A large cone-shaped container (height H and radius R) is fed a liquid solution of density ρ at aconstant flow rate q0 . The solution evaporates from its top surface exposed to the sun.(a) Assuming that the rate of evaporation is proportional to the area of the surface with aconstant K (kg/m 2 .s), develop a differential equation for the variation with time of the level ofthe liquid in the container.(b) What should be the feed flow rate to maintain the fluid level constant once it reaches adesired value h*?(c) If the feed was zero, would the rate of change of the level of the fluid depend on the shapeof the cone-shaped container (H,R dimensions)
A large cone-shaped container (height H and radius R) is fed a liquid solution of density ρ at aconstant flow rate q0 . The solution evaporates from its top surface exposed to the sun.(a) Assuming that the rate of evaporation is proportional to the area of the surface with aconstant K (kg/m 2 .s), develop a differential equation for the variation with time of the level ofthe liquid in the container.(b) What should be the feed flow rate to maintain the fluid level constant once it reaches adesired value h*?(c) If the feed was zero, would the rate of change of the level of the fluid depend on the shapeof the cone-shaped container (H,R dimensions)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
A large cone-shaped container (height H and radius R) is fed a liquid solution of density ρ at a
constant flow rate q0 . The solution evaporates from its top surface exposed to the sun.
(a) Assuming that the rate of evaporation is proportional to the area of the surface with a
constant K (kg/m 2 .s), develop a differential equation for the variation with time of the level of
the liquid in the container.
(b) What should be the feed flow rate to maintain the fluid level constant once it reaches a
desired value h*?
(c) If the feed was zero, would the rate of change of the level of the fluid depend on the shape
of the cone-shaped container (H,R dimensions)
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