Two cylindrical water tanks are vertically connected to each other. Initially, the top and bottom tank contain 100 litres and 200 litres of water, respectively. At time t = 0, the valve between the tanks is opened. The flow rate through each of these valves is proportional to the volume of the water in the tank above the valve. The rate at which the volume for both tanks are given in the following differential equations. dvi = Vy dt Rate of volume change for the top tank, Rate of volume change for the bottom tank, dvz dt a) By taking Llv, ()) = V,(6) and L[vz(t)] = V,(6), show that %3D 100s 100 200 V,(s) = 5 +1 200s V2(s) = +1 s +1 and %3D s +1 b) Use Laplace transforms to determine v, (t) and v2 (t). Then, find the volume of the water in the top and bottom tank after 30 minutes.

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
Two cylindrical water tanks are vertically connected to each other. Initially, the top and
bottom tank contain 100 litres and 200 litres of water, respectively. At time t= 0, the valve
between the tanks is opened. The flow rate through each of these valves is proportional to
the volume of the water in the tank above the valve. The rate at which the volume for both
tanks are given in the following differential equations.
dvi
= V,
dt
Rate of volume change for the top tank,
Rate of volume change for the bottom tank, dvz
dt
= -V
a) By taking Llv, ()) = V,(6) and L[vz(t)] = V,(6), show that
%3D
100s
100
200
V,(s) = 5 +1
200s
V,(s) = 52 +1
and
s? + 1
g2 +1
b)
Use Laplace transforms to determine v, (t) and v2 (t). Then, find the volume of the
water in the top and bottom tank after 30 minutes.
Transcribed Image Text:Two cylindrical water tanks are vertically connected to each other. Initially, the top and bottom tank contain 100 litres and 200 litres of water, respectively. At time t= 0, the valve between the tanks is opened. The flow rate through each of these valves is proportional to the volume of the water in the tank above the valve. The rate at which the volume for both tanks are given in the following differential equations. dvi = V, dt Rate of volume change for the top tank, Rate of volume change for the bottom tank, dvz dt = -V a) By taking Llv, ()) = V,(6) and L[vz(t)] = V,(6), show that %3D 100s 100 200 V,(s) = 5 +1 200s V,(s) = 52 +1 and s? + 1 g2 +1 b) Use Laplace transforms to determine v, (t) and v2 (t). Then, find the volume of the water in the top and bottom tank after 30 minutes.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
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,