A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: V = µh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above.
A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: V = µh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above.
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
slove 1,2 and 3
Transcribed Image Text:Activity 2:
A spherical tank is used to hold water as shown below. The volume of water in tank can be
computed using the following equation:
-
V = πh² (³R = h)
where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m.
R
Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using:
(2-A) the graphical estimation method (by hand)
(2-B) the Bi-section method. You are required to continue with the iterations until you reach an
absolute error below 0.0001.
(2-C) the Newton-Raphson method. You are required to continue with the iterations until you
reach an absolute error below 0.0001.
Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed.
Support your comments using findings above.
(Hint: find the exact estimation analytically and use it as a benchmark)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 9 steps with 9 images
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,
