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Part 1 : Draining a Cylindrical Tank A ) Suppose a cylindrical tank with a drainage valve at its base is full of water so
Part : Draining a Cylindrical Tank
A Suppose a cylindrical tank with a drainage valve at its base is full of water so that the
initial water level is the height of the tank, which we will write as in meters The
tank has a diameter of in meters and its drainage valve has a diameter of in
meters When the drainage valve opens, water exits the tank, causing the water level to
drop until the tank is empty. Let the water level in the tank be in meters where
represents time in seconds The mathematical model for this system is given below as
a first order differential equation.
Solve this IVP by hand using separation of variables. Show all steps and provide all
relevant work. From the solution of this differential equation, determine how long it will
take for the tank to drain. Use and
B In MATLAB, write a script that creates a direction field for this differential equation.
Describe why the direction field looks the way it does. Provide the plot and the code
used in your final submission.
C In MATLAB, write a script that applies Euler's, Improved Euler's, and the Runge
Kutta RK numerical methods for the drainage of the cylindrical tank. Plot all three
results onto a single set of axes. Use different colors for each plot to distinguish between
them and use a step size no larger than Provide the plot and the code used in
your final submission.
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