The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be computed using the following equation: v = v2gH * tanh H √√2gH 2L Where g is the gravity acceleration (m/s²), H is the initial height of water in the tank (m), L is the pipe length (m), and t is the elapsed time (s). Given that g = 9.81 (m/s²), H = 5 (m), and L=10 (m). Determine the time needed to achieve discharge velocity (v) of 9 m/s by using: 1-A) The graphical estimation method (Show table using hand calculation and use software for the plot). 1-B) The Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. 1-C) The Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (Hint: (tanh(f(x)))' = f(x)' sech²(f(x))).
The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be computed using the following equation: v = v2gH * tanh H √√2gH 2L Where g is the gravity acceleration (m/s²), H is the initial height of water in the tank (m), L is the pipe length (m), and t is the elapsed time (s). Given that g = 9.81 (m/s²), H = 5 (m), and L=10 (m). Determine the time needed to achieve discharge velocity (v) of 9 m/s by using: 1-A) The graphical estimation method (Show table using hand calculation and use software for the plot). 1-B) The Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. 1-C) The Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (Hint: (tanh(f(x)))' = f(x)' sech²(f(x))).
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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Transcribed Image Text:Activity 1:
The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be
computed using the following equation:
v = v2gH * tanh
10
2gH
2L
Where g is the gravity acceleration (m/s²), H is the initial height of water in the tank (m), L
is the pipe length (m), and t is the elapsed time (s). Given that g = 9.81 (m/s²),
H = 5 (m), and L=10 (m). Determine the time needed to achieve discharge velocity (v) of
9 m/s by using:
(1-A) The graphical estimation method (Show table using hand calculation and use software
for the plot).
(1-B) The Bi-section method. You are required to continue with the iterations until you reach
an absolute error below 0.0001.
(1-C) The Newton-Raphson method. You are required to continue with the iterations until you
reach an absolute error below 0.0001. (Hint: (tanh(f(x)))' = f(x)' sech²(ƒ(x))).
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