Question

The following equation describes a certain dilution process, where y(t) is the concentration of salt in a tank of freshwater to which salt brine is being added.

 

Suppose that y(0) = 0. Plot y(t) for 0 ≤ t ≤ 10.

Answer 1

Let y(t) be the concentration of salt in a tank.

 

The dilution process is governed by the equation

dt/dt + 2/(10 + 2t)y = 4 and y(0) = 0

 

Solve this equation using ‘ode45’ command and function file called ‘conc’, which contains the first order derivative of concentration expression.

 

Plot the variation of concentration of salt with time.

 

Mat-lab code for Required problem is provided below.

Save this program as ‘problem7_29.m’.

% Concentration of salt in a tank of fresh water

[t,y] = ode45(@conc, [0,10],0);

plot(t,y);

xlabel(\'Time(Sec)\');

ylabel(\'Concentration\');

title(\'Salt brine concentration after adding for 10s\');

Save the function file as ‘conc.m’.

function ydot = conc(t,y)

ydot = 4 - (2/(10+2*t))*y;

The output of the code ‘Required problem’ in the figure window is shown below.

After 10 seconds, the concentration of salt brine reaches 25 concentration value.

Let y(t) be the concentration of salt in a tank.

 

The dilution process is governed by the equation

dt/dt + 2/(10 + 2t)y = 4 and y(0) =