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
icon
Related questions
Question
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 -> ∞)?
Transcribed Image Text: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 -> ∞)?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

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. 

Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,