MATH103 April 2010
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Question 06 (b)
The height of fluid, in a cylindrical container is controlled by a pump so that it satisfies the differential equation
where , are constants, and is the initial height of the fluid.
(b) At what time will the container be empty?
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The container is empty when the height of the fluid in the container is zero.
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To find the time tempty when the height h(tempty) is zero we calculate
Solving for tempty yields
Note: The differential equation is no longer valid after this time, because a negative height of fluid in a tank does not make sense.
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