22. Burning fuel droplet-D. A droplet of liquid fuel has an initial diameter of Do. As it burns in air, it loses mass at a rate proportional to its current surface area. If the droplet takes a time t, to burn completely, prove that its diameter D varies with time according to: t D = Do ( 1 to If the droplet falls in laminar flow under gravity, prove that the distance x it has descended is governed by the differential equation: dx 1 18µ 3DD,\ dx g = dt = 0, dt2 D2 to where p is the droplet density (much greater than that of air) and u is the viscosity of the air. (Since D depends on t, this differential equation is fairly complicated, and its solution would most readily be obtained by a numerical method.) If the droplet is always essentially at its terminal velocity, prove that the distance L it will fall before complete combustion is given by: Dipgts L = 54и
22. Burning fuel droplet-D. A droplet of liquid fuel has an initial diameter of Do. As it burns in air, it loses mass at a rate proportional to its current surface area. If the droplet takes a time t, to burn completely, prove that its diameter D varies with time according to: t D = Do ( 1 to If the droplet falls in laminar flow under gravity, prove that the distance x it has descended is governed by the differential equation: dx 1 18µ 3DD,\ dx g = dt = 0, dt2 D2 to where p is the droplet density (much greater than that of air) and u is the viscosity of the air. (Since D depends on t, this differential equation is fairly complicated, and its solution would most readily be obtained by a numerical method.) If the droplet is always essentially at its terminal velocity, prove that the distance L it will fall before complete combustion is given by: Dipgts L = 54и
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:22. Burning fuel droplet-D. A droplet of liquid fuel has an initial diameter
of Do. As it burns in air, it loses mass at a rate proportional to its current surface
area. If the droplet takes a time t, to burn completely, prove that its diameter D
varies with time according to:
D = Do ( 1
to
(1-).
If the droplet falls in laminar flow under gravity, prove that the distance x it
has descended is governed by the differential equation:
18u
3DDo
dx
g = 0,
1
dt2
D2
to
dt
where p
the droplet density (much greater than that of air) and u is the viscosity
of the air. (Since D depends on t, this differential equation is fairly complicated,
and its solution would most readily be obtained by a numerical method.)
If the droplet is always essentially at its terminal velocity, prove that the
distance L it will fall before complete combustion is given by:
Dipgt.
L =
54µ
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