You have a spherical storage tank containing oil. The tank has a diameter of 6ft. You are asked to calculate the height h to which a dipstick 8 ft long would be wet with oil when immersed in the tank when it contains 6ft' of oil. - Dipstick -Spherical Storage Tank Figure 1. Spherical storage tank problem. The final equation that gives the height h of the liquid in the spherical tank for the given volume (6 ft') and radius (3 ft) is given by: f(h) = h-9h +3.8197=0 Use (a) the Newton-Raphson method and (b) the Secant method of finding roots of equations to find the height h to which the dipstick is wet with oil. Conduct three iterations to estimate the root of the above equation. Find the relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration considering the prespecified error = 5%. Show complete solutions.
You have a spherical storage tank containing oil. The tank has a diameter of 6ft. You are asked to calculate the height h to which a dipstick 8 ft long would be wet with oil when immersed in the tank when it contains 6ft' of oil. - Dipstick -Spherical Storage Tank Figure 1. Spherical storage tank problem. The final equation that gives the height h of the liquid in the spherical tank for the given volume (6 ft') and radius (3 ft) is given by: f(h) = h-9h +3.8197=0 Use (a) the Newton-Raphson method and (b) the Secant method of finding roots of equations to find the height h to which the dipstick is wet with oil. Conduct three iterations to estimate the root of the above equation. Find the relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration considering the prespecified error = 5%. Show complete solutions.
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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numerical method
Transcribed Image Text:You have a spherical storage tank containing oil. The tank has a diameter of 6ft. You are
asked to calculate the height h to which a dipstick 8 ft long would be wet with oil when
immersed in the tank when it contains 6ft' of oil.
- Dipstick
-Spherical Storage Tank
Figure 1. Spherical storage tank problem.
The final equation that gives the height h of the liquid in the spherical tank for the given
volume (6 ft') and radius (3 ft) is given by:
f(h) = h-9h +3.8197=0
Use (a) the Newton-Raphson method and (b) the Secant method of finding roots of
equations to find the height h to which the dipstick is wet with oil. Conduct three iterations
to estimate the root of the above equation. Find the relative approximate error at the end of
each iteration and the number of significant digits at least correct at the end of each iteration
considering the prespecified error = 5%. Show complete solutions.
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