Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Two cylindrical water tanks are vertically conected to each otner. ly, the 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. dv1 = v2 dt Rate of volume change for the top tank, Rate of volume change for the bottom tank, dv2 =ーV1 dt a) By taking L[v (t)] = V, (s) and L[v2(t)] = V2 (s), show that %3D 200 100s 200s 100 V, (s) = and V2 (s) = s2 +1 s2 +1 s2 + 1 s2 +1 b) Use Laplace transforms to determine v, (t) and v, (t). Then, find the volume of the water in the top and bottom tank after 30 minutes.

Two cylindrical water tanks are vertically conected to each otner. ly, the 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. dv1 = v2 dt Rate of volume change for the top tank, Rate of volume change for the bottom tank, dv2 =ーV1 dt a) By taking L[v (t)] = V, (s) and L[v2(t)] = V2 (s), show that %3D 200 100s 200s 100 V, (s) = and V2 (s) = s2 +1 s2 +1 s2 + 1 s2 +1 b) Use Laplace transforms to determine v, (t) and v, (t). Then, find the volume of the water in the top and bottom tank after 30 minutes.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
See similar textbooks
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 Rate of volume change for the top tank, = v2 dt Rate of volume change for the bottom tank, dvz = -v1 dt a) By taking L[v, (t)] = V, (s) and L[v2(t)] = V2(s), show that 200 100s 200s 100 V1 (s) and V2 (s): %3D s2 + 1 s2 + 1 s2 +1 s2 + 1 b) Use Laplace transforms to determine v, (t) and v, (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 Rate of volume change for the top tank, = v2 dt Rate of volume change for the bottom tank, dvz = -v1 dt a) By taking L[v, (t)] = V, (s) and L[v2(t)] = V2(s), show that 200 100s 200s 100 V1 (s) and V2 (s): %3D s2 + 1 s2 + 1 s2 +1 s2 + 1 b) Use Laplace transforms to determine v, (t) and v, (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 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS