% 1.72 Problem Set #2 % Problem 1, Least-squares fit of falling permeameter data % All data are in inches; t is in seconds data = [0 5 5 6 15 6.875 30 8 45 9.25 60 10.375 75 11.5 90 12.625 120 14.375 300 20.5 540 23.375 780 25 1200 26.375 2400 27.5 3600 27.5]; t = data(:,1); h = data(:,2); H0 = 32; h0 = h(1); L = 28.5; D = 2.5; d = 0.75; a = (H0 + h0*(d/D)^2)/(1+(d/D)^2); b = -(H0 - h0)/(1 + (d/D)^2); c = (1 + (D/d)^2)/L; % Fit K using all data points y1 = -log((h-a)/b)/c; K1 = t\y1; % least-squares solution in Matlab yhat1 = t*K1; % predicted values for y using estimated K % Fit K without last 5 points y2 = y1(1:end-5); t2 = t(1:end-5); K2 = t2\y2; yhat2 = t2*K2; % Plot results subplot(211) plot(t,y1,'o',t,yhat1,'-') legend('Measured','Predicted',4) title(['Fit using all data: K = ',num2str(K1),' in/sec']) xlabel('t [s]'); ylabel('-log((h-a)/b)/c'); subplot(212) plot(t2,y2,'o',t2,yhat2,'-') legend('Measured','Predicted',4) title(['Fit for t<=300: K = ',num2str(K2),' in/sec']); xlabel('t [s]'); ylabel('-log((h-a)/b)/c');