============================================================
   PIPE FLOW CALCULATOR — DARCY-WEISBACH METHOD
============================================================

--- PIPE GEOMETRY ---
  Inner Diameter (D)      =        80.00 mm
  Pipe Length (L)         =     200.0000 m
  Surface Roughness (eps)   =   4.5000E-05 m
  Relative Roughness eps/D  =   5.6250E-04
  Cross-Section Area      =   5.0265E-03 m2

--- FLUID PROPERTIES ---
  Density (rho)             =       998.00 kg/m3
  Dynamic Viscosity (mu)   =   1.0020E-03 Pa.s
  Kinematic Viscosity (nu) =   1.0040E-06 m2/s

--- FLOW CONDITIONS ---
  Volume Flow Rate (Q)    =   1.3333E-02 m3/s
  Volume Flow Rate        =     800.0000 L/min
  Mean Velocity (U)       =       2.6526 m/s
  Reynolds Number (Re)    =   2.1136E+05
  Flow Regime             = Turbulent

--- FRICTION FACTOR ---
  f (Darcy)               = 1.904313E-02
  f_laminar (64/Re)       = 3.028017E-04
  f_smooth (Petukhov)     = 1.544516E-02
  f_rough (Colebrook)     = 1.904313E-02
  Colebrook iterations    =    6 (converged)

--- MAJOR LOSSES (friction) ---
  Pressure Drop (deltaP)     =    167153.97 Pa
  Pressure Drop           =     167.1540 kPa
  Head Loss (h_f)         =      17.0733 m

--- MINOR LOSSES (fittings) ---
  Total K coefficient     =       6.5000
  Minor Pressure Drop     =     22821.89 Pa
  Minor Head Loss         =       2.3311 m

--- TOTAL RESULTS ---
  Total Pressure Drop     =    189975.86 Pa
  Total Pressure Drop     =     189.9759 kPa
  Total Head Loss         =      19.4043 m
  Required Pump Power     =    2533.0115 W

--- FRICTION FACTOR vs Re (for Moody chart) ---
  Re            f_smooth      f_rough       f_laminar
  ---
  5.0119E+02    0.09343917    0.08144519    0.12769679
  7.0514E+02    0.07974717    0.07144222    0.09076201
  9.9209E+02    0.06885815    0.06310429    0.06451018
  1.3958E+03    0.06005614    0.05609898    0.04585138
  1.9638E+03    0.05283999    0.05017165    0.03258941
  2.7630E+03    0.04685041    0.04512541      ---
  3.8874E+03    0.04182438    0.04080666      ---
  5.4693E+03    0.03756578    0.03709479      ---
  7.6950E+03    0.03392598    0.03389455      ---
  1.0826E+04    0.03079064    0.03113040      ---
  1.5232E+04    0.02807068    0.02874231      ---
  2.1431E+04    0.02569583    0.02668238      ---
  3.0152E+04    0.02361009    0.02491222      ---
  4.2422E+04    0.02176836    0.02340061      ---
  5.9685E+04    0.02013402    0.02212146      ---
  8.3973E+04    0.01867705    0.02105191      ---
  1.1814E+05    0.01737270    0.02017066      ---
  1.6622E+05    0.01620036    0.01945671      ---
  2.3387E+05    0.01514280    0.01888875      ---
  3.2903E+05    0.01418552    0.01844521      ---
  4.6293E+05    0.01331623    0.01810488      ---
  6.5132E+05    0.01252446    0.01784790      ---
  9.1637E+05    0.01180126    0.01765650      ---
  1.2893E+06    0.01113894    0.01751554      ---
  1.8139E+06    0.01053085    0.01741267      ---
  2.5521E+06    0.00997123    0.01733811      ---
  3.5906E+06    0.00945506    0.01728436      ---
  5.0518E+06    0.00897796    0.01724576      ---
  7.1076E+06    0.00853608    0.01721811      ---
  1.0000E+07    0.00812604    0.01719836      ---

--- EQUATIONS USED ---
  Darcy-Weisbach: deltaP = f(L/D)(rhoU2/2)
  Colebrook:      1/√f = -2log1₀(eps/D/3.7 + 2.51/(Re√f))
  Minor losses:   deltaP_minor = ΣK(rhoU2/2)
  Head loss:      h_f = deltaP/(rhog)