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Least Squares method using Maple7 to find surface tension of Boys' Soap Solution
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> with(stats[fit]);
> R(0) := 0.0267;
> R(t0):= 0.0267;
> R(t1):=0.02615;
> R(t2):=0.02565;
> R(t3):=0.02535;
> R(t4):=0.02475;
> R(t5):=0.0239;
> R(t6):=0.02325;
> R(t7):=0.02235;
> R(t8):=0.02175;
> R(t9):=0.02075;
> R(t10):=0.01985;
> R(t11):=0.0188;
> R(t12):=0.0171;
> R(t13):=0.01555;
> R(t14):=0.0126;
> R(t15):=0.0075;
> R(t16):=0.0;
> t:=[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]:
> radius:=[(R(0)^(4)- R(t0)^(4)), (R(0)^(4) -R(t1)^(4)), (R(0)^(4)- R(t2)^(4)), (R(0)^(4)- R(t3)^(4)), (R(0)^(4)- R(t4)^(4)), (R(0)^(4)- R(t5)^(4)), (R(0)^(4)- R(t6)^(4)), (R(0)^(4)- R(t7)^(4)), (R(0)^(4)- R(t8)^(4)), (R(0)^(4)- R(t9)^(4)), (R(0)^(4)-R(t10)^(4)), (R(0)^(4)- R(t11)^(4)), (R(0)^(4) -R(t12)^(4)), (R(0)^(4)- R(t13)^(4)), (R(0)^(4)- R(t14)^(4)), (R(0)^(4)- R(t15)^(4)), (R(0)^(4)- R(t16)^(4))]:
> data:= eval(radius);
> with(stats):
Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform
> with(plots):
Warning, the name changecoords has been redefined
> with(fit):
Warning, the names leastmediansquare and leastsquare have been redefined
> points:=pointplot(zip((x,y)->[x,y],t, data)):
> eq:=leastsquare[[x,y],y=a*x,{a}]([t, data]);
> curve:=plot(rhs(eq),x=0..23,color= blue):
> display([points,curve]);
> restart;
> Surf_Tension:= 4*m*mu*L/(a^4);
> sigma := eval(Surf_Tension,[L = .305, mu = 1.7*10^(-5),a =.1981200000e-2, m = .3431851962e-7]);
> restart;
> R:=t->( Ro^4 - (sigma*a^4)*t/(4*mu*L))^(1/4);
> radius_vs_time:= eval(R(t), [L = .305, mu = 1.7*10^(-5),a =.1981200000e-2, Ro=.267e-1, sigma=.4619808996e-1]);
> plot( radius_vs_time, t=0..16);
>