(1) From assumption (b), show that the radius of the water droplet at time t is r(t) = ()t+ro. %3D (Hint: m = pV,V =tr³, S = 4r²). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is v' + v%3 g. t+To If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.
(1) From assumption (b), show that the radius of the water droplet at time t is r(t) = ()t+ro. %3D (Hint: m = pV,V =tr³, S = 4r²). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is v' + v%3 g. t+To If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.
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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Question no.3
![A water droplet evaporates before they reach the ground.
ond orde
E
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.
quati
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
on
er
r(t) = () t + ro-
%3D
(or
(Hint: m = pV,V =nr³, S = 4r2).
4
%3D
3
%3D
(2) From assumption (c), the velocity (v) at time (t) of the water droplet is
ou
3
v' +
t+ro
If the water drops from stationary, solve for v(t).
(3) Determine the time when the water droplet has evaporated entirely, given that
ro = 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fbbe91e-b101-441b-b5fc-9477065585b8%2F0ff458eb-9125-4735-ba3a-41dcb98cff21%2Fkeky5wb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A water droplet evaporates before they reach the ground.
ond orde
E
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.
quati
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
on
er
r(t) = () t + ro-
%3D
(or
(Hint: m = pV,V =nr³, S = 4r2).
4
%3D
3
%3D
(2) From assumption (c), the velocity (v) at time (t) of the water droplet is
ou
3
v' +
t+ro
If the water drops from stationary, solve for v(t).
(3) Determine the time when the water droplet has evaporated entirely, given that
ro = 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.
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