Question

n Consider a 400/of a tank that initially contains a mixture of water and SO ke of salt. The water containing a salt concentration of 1/4 kg flowed into the tank at a rate, rof 3er and replaced the mixture flowing out. The mixture in the tank is draining from the tank at the same rate, as shown in Figure 1. Assuming the water is cold so that the salt is insoluble. After 180 seconds, the process is stopped the tank filled with the leftover salt. The original mixture in the tank will be replaced by the mixture flowing in. Therefore, the limiting amount of salt in the tank. Sy would be SO2 rl/sec, kg r/sec Figure 1: Tank flow The differential equation governs this process as shown in Figure 1 is represented by -rt s(t) = S1 + (SO - SI)e 100 (1) where SO is the initial amount of salt, Sy is the ending amount of salt and is the rate of water flows. The S is represented by 0/2 You are requlred to develop a MATLAB program to describe the above situation to calculate and visualise the amount of salt. Your program should be able to: 1. Request the user input for the initial amount of salt, 10 2. Find the amount of the salt at any time during 180 seconds of flow process (Hint: use length(x) to determine the length of the vector.] 3. Plot the graph of the amount of salt at any time, Plot the initial amount of salt, so at the same axls to visualise the behaviour of salt in the tank during the flow process. 11. Plot the limiting salt in the tank at the end of the flow process at the same axis. Rii. Label the graph and set up a sultable legend to differentiate the graphs P/S: Please submit your answer in M-files (.m).

Answer 1

The detailed solution is given below.

clear; clc; 1 2 3 4 5 6 r = 3; % [1/sec] SO = input('Enter the intial amount of salt, so [kg]: '); sl so/2; 7 8 s = @(t) si + (SO - sl) *exp(-r.*t/100); t = 0:0.1:180; St = s(t); 9 10 11 12 13 14 15 figure (1) hold on plot ( [0 180], [So so], 'b-.', 'Linewidth",2,'DisplayName','Initial amount of Salt') plot ( [0 180], [si si],'k-.-', 'Linewidth',2, 'DisplayName', 'Limiting Salt') 16 17 18 19 20 21 22 plot(t,st,'r-','Linewidth',2,'DisplayName', 's(t)) xlabel('Time [s]') ylabel('Amount of Salt [kg]') grid on legend show

clear;
clc;

r = 3; % [l/sec]
SO = input('Enter the intial amount of salt, SO [kg]: ');
Sl = SO/2;

S = @(t) Sl + (SO - Sl)*exp(-r.*t/100);

t = 0:0.1:180;
St = S(t);

figure(1)
hold on
plot([0 180], [SO SO],'b-.','Linewidth',2,'DisplayName','Initial Amount of Salt')
plot([0 180], [Sl Sl],'k-.','Linewidth',2,'DisplayName','Limiting Salt')

plot(t,St,'r-','Linewidth',2,'DisplayName','S(t)')
xlabel('Time [s]')
ylabel('Amount of Salt [kg]')
grid on
legend show

Enter the intial amount of salt, so [kg]: 10 >> |

10 -Initial Amount of Salt Limiting Salt -S(t) 9.5 9 00 Amount of Salt [kg] Сл 6.5 5.5 5 0 20 40 60 120 140 160 180 80 100 Time [s]

Please rate the solution if found satisfactory.