Question

Problem 2 - MSH Ch5 Energy Balance and Ch 7 Packed Bed (20 pts). Design a porous straw for camping that can remove contaminant from water, so the water is safe to drink. You would want the straw to feel normal in a mouth. Normal straws have 0.60-cm inner diameters and are usually about 19.5 cm long. The suction strength of a normal adult is about 4000 Pa. Assume the contaminated water (only mildly "dirty" or the straw would clog) has physical properties of water. Assume all numbers have at least two significant figures. a) Determine the maximum volumetric flowrate through a normal length straw for a normal adult using full suction as a point of comparison. Most people do not drink a full suction all the time, as that would be tiring. However, when one drinks a milkshake, for example, one does use full suction sometimes. b) Determine the volumetric flowrate through the straw now packed with a resin that is a smooth rigid spherical bead with a density of 2550 kg/m' and a particle diameter of 0.45 mm and a porosity of 0.35. c) Is this flowrate acceptable? Think about how long would you be willing to wait for your drinking water. If not, what parameters to the straw design could be changed to improve the flowrate and still be acceptable to a user. FYI: The contact time of the water with the resin still needs to be maintained to remove the impurities.

Answer 1

flow in a (a) Hagen - Poiseuille's equation for fluid tube is given by, Ap= 8MLQ TR4 where = Length of pipe Q= Volumetric Flow rate. Ap- presure difference R = Radius of pipe. I Me Dynamic Viscosity So, Q = TR? AP = 3.14x (0.3x102) (4000) 8 ML - 8x68,9x6047895x103) = Q = 101.74 x 10s - 0.07327x10-2 m3/s. 1388.4 x 106 - = 7.3277 10 4 m/s = 732.7x10 m/s = 732.7 mils

(b)

(6) Assumptions: 1. Linear Flow 2. Randomly packed beads. att 11Q = Fluid flow 0.45mm Schematic 10.6cm - 6 mm Solecion: Carman Kozeny equation for a with packed spherical beads is column OP = 180 MQ (1.282 where - Porosity of beads dp- diameter of bead M² Dynamic viscosity of flowing fluid AP Suction Pressure Length of size Q = Flow rate

ISOLA Hoool 0.45X70-3)(0:35) 180(19.5410-2)(8.9x104) (0.65) = Q = 15.628x10-9 - 21.82 x 10 m/ 8.58 x 10-3 Q = 1.82x10 3e/sor 1.82mL/8 Note: Ergan equation can also be used here.
(c)

(c) The flow rate of 1.82 mL/s is too lon for dünking water. I would want the tion rate at leart 10 timer higher than this site se nearly 20 mL/s. -- Q = AP 3 ISCL HC-2)3 nity (E), bead diameter (dp) and length of straw (2) can be changed to get a higher speed. The bead diameter can be increased to get better flow rate.