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, r,is 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 ρV,V = έπr', s= 4πr). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is -v = g. 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.
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, r,is 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 ρV,V = έπr', s= 4πr). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is -v = g. 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.
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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![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, r,is 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 = ρV, V = ;πηό, S 4πr ?).
(2) From assumption (c), the velocity (v) at time (t) of the water droplet is
g.
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%2F4d8c10a9-e41a-481c-9035-6fd4af1c6723%2F6159132f-0b5d-4793-aa1d-b6d4c53672a0%2Fvqu2g1j_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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, r,is 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 = ρV, V = ;πηό, S 4πr ?).
(2) From assumption (c), the velocity (v) at time (t) of the water droplet is
g.
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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