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ChemE_3230_PS2_2011 - through 10 miles of piping[30 points...

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ChemE 3230 (Spring 2011) Problem Set #2 (Due by 02/18/2011) 1.0 You are given a liquid (SG = 0.97) and asked to determine its viscosity. You place the fluid in a large open container to which a 20 cm long, smooth vertical tube, with inside diameter of 4 mm, is attached at the bottom. When the depth of the liquid in the large container is 10 cm., you observe that it drains out through the opening at the end of the tube at a rate of 0.25 cm 3 /s. If the diameter of the container is much larger than that of the tube, what is the liquid’s viscosity? [20 points] 2.0 Water is flowing at a rate rate of 700 gpm through a horizontal 2 in. schedule 40S commercial steel pipeline at 90 o F. If the pressure drops by 2.23 psi over a 100 ft length of pipeline: (a) What is the value of the Reynolds number? (b) What is the magnitude of the pipe wall roughness? (c) What is the differential pressure required move the water at this flow rate
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Unformatted text preview: through 10 miles of piping? [30 points] 3.0 A series of experiments suggest that the electrical power P required to drive a ceiling fan principally depends upon the impeller diameter ( D ), the impeller rotational speed ( ω ), the air density ( ρ ), and the volumetric flow rate of air moved, Q . (a) Explain why the viscosity of the air μ is not important in this case. (b) What is the minimum number of fundamental dimensions required to define these variables? (c) How many dimensionless groups are required to determine the relationship between P and the other variables? (d) Find these groups by dimensional analysis, and arrange your results so that the power and volume flow rate appear in only one group. (e) How might one use your result to design a much larger scale fan for use in a football stadium? [35 points] 4.0 Denn 3.7 [20 points] 5.0 Denn 3.9 [25 points]...
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