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   PIPE FLOW CALCULATOR — DARCY-WEISBACH METHOD
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--- PIPE GEOMETRY ---
  Inner Diameter (D)      =       150.00 mm
  Pipe Length (L)         =      15.0000 m
  Surface Roughness (eps)   =   1.5000E-06 m
  Relative Roughness eps/D  =   1.0000E-05
  Cross-Section Area      =   1.7671E-02 m2

--- FLUID PROPERTIES ---
  Density (rho)             =         1.20 kg/m3
  Dynamic Viscosity (mu)   =   1.8000E-05 Pa.s
  Kinematic Viscosity (nu) =   1.5000E-05 m2/s

--- FLOW CONDITIONS ---
  Volume Flow Rate (Q)    =   5.0000E-02 m3/s
  Volume Flow Rate        =    3000.0000 L/min
  Mean Velocity (U)       =       2.8294 m/s
  Reynolds Number (Re)    =   2.8294E+04
  Flow Regime             = Turbulent

--- FRICTION FACTOR ---
  f (Darcy)               = 2.383558E-02
  f_laminar (64/Re)       = 2.261947E-03
  f_smooth (Petukhov)     = 2.397879E-02
  f_rough (Colebrook)     = 2.383558E-02
  Colebrook iterations    =    8 (converged)

--- MAJOR LOSSES (friction) ---
  Pressure Drop (deltaP)     =        11.45 Pa
  Pressure Drop           =       0.0114 kPa
  Head Loss (h_f)         =       0.9726 m

--- MINOR LOSSES (fittings) ---
  Total K coefficient     =       0.0000
  Minor Pressure Drop     =         0.00 Pa
  Minor Head Loss         =       0.0000 m

--- TOTAL RESULTS ---
  Total Pressure Drop     =        11.45 Pa
  Total Pressure Drop     =       0.0114 kPa
  Total Head Loss         =       0.9726 m
  Required Pump Power     =       0.5725 W

--- FRICTION FACTOR vs Re (for Moody chart) ---
  Re            f_smooth      f_rough       f_laminar
  ---
  5.0119E+02    0.09343917    0.08117170    0.12769679
  7.0514E+02    0.07974717    0.07114297    0.09076201
  9.9209E+02    0.06885815    0.06277290    0.06451018
  1.3958E+03    0.06005614    0.05572796    0.04585138
  1.9638E+03    0.05283999    0.04975215    0.03258941
  2.7630E+03    0.04685041    0.04464679      ---
  3.8874E+03    0.04182438    0.04025617      ---
  5.4693E+03    0.03756578    0.03645707      ---
  7.6950E+03    0.03392598    0.03315115      ---
  1.0826E+04    0.03079064    0.03025925      ---
  1.5232E+04    0.02807068    0.02771722      ---
  2.1431E+04    0.02569583    0.02547266      ---
  3.0152E+04    0.02361009    0.02348253      ---
  4.2422E+04    0.02176836    0.02171125      ---
  5.9685E+04    0.02013402    0.02012930      ---
  8.3973E+04    0.01867705    0.01871204      ---
  1.1814E+05    0.01737270    0.01743887      ---
  1.6622E+05    0.01620036    0.01629253      ---
  2.3387E+05    0.01514280    0.01525856      ---
  3.2903E+05    0.01418552    0.01432488      ---
  4.6293E+05    0.01331623    0.01348144      ---
  6.5132E+05    0.01252446    0.01271995      ---
  9.1637E+05    0.01180126    0.01203369      ---
  1.2893E+06    0.01113894    0.01141728      ---
  1.8139E+06    0.01053085    0.01086650      ---
  2.5521E+06    0.00997123    0.01037804      ---
  3.5906E+06    0.00945506    0.00994923      ---
  5.0518E+06    0.00897796    0.00957769      ---
  7.1076E+06    0.00853608    0.00926087      ---
  1.0000E+07    0.00812604    0.00899571      ---

--- 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)