The temporal evolution of the height of water h in a cylindrical tank of radius r = 1m with periodic inflow and an outlet pipe can be determined by solving the following ODE (see for example class notes), where dh f(t) pApipe√2gh dt pAtank (2) C = 90kg/s, w = 25 Hz, p = f(t)=c[2+ sin (wt + cos(2wt))], (3) 1000kg/m³, g = 9.81m/s², t is time, and Atank and Apipe are the cross-sectional areas of the tank and the outlet pipe. Note that the cosine in f(t) is inside the sine and both are in radians. The outlet pipe has a radius of "pipe = 0.15m. At the initial time of t = 0s, the height of water in the tank is h(t = 0s) = 0.3m. For a step size of At = 1s, determine by hand the height of water in the tank at t = 1s using the a) Explicit Euler method b) RK-2 modified Euler method c) Classical RK-4 method
The temporal evolution of the height of water h in a cylindrical tank of radius r = 1m with periodic inflow and an outlet pipe can be determined by solving the following ODE (see for example class notes), where dh f(t) pApipe√2gh dt pAtank (2) C = 90kg/s, w = 25 Hz, p = f(t)=c[2+ sin (wt + cos(2wt))], (3) 1000kg/m³, g = 9.81m/s², t is time, and Atank and Apipe are the cross-sectional areas of the tank and the outlet pipe. Note that the cosine in f(t) is inside the sine and both are in radians. The outlet pipe has a radius of "pipe = 0.15m. At the initial time of t = 0s, the height of water in the tank is h(t = 0s) = 0.3m. For a step size of At = 1s, determine by hand the height of water in the tank at t = 1s using the a) Explicit Euler method b) RK-2 modified Euler method c) Classical RK-4 method
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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Hi, can you please help me with PART B ONLY? I have already solved with the other two methods.
![The temporal evolution of the height of water h in a cylindrical tank of radius r = 1m with periodic inflow and an outlet pipe can
be determined by solving the following ODE (see for example class notes),
where
dh f(t) pApipe√2gh
dt
pAtank
(2)
C = 90kg/s, w = 25 Hz, p =
f(t)=c[2+ sin (wt + cos(2wt))],
(3)
1000kg/m³, g = 9.81m/s², t is time, and Atank and Apipe are the cross-sectional areas of the
tank and the outlet pipe. Note that the cosine in f(t) is inside the sine and both are in radians. The outlet pipe has a radius of
"pipe
=
0.15m. At the initial time of t = 0s, the height of water in the tank is h(t = 0s) = 0.3m. For a step size of At = 1s,
determine by hand the height of water in the tank at t = 1s using the
a) Explicit Euler method
b) RK-2 modified Euler method
c) Classical RK-4 method](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fe12990-e023-482e-b81f-63883b657c8e%2F1c6bdc3f-eff5-45a4-b252-2186cf812112%2F27316ee_processed.png&w=3840&q=75)
Transcribed Image Text:The temporal evolution of the height of water h in a cylindrical tank of radius r = 1m with periodic inflow and an outlet pipe can
be determined by solving the following ODE (see for example class notes),
where
dh f(t) pApipe√2gh
dt
pAtank
(2)
C = 90kg/s, w = 25 Hz, p =
f(t)=c[2+ sin (wt + cos(2wt))],
(3)
1000kg/m³, g = 9.81m/s², t is time, and Atank and Apipe are the cross-sectional areas of the
tank and the outlet pipe. Note that the cosine in f(t) is inside the sine and both are in radians. The outlet pipe has a radius of
"pipe
=
0.15m. At the initial time of t = 0s, the height of water in the tank is h(t = 0s) = 0.3m. For a step size of At = 1s,
determine by hand the height of water in the tank at t = 1s using the
a) Explicit Euler method
b) RK-2 modified Euler method
c) Classical RK-4 method
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