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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.

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.

Advanced Engineering Mathematics
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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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 - nh(38- A) R-H) πh2 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)
Transcribed Image Text: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 - nh(38- A) R-H) πh2 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)
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