5. A cylindrical vertical tank of diameter D = 2 ft has a hole of diameter d = 2 in. near its bottom. Water enters the tank through a pipe at the top at a rate of Q=0.15 ft³/s. The time, t, that is required for the height of the water level in the tank to change from its initial (t = 0) level of h₁ = 9 ft to level of h is given by: t = St 40 d2 dy πD² D2√28y where g = 32.2 ft/s². Determine how long it would take for the height of the water level to change to h=5 ft. Use at least 3 methods that apply for the problem. You can use computer software as Matlab user-defined functions or MathCad explicit solution. Compare results and rank methods from best to worse. h D
5. A cylindrical vertical tank of diameter D = 2 ft has a hole of diameter d = 2 in. near its bottom. Water enters the tank through a pipe at the top at a rate of Q=0.15 ft³/s. The time, t, that is required for the height of the water level in the tank to change from its initial (t = 0) level of h₁ = 9 ft to level of h is given by: t = St 40 d2 dy πD² D2√28y where g = 32.2 ft/s². Determine how long it would take for the height of the water level to change to h=5 ft. Use at least 3 methods that apply for the problem. You can use computer software as Matlab user-defined functions or MathCad explicit solution. Compare results and rank methods from best to worse. h D
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:5.
A cylindrical vertical tank of diameter D = 2 ft has a hole of diameter
d = 2 in. near its bottom. Water enters the tank through a pipe at the top at a
rate of Q=0.15 ft³/s. The time, t, that is required for the height of the water
level in the tank to change from its initial (t = 0) level of h₁ = 9 ft to level
of h is given by:
t =
St
40 d2
dy
πD² D2√28y
where g =
32.2 ft/s².
Determine how long it would take for the height of the water level to
change to h=5 ft. Use at least 3 methods that apply for the problem. You
can use computer software as Matlab user-defined functions or MathCad
explicit solution. Compare results and rank methods from best to worse.
h
D
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