
           ┃┓           ┓           /┓
           ┃┃           ┃            ┃
           ┃┃           ┃            ┃
           ┃┃           ┃            ┃
           ┃┃           ┣╸Pipe.C    /┣╸Q[1]
      Cost╺┫┃           ┃ (176,080)  ┃ (0.18m³/s, fixed)
 (234,504) ┃┣╸LCC       ┃            ┃
           ┃┃ (234,504) ┃            ┃
           ┃┃           ┛           /┛
           ┃┃           ┣╸C_nrg╶⎨
           ┃┃           ┛ (35,769)
           ┃┛           ┣╸Pump.C╶⎨



          ┃┓      ┓
          ┃┃      ┣╸C ≥ c_mat⋅W
          ┃┃      ┛
          ┃┣╸Pipe ┣╸W ≥ rho_m⋅3.14⋅D⋅t⋅L
          ┃┃      ┛
          ┃┛      ┣╸A = 0.785⋅D²
          ┃┓          ┣╸Q[2] ≤ V[2]⋅A
          ┃┃          ┣╸P[2] ≥ dp[2]⋅Q[2]/eta
          ┃┣╸PipeFlow ┓
 Pipeline╺┫┃          ┣╸[13 terms]
          ┃┛          ┛
          ┃┓
          ┃┃
          ┃┣╸LCC ≥ Pipe.C + Pump.C + C_nrg
          ┃┛
          ┃┓
          ┃┣╸sigma ≥ p_sys⋅D/(2⋅t) + 4⋅M/(3.14⋅D²⋅t)
          ┃┛
          ┃┣╸SpanLoading╶⎨
          ┃┣╸[3 terms]


Optimal Cost
------------
Pipeline.LCC : 2.345e+05

Solution
--------
Pipeline
C_nrg : 3.577e+04                    lifetime energy cost
  LCC : 2.345e+05                    life-cycle cost: pipe + pump + lifetime energy
...constants
p_sys : 16        [bar]    (+0.4963) system pressure rating
c_nrg : 0.1       [1/h/kW] (+0.1525) energy price

Pipeline.Fluid
...constants
rho : 1000  [kg/m³] (+0.4538)  density
 mu : 0.001 [Pa⋅s]  (+0.04983) dynamic viscosity

Pipeline.Pipe
    A : 0.1455    [m²]              flow area
    C : 1.761e+05                   installed cost
    D : 0.4304    [m]               inner diameter
    W : 2.935e+04 [kg]              mass
    t : 0.002783  [m]               wall thickness
...constants
    L : 1000      [m]     (+1)      run length
rho_m : 7800      [kg/m³] (+0.8022) wall material density
sigma : 200       [MPa]   (-0.8022) allowable stress
c_mat : 6         [1/kg]  (+0.7509) installed material cost
t_min : 2         [mm]    (~0)      minimum gauge

Pipeline.PipeFlow
    P[:] : [ 1.16e+03  6.02e+03  2.52e+04 ] [W]    pumping power
   Re[:] : [ 2.96e+05  5.32e+05  8.87e+05 ]        Reynolds number
    V[:] : [ 0.687     1.24      2.06     ] [m/s]  bulk velocity
   dp[:] : [ 8.13e+03  2.34e+04  5.87e+04 ] [Pa]   pressure drop
    f[:] : [ 0.0148    0.0132    0.0119   ]        Darcy friction factor
...constants
    Q[:] : [ 0.1      0.18     0.3     ] [m³/s] flow demand
      sens ( +0.0971  +0.18    +0.421  )
hours[:] : [ 7e+04    2.5e+04  5e+03   ] [h]    lifetime operating hours at this condition
      sens ( +0.0347  +0.0642  +0.0537 )

Pipeline.Pump
      C : 2.265e+04                  capital cost
P_rated : 25.17     [kW]             rating, set by the peak condition
...constants
    eta : 0.7              (-0.2491) efficiency
 c_unit : 900       [1/kW] (+0.0966) capital cost per rated kW

Pipeline.SpanLoading
     M : 3.087e+04 [m⋅N]           midspan bending moment
...constants
L_span : 12        [m]   (+0.6118) support spacing

Most Sensitive Constraints
--------------------------
Pipeline
+1      : LCC ≥ C + C + C_nrg
+0.8022 : sigma ≥ p_sys⋅D/(2⋅t) + 4⋅M/(3.14⋅D²⋅t)
+0.1525 : C_nrg ≥ c_nrg⋅(P[:]⋅hours[:]).sum()
+0.0966 : P[2] ≤ P_rated

Pipeline.Pipe
+0.7509 : C ≥ c_mat⋅W
+0.7509 : W ≥ rho_m⋅3.14⋅D⋅t⋅L
+0.1939 : A = 0.785⋅D²

Pipeline.PipeFlow
+0.2705  : Q[2] ≤ V[2]⋅A
+0.1503  : P[2] ≥ dp[2]⋅Q[2]/eta
+0.1503  : dp[2] ≥ f[2]⋅L/D⋅rho⋅V[2]²/2
+0.1503  : f[2] ≥ Re[2]^-0.2⋅0.184
+0.1156  : Q[1] ≤ V[1]⋅A
+0.0642  : P[1] ≥ dp[1]⋅Q[1]/eta
+0.0642  : dp[1] ≥ f[1]⋅L/D⋅rho⋅V[1]²/2
+0.0642  : f[1] ≥ Re[1]^-0.2⋅0.184
+0.0624  : Q[0] ≤ V[0]⋅A
+0.03467 : P[0] ≥ dp[0]⋅Q[0]/eta
+0.03467 : dp[0] ≥ f[0]⋅L/D⋅rho⋅V[0]²/2
+0.03467 : f[0] ≥ Re[0]^-0.2⋅0.184
+0.03005 : Re[2] ≤ rho⋅V[2]⋅D/mu
+0.01284 : Re[1] ≤ rho⋅V[1]⋅D/mu

Pipeline.Pump
+0.0966 : C ≥ c_unit⋅P_rated

Pipeline.SpanLoading
+0.3059 : M ≥ (rho_m⋅3.14⋅D⋅t⋅9.81 + rho⋅A⋅9.81)⋅L_span²/8