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//Variable declaration:
//For 1-inch %pipe schedule 40:
Di = 1.049/12 //Inside diameter (ft)
Do = 1.315/12 //Outside diameter (ft)
L = 8000 //Length of %pipe (ft)
hi = 2000 //Heat transfer coefficient inside of the %pipe (Btu/h.ft^2. F)
ho = 100 //Outside heat transfer coefficient (Btu/h.ft. F)
kl = 0.01 //Thermal conductivity of insulation (Btu/h.ft. F)
T1 = 240 //Steam temperature ( F)
T2 = 20 //Air temperature ( F)
k = 24.8 //Thermal conductivity for steel (Btu/h.ft. F)
Dxl = ([3/8,1/2,3/4,1])/12 //thickness(ft)
amt = ([1.51,3.54,5.54,8.36])/6 //Cost per feet($)
//Calculation:
D_ = (Do-Di)/log(Do/Di) //log-mean diameter of the %pipe (ft)
Dl = Do+2*(Dxl) //Insulation thickness (ft)
D_l = [ 0.13849079 0.14734319 0.16423045 0.18025404]
//D_l = (Dl-Do)/log(Dl/Do) //log mean diameter of %pipe (ft)
Dxw = (Do-Di)/2 //%pipe thickness (ft)
Rw = Dxw/(k*%pi*D_*L) //Wall resistance ((Btu/h. F)^-1)
Ri = 1/(hi*%pi*Di*L) //Inside steam convection resistance ((Btu/h. F)^-1)
Rl = [ 0.00089782 0.00112517 0.00151421 0.00183947] //Dxl/(kl*%pi*D_l*L) //Insulation resistance ((Btu/h. F)^-1)
Ro = [ 2.31217835e-06 2.06248306e-06 1.69614504e-06 1.44031623e-06] //1/(ho*%pi*Dl*L) //Outside air convection resistance ((Btu/h. F)^-1)
R = [ 0.00090054, 0.00112764,0.00151632,0.00184132] //Total resistance ((Btu/h. F)^-1)
Uo = [ 0.25675435 0.18290211 0.11185958 0.07822176] //Overall outside heat transfer coefficient (Btu/h.ft^2. F)
Ui = [ 0.50543158 0.40364002 0.30017609 0.24719271] //Overall inside heat transfer coefficient (Btu/h.ft^2. F)
dT = T1-T2
Ai = %pi*Di*L //Inside area (ft^2)
Q = Ui*Ai*dT //Energy loss (Btu/h)
function [a] =energyPerDollar(Q1,Q2,amt1,amt2)
a = ((Q1-Q2)/(8000*(amt2-amt1)))
endfunction
//Results:
printf("Energy saved per dollar ingoing from 3/8 to 1/2 inch is : %.1f Btu/h.$",energyPerDollar(Q(1),Q(2),amt(1),amt(2)))
printf("Energy saved per dollar ingoing from 1/2 to 3/4 inch is : %.1f Btu/h.$",energyPerDollar(Q(2),Q(3),amt(2),amt(3)))
printf("Energy saved per dollar ingoing from 3/4 to 1 inch is : %.1f Btu/h.$",energyPerDollar(Q(3),Q(4),amt(3),amt(4)))
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