{
  "version": "hydraulics-packet01-v2",
  "conditions": "constant density and viscosity, circular fully filled bore, selected static configuration; graphical values are illustrative readings, not project limits",
  "equations": {
    "continuity": "Q_m3_h=3600*pi*d_i_m^2*v_m_s/4",
    "Re": "rho*v*d_i/mu",
    "loss": "lambda*L*rho*v^2/(2*d_i)",
    "length": "L=straight_length+sum(n*multiplier*D_nominal_m)",
    "Fanning_conversion": "lambda=4*f_Fanning"
  },
  "roughness": {
    "nominal_index_equation": "relative_index=epsilon_um/(1000*DN_mm)",
    "materials": [
      {
        "label": "Carbon steel/alloy",
        "epsilon_um": 50
      },
      {
        "label": "Bitumen-lined",
        "epsilon_um": 120
      },
      {
        "label": "Cast iron",
        "epsilon_um": 260
      },
      {
        "label": "Cement-lined",
        "epsilon_um": 1500
      }
    ],
    "smooth_cement_lining": {
      "minimum_DN_mm": 400,
      "epsilon_um": 50
    },
    "distinction": "label arithmetic at DN200 yields 0.00025; worked graphical route reads approximately 0.0002"
  },
  "friction": {
    "exact_textual_worked_reading": {
      "DN_mm": 200,
      "Re": 70000,
      "relative_roughness": 0.0002,
      "lambda": 0.0205
    },
    "laminar_graphical_points": [
      [
        1000,
        0.064
      ],
      [
        2000,
        0.032
      ]
    ],
    "transition_Re": [
      2300,
      4000
    ],
    "multi_curve_lookup": {
      "curves": [
        {
          "relative_roughness": 0.05,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0716
            },
            {
              "Re": 101000,
              "lambda": 0.0717
            },
            {
              "Re": 182300,
              "lambda": 0.0717
            },
            {
              "Re": 491500,
              "lambda": 0.0717
            },
            {
              "Re": 1000700,
              "lambda": 0.0717
            },
            {
              "Re": 5048800,
              "lambda": 0.0718
            },
            {
              "Re": 10108500,
              "lambda": 0.0718
            },
            {
              "Re": 50155200,
              "lambda": 0.0718
            }
          ]
        },
        {
          "relative_roughness": 0.01,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0391
            },
            {
              "Re": 101000,
              "lambda": 0.0384
            },
            {
              "Re": 182300,
              "lambda": 0.0382
            },
            {
              "Re": 491500,
              "lambda": 0.0381
            },
            {
              "Re": 1000700,
              "lambda": 0.0381
            },
            {
              "Re": 5048800,
              "lambda": 0.0381
            },
            {
              "Re": 10108500,
              "lambda": 0.0381
            },
            {
              "Re": 50155200,
              "lambda": 0.0381
            }
          ]
        },
        {
          "relative_roughness": 0.004,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0309
            },
            {
              "Re": 101000,
              "lambda": 0.0296
            },
            {
              "Re": 182300,
              "lambda": 0.029
            },
            {
              "Re": 491500,
              "lambda": 0.0285
            },
            {
              "Re": 1000700,
              "lambda": 0.0283
            },
            {
              "Re": 5048800,
              "lambda": 0.0283
            },
            {
              "Re": 10108500,
              "lambda": 0.0283
            },
            {
              "Re": 50155200,
              "lambda": 0.0283
            }
          ]
        },
        {
          "relative_roughness": 0.002,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0268
            },
            {
              "Re": 101000,
              "lambda": 0.0252
            },
            {
              "Re": 182300,
              "lambda": 0.0243
            },
            {
              "Re": 491500,
              "lambda": 0.0238
            },
            {
              "Re": 1000700,
              "lambda": 0.0236
            },
            {
              "Re": 5048800,
              "lambda": 0.0236
            },
            {
              "Re": 10108500,
              "lambda": 0.0236
            },
            {
              "Re": 50155200,
              "lambda": 0.0236
            }
          ]
        },
        {
          "relative_roughness": 0.0004,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0228
            },
            {
              "Re": 101000,
              "lambda": 0.0203
            },
            {
              "Re": 182300,
              "lambda": 0.0187
            },
            {
              "Re": 491500,
              "lambda": 0.0171
            },
            {
              "Re": 1000700,
              "lambda": 0.0166
            },
            {
              "Re": 5048800,
              "lambda": 0.0162
            },
            {
              "Re": 10108500,
              "lambda": 0.0162
            },
            {
              "Re": 50155200,
              "lambda": 0.0162
            }
          ]
        },
        {
          "relative_roughness": 0.0002,
          "samples": [
            {
              "Re": 48900,
              "lambda": 0.0214
            },
            {
              "Re": 101000,
              "lambda": 0.0187
            },
            {
              "Re": 182300,
              "lambda": 0.0176
            },
            {
              "Re": 491500,
              "lambda": 0.0155
            },
            {
              "Re": 1000700,
              "lambda": 0.0146
            },
            {
              "Re": 5048800,
              "lambda": 0.0139
            },
            {
              "Re": 10108500,
              "lambda": 0.0138
            },
            {
              "Re": 50155200,
              "lambda": 0.0137
            }
          ]
        }
      ],
      "Re_domain": [
        48900,
        50155200
      ],
      "relative_roughness_domain": [
        0.0002,
        0.05
      ],
      "graphical_lambda_allowance_relative": 0.05,
      "approximation": "Piecewise linear lambda against log(Re) along each saved curve only. For an intermediate roughness, report the two bounding curve factors and their graphical allowances; no exact roughness interpolation. No extrapolation or transition interpolation.",
      "trace_identity": "Recovered solid curve family; a dashed worked projection is excluded; the stated worked reading remains distinct."
    }
  },
  "water_loss": {
    "material": "carbon steel",
    "panel_flow_ranges_m3_h": [
      [
        1,
        10
      ],
      [
        10,
        300
      ],
      [
        300,
        10000
      ]
    ],
    "temperature_headings_C": [
      2,
      20,
      20
    ],
    "temperature_resolution": "unresolved; do not join first panel to continuations as one calibrated temperature basis",
    "sample_panel": 2,
    "pipe_bore_and_roughness": "not stated numerically for pressure-chart curves; do not infer from separate flow table",
    "interpolation": "Within each saved curve span only; no inter-DN size interpolation or panel joins.",
    "recovered_curves": [
      {
        "DN_mm": 100,
        "samples": [
          {
            "flow_m3_h": 11.8,
            "gradient_bar_per_100m": 0.02
          },
          {
            "flow_m3_h": 15.7,
            "gradient_bar_per_100m": 0.034
          },
          {
            "flow_m3_h": 19.4,
            "gradient_bar_per_100m": 0.05
          },
          {
            "flow_m3_h": 25.5,
            "gradient_bar_per_100m": 0.083
          },
          {
            "flow_m3_h": 28.2,
            "gradient_bar_per_100m": 0.1
          },
          {
            "flow_m3_h": 35.2,
            "gradient_bar_per_100m": 0.149
          },
          {
            "flow_m3_h": 51.4,
            "gradient_bar_per_100m": 0.3
          },
          {
            "flow_m3_h": 77.2,
            "gradient_bar_per_100m": 0.627
          },
          {
            "flow_m3_h": 99.5,
            "gradient_bar_per_100m": 1
          },
          {
            "flow_m3_h": 124.2,
            "gradient_bar_per_100m": 1.5
          },
          {
            "flow_m3_h": 137.2,
            "gradient_bar_per_100m": 1.8
          }
        ]
      },
      {
        "DN_mm": 150,
        "samples": [
          {
            "flow_m3_h": 35.6,
            "gradient_bar_per_100m": 0.02
          },
          {
            "flow_m3_h": 47.6,
            "gradient_bar_per_100m": 0.034
          },
          {
            "flow_m3_h": 58.8,
            "gradient_bar_per_100m": 0.05
          },
          {
            "flow_m3_h": 77.8,
            "gradient_bar_per_100m": 0.083
          },
          {
            "flow_m3_h": 86.2,
            "gradient_bar_per_100m": 0.1
          },
          {
            "flow_m3_h": 107.3,
            "gradient_bar_per_100m": 0.149
          },
          {
            "flow_m3_h": 157.7,
            "gradient_bar_per_100m": 0.3
          },
          {
            "flow_m3_h": 236.3,
            "gradient_bar_per_100m": 0.627
          }
        ]
      },
      {
        "DN_mm": 200,
        "samples": [
          {
            "flow_m3_h": 78.9,
            "gradient_bar_per_100m": 0.02
          },
          {
            "flow_m3_h": 105.7,
            "gradient_bar_per_100m": 0.034
          },
          {
            "flow_m3_h": 130.4,
            "gradient_bar_per_100m": 0.05
          },
          {
            "flow_m3_h": 172.1,
            "gradient_bar_per_100m": 0.083
          },
          {
            "flow_m3_h": 190.7,
            "gradient_bar_per_100m": 0.1
          },
          {
            "flow_m3_h": 236.9,
            "gradient_bar_per_100m": 0.149
          }
        ]
      }
    ],
    "approximation": "Piecewise straight joining in log(flow)-log(gradient) space between sampled original trace intersections; no extrapolation. No physical curve fit or hidden-bore assignment.",
    "graphical_gradient_allowance_relative": 0.15,
    "worked_comparison": {
      "flow_m3_h": 130,
      "basis": "Middle carbon-steel-water pressure chart, headed20\u00b0C; only chart nominal DN basis, not assumed continuity-table bores",
      "rows": [
        {
          "DN_mm": 100,
          "gradient_bar_per_100m": 1.6307793963959238
        },
        {
          "DN_mm": 150,
          "gradient_bar_per_100m": 0.211182910308549
        },
        {
          "DN_mm": 200,
          "gradient_bar_per_100m": 0.049718693838114794
        }
      ]
    }
  },
  "printed_flow_table_dimensions": [
    {
      "DN_mm": 6.0,
      "schedule": 80,
      "inside_diameter_mm": 5.48,
      "printed_area_cm2": 0.235
    },
    {
      "DN_mm": 8.0,
      "schedule": 80,
      "inside_diameter_mm": 7.66,
      "printed_area_cm2": 0.462
    },
    {
      "DN_mm": 10.0,
      "schedule": 80,
      "inside_diameter_mm": 10.7,
      "printed_area_cm2": 0.906
    },
    {
      "DN_mm": 15.0,
      "schedule": 80,
      "inside_diameter_mm": 13.84,
      "printed_area_cm2": 1.51
    },
    {
      "DN_mm": 20.0,
      "schedule": 80,
      "inside_diameter_mm": 18.88,
      "printed_area_cm2": 2.79
    },
    {
      "DN_mm": 25.0,
      "schedule": 80,
      "inside_diameter_mm": 24.3,
      "printed_area_cm2": 4.64
    },
    {
      "DN_mm": 40.0,
      "schedule": 80,
      "inside_diameter_mm": 38.14,
      "printed_area_cm2": 11.4
    },
    {
      "DN_mm": 50.0,
      "schedule": 40,
      "inside_diameter_mm": 52.48,
      "printed_area_cm2": 21.67
    },
    {
      "DN_mm": 65.0,
      "schedule": 40,
      "inside_diameter_mm": 62.71,
      "printed_area_cm2": 30.89
    },
    {
      "DN_mm": 80.0,
      "schedule": 40,
      "inside_diameter_mm": 77.92,
      "printed_area_cm2": 47.67
    },
    {
      "DN_mm": 100.0,
      "schedule": 40,
      "inside_diameter_mm": 102.3,
      "printed_area_cm2": 82.11
    },
    {
      "DN_mm": 150.0,
      "schedule": 40,
      "inside_diameter_mm": 154.1,
      "printed_area_cm2": 186.3
    },
    {
      "DN_mm": 200.0,
      "schedule": 30,
      "inside_diameter_mm": 205.0,
      "printed_area_cm2": 330.2
    },
    {
      "DN_mm": 250.0,
      "schedule": 30,
      "inside_diameter_mm": 257.4,
      "printed_area_cm2": 520.5
    },
    {
      "DN_mm": 300.0,
      "schedule": 30,
      "inside_diameter_mm": 307.1,
      "printed_area_cm2": 740.5
    },
    {
      "DN_mm": 350.0,
      "schedule": 30,
      "inside_diameter_mm": 336.6,
      "printed_area_cm2": 889.5
    },
    {
      "DN_mm": 400.0,
      "schedule": 30,
      "inside_diameter_mm": 387.4,
      "printed_area_cm2": 1177.0
    },
    {
      "DN_mm": 450.0,
      "schedule": 30,
      "inside_diameter_mm": 434.9,
      "printed_area_cm2": 1486.0
    },
    {
      "DN_mm": 500.0,
      "schedule": 30,
      "inside_diameter_mm": 482.6,
      "printed_area_cm2": 1829.0
    },
    {
      "DN_mm": 600.0,
      "schedule": 30,
      "inside_diameter_mm": 581.1,
      "printed_area_cm2": 2650.0
    },
    {
      "DN_mm": 750.0,
      "schedule": 30,
      "inside_diameter_mm": 730.2,
      "printed_area_cm2": 4186.0
    },
    {
      "DN_mm": 500.0,
      "schedule": 20,
      "inside_diameter_mm": 489.0,
      "printed_area_cm2": 1876.0
    },
    {
      "DN_mm": 600.0,
      "schedule": 20,
      "inside_diameter_mm": 590.6,
      "printed_area_cm2": 2744.0
    },
    {
      "DN_mm": 750.0,
      "schedule": 20,
      "inside_diameter_mm": 736.6,
      "printed_area_cm2": 4263.0
    },
    {
      "DN_mm": 500.0,
      "schedule": 10,
      "inside_diameter_mm": 495.3,
      "printed_area_cm2": 1925.0
    },
    {
      "DN_mm": 600.0,
      "schedule": 10,
      "inside_diameter_mm": 596.9,
      "printed_area_cm2": 2799.0
    },
    {
      "DN_mm": 750.0,
      "schedule": 10,
      "inside_diameter_mm": 746.2,
      "printed_area_cm2": 4373.0
    }
  ],
  "preliminary_liquid_chart": {
    "flow_panels_m3_h": [
      [
        0.1,
        10
      ],
      [
        10,
        1000
      ],
      [
        1000,
        10000
      ]
    ],
    "basis": "water at 20\u00b0C",
    "suction_gradient_bar_per_100m": [
      0.034,
      0.083
    ],
    "discharge_gradient_bar_per_100m": [
      0.149,
      0.627
    ],
    "length_choice": "if multiple sizes, smaller up to 100 m, larger over 100 m; local preliminary procedure only"
  },
  "example": {
    "status": "hypothetical constant-property liquid",
    "density_kg_m3": 1000,
    "dynamic_viscosity_Pa_s": 0.002,
    "DN_mm": 200,
    "inside_diameter_m": 0.205,
    "straight_length_m": 100,
    "elbows_90_R_1_5D": 2,
    "fully_open_standard_bore_gate_valves": 1,
    "equivalent_length_D_m": 0.2,
    "equivalent_length_m": 10.600000000000001,
    "total_length_m": 110.6,
    "velocity_m_s": 0.6829268292682927,
    "flow_m3_h": 81.14733824222434,
    "Re": 70000,
    "lambda_graph_reading": 0.0205,
    "loss_Pa": 2579.131469363475,
    "loss_bar": 0.02579131469363475,
    "loss_m_liquid": 0.2629084066629434
  },
  "graphical_data_status": "Approximate recovered chart domain; author-estimated allowances are reading resolutions, not statistical confidence or design margins"
}