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HW1+Solution Spring 2011 - EMA 4121 Homework solution Set#1...

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EMA 4121 Homework solution: Set #1 1. Impinging air jets may be used to clean particles from surfaces. The kinetic energy per unit volume (J/m 3 ) of an air jet at a surface, E r , may be written as: 3 . 1 2 2 - = kd v E r ρ Where: ρ = density of air (1.3 kg/m 3 ) v = air velocity k = proportionality constant (0.4 mm 1.3 ) d = distance from the jet nozzle (10 mm). For a sphere adhered to a flat surface (H 11 = 1x10 -19 J across vacuum, or air): i. What size of particle (diameter) could a hurricane force wind (v = 20 m/s) remove from a surface (assume separation distance of 3 nm)? ii. What size of particle can be removed at v = 340 m/s (speed of sound)? iii. What air velocity would be required to remove a 10 nm particle and a 100 nm particle (assume separation distance of 3 nm)? Solution 1) Assuming that the energy to remove the particle is only the van der Waals interaction, then the required energy is: h 6 R H W 11 vdw - = The energy the jet can provide is E r × V particle and to remove the particle is has to be at least equal with the van der Waals interaction.
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