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

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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