A 1000 m³ capacity rectangular reservoir is 80% filled with pure water. Staring at 7:00 am on Feb 1, a 5% chloric acid solution flows in at 10 L/sec and well-stirred mixture flows out at 20 L/sec. (a) Develop a model for the volume V of the solution in the reservoir and the amount A of dissolved chloric acid as functions of time. Your model should specify a consistent system of units, describe the variables and include differential equations and initial conditions. Note: 1 m³ 1000 L (b) Solve the initial value problems in part (a). (c) At what time of the day will the volume of the liquid in the reservoir drop to 20% of reservoir's capacity? Round off the answer to the nearest minute if necessary. = (d) Determine the formula for the concentration of the chloric acid in the reservoir as a function of time and use it to calculate the concentration of the chloric acid in the reservoir at 5:00 pm on the same day.
A 1000 m³ capacity rectangular reservoir is 80% filled with pure water. Staring at 7:00 am on Feb 1, a 5% chloric acid solution flows in at 10 L/sec and well-stirred mixture flows out at 20 L/sec. (a) Develop a model for the volume V of the solution in the reservoir and the amount A of dissolved chloric acid as functions of time. Your model should specify a consistent system of units, describe the variables and include differential equations and initial conditions. Note: 1 m³ 1000 L (b) Solve the initial value problems in part (a). (c) At what time of the day will the volume of the liquid in the reservoir drop to 20% of reservoir's capacity? Round off the answer to the nearest minute if necessary. = (d) Determine the formula for the concentration of the chloric acid in the reservoir as a function of time and use it to calculate the concentration of the chloric acid in the reservoir at 5:00 pm on the same day.
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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Transcribed Image Text:A 1000 m³ capacity rectangular reservoir is 80% filled with pure water. Staring at 7:00 am
on Feb 1, a 5% chloric acid solution flows in at 10 L/sec and well-stirred mixture flows out
at 20 L/sec.
(a) Develop a model for the volume V of the solution in the reservoir and the amount A of
dissolved chloric acid as functions of time. Your model should specify a consistent system
of units, describe the variables and include differential equations and initial conditions.
Note: 1 m³ 1000 L
(b) Solve the initial value problems in part (a).
(c) At what time of the day will the volume of the liquid in the reservoir drop to 20% of
reservoir's capacity? Round off the answer to the nearest minute if necessary.
=
(d) Determine the formula for the concentration of the chloric acid in the reservoir as a
function of time and use it to calculate the concentration of the chloric acid in the
reservoir at 5:00 pm on the same day.
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