01-1. Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV :-kA dt where V = volume (mm³), t = time (min), k = the evaporation rate (mm/min), and A = surface area (mm?). Use Euler's method to compute the volume of the droplet from t = o to 10 min using a step size of o.25 min. Assume that k = 0.1 mm/min and that the droplet initially has a radius of 3 mm. Assess the validity of your results by detemining the radius of your final computed volume and verifying that it is consistent with the evaporation rate.
01-1. Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV :-kA dt where V = volume (mm³), t = time (min), k = the evaporation rate (mm/min), and A = surface area (mm?). Use Euler's method to compute the volume of the droplet from t = o to 10 min using a step size of o.25 min. Assume that k = 0.1 mm/min and that the droplet initially has a radius of 3 mm. Assess the validity of your results by detemining the radius of your final computed volume and verifying that it is consistent with the evaporation rate.
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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Transcribed Image Text:01-1. Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area.
dv
= -kA
dt
where V = volume (mm³), t = time (min), k = the evaporation rate (mm/min), and A = surface area
(mm?). Use Euler's method to compute the volume of the droplet from t = 0 to 10 min using a step
size of 0.25 min. Assume that k = 0.1 mm/min and that the droplet initially has a radius of 3 mm.
Assess the validity of your results by determining the radius of your final computed volume and
verifying that it is consistent with the evaporation rate.
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