2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), t = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area 4 of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.
2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area. dV = -kA dt where V = volume in (mm³), t = time in (min), k = the evaporation rate in (mm/min), and A = surface area in (mm³). (a) Express the area 4 of the differential equation above in terms of V. Using the resulting differential equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm. The table is similar to this: (b) Asses the validity of the result by determining the radius of your final computed volume, and compute the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this value with the given evaporation rate k.
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:2. A spherical droplet of liquid evaporates at a rate that is proportional to its surface area.
dV
= -kA
dt
where V = volume in (mm³), 1 = time in (min), k = the evaporation rate in (mm/min), and A = surface area
in (mm³).
(a) Express the area A of the differential equation above in terms of V. Using the resulting differential
equation, apply Euler's method to compute the volume of the droplet from t = 0 to t = 10 min using a step
size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 5 mm.
The table is similar to this:
(b) Asses the validity of the result by determining the radius of your final computed volume, and compute
the evaporation rate (initial radius minus final radius all over time, which is 10 min) then compare this
value with the given evaporation rate k.
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