A water droplet evaporates before they reach the ground. Figure 1: Water droplets (source) In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at time t is r(t) = () t + ro. (Hint: m a oY Y =T
A water droplet evaporates before they reach the ground. Figure 1: Water droplets (source) In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at time t is r(t) = () t + ro. (Hint: m a oY Y =T
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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