Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
See similar textbooks
icon
Related questions
Question

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
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS