Problem4A small river stream flows into a large reservoir and fills it with water. We will assume that the reservoiris cylindrical with a cross sectional area A and height H. The flow in the stream varies with the seasonsand you propose to model it with a sinusoidal function of the form qi(t)=Qo[1-cos(oot)] (m³/s).Use conservation laws to determine the expression of the variation with time of the level of water in thereservoir; h(t). Assume that the reservoir is initially empty at the dry season.What will be the level of water in the reservoir at very long time (t -> ∞)?

At very long time (t -> ∞), the level of water in the reservoir will be at its steady state…

Answered: Problem4 A small river stream flows…

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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Problem4
A small river stream flows into a large reservoir and fills it with water. We will assume that the reservoir
is cylindrical with a cross sectional area A and height H. The flow in the stream varies with the seasons
and you propose to model it with a sinusoidal function of the form qi(t)=Qo[1-cos(oot)] (m³/s).
Use conservation laws to determine the expression of the variation with time of the level of water in the
reservoir; h(t). Assume that the reservoir is initially empty at the dry season.
What will be the level of water in the reservoir at very long time (t -> ∞)?

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Reconsider the previous problem of flow in a water reservoir. In order to control the level of water in the reservoir, and avoid overflow that may flood the surrounding areas, a pump is used to remove water from the reservoir.

An automatic control valve coupled with a sensor allows to adjust the output flow rate by the pump such that it varies with the level of water in the reservoir; qu.h(t) where a has units of m³/s. Determine how the level of water varies when the pump is used. Assume again that the reservoir is initially empty.

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