coefficient of drag of the sphere can be determined from the graph provided below as a function the Reynolds number. Darcy friction factor, f 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.025 0.02 ●‒‒‒‒‒ Laminar Transitional Turbulent flow flow flow N 0.01 0.009 0.008 Laminar flow 64/Re Material 0.015 Glass, plastic Concrete Wood stave Rubber, smoothed Copper or brass tubing Cast iron Galvanized iron Wrought Iron Stainless steel Commercial steel ft 0 0.003-0.03 0.0016 0.000033 0.000005 0.00085 0.0005 0.00015 0.000007 0.00015 Moody Diagram Roughness, mm 0 0.9-9 05 0.01 0.0015 0.26 015 0.046 0.002 0.045 Fully rough turbulent flow (f levels off) Smooth pipes e/D=0 e/D-0.000005 0.05 0.04 0.03 0.02 0.015 0.01 0.008 0.006 0.004 0.002 0.001 0.0008 0.0006 0.0004 0.0002 0.0001 0.00005 /D-0.000001 --▬▬▬▬▬▬▬▬ 0.00001 103 2(10) 3 4 5 6 8 104 2(10) 3 4 5 6 8 105 2(10) 3 4 5 6 8 10 2(10) 3 4 5 6 8 107 2(10) 3 4 5 6 8 108 Source: Cengel and Cimbala, 2006. Figure A-12. Reynolds number, Re Relative roughness, e/D

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