. A dolphin tank at Sea World is being filled. The tank has a volume of 50,000 liters. In order not to keep the dolphins in their small holding pools too long, they are released into the large tank when it is half full. Pure water is being pumped into the tank at 100 L/min. The dolphins release waste into the tank at a rate of 200 mg/min. Even though the tank is being filled, the waste removal system is operating and pumps 2 L/min of fluid from the tank. A) Derive a differential equation for the amount of waste in the tank as time goes on. B) Solve the differential equation (as much as possible by hand). C) How much waste will be in the tank when it finally fills?
. A dolphin tank at Sea World is being filled. The tank has a volume of 50,000 liters. In order not to keep the dolphins in their small holding pools too long, they are released into the large tank when it is half full. Pure water is being pumped into the tank at 100 L/min. The dolphins release waste into the tank at a rate of 200 mg/min. Even though the tank is being filled, the waste removal system is operating and pumps 2 L/min of fluid from the tank. A) Derive a differential equation for the amount of waste in the tank as time goes on. B) Solve the differential equation (as much as possible by hand). C) How much waste will be in the tank when it finally fills?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:. A dolphin tank at Sea World is being filled. The
tank has a volume of 50,000 liters. In order not to
keep the dolphins in their small holding pools too
long, they are released into the large tank when it
is half full. Pure water is being pumped into the
tank at 100 L/min. The dolphins release waste into
the tank at a rate of 200 mg/min. Even though the
tank is being filled, the waste removal system is
operating and pumps 2 L/min of fluid from the
tank.
A) Derive a differential equation for the amount of
waste in the tank as time goes on.
B) Solve the differential equation (as much as
possible by hand).
C) How much waste will be in the tank when it
finally fills?
D) Once the tank fills, only the waste removal
system is operating, so 2 L/min of water is removed
from the tank, cleaned, and then returned to the
tank. Derive a differential equation for the amount
of waste in the tank after it fills.
E) Solve the new differential equation.
F) What is the long term outlook for the amount of
waste in the tank?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
