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(ot)] (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 -> ∞)?
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(ot)] (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 -> ∞)?
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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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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