{
  "id": "pressure-drop",
  "version": "fe60ee7472d4",
  "status": "published",
  "name": "Pressure Drop Calculator",
  "question": "What is the pressure drop in my pipe?",
  "summary": "Pressure drop calculator for pipe flow: the Darcy-Weisbach pressure and head loss from the flow rate or velocity, pipe size, length and material, with the friction factor, Reynolds number and flow regime.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/pressure-drop-calculator",
  "markdown": "https://www.acalculator.org/physics/pressure-drop-calculator.md",
  "kind": "function",
  "method": "Δp = f × (L ÷ D) × ρv² ÷ 2; h = Δp ÷ ρg; Re = ρvD ÷ μ; f = 64 ÷ Re for Re < 2,000; f = 0.25 ÷ [log10(ε ÷ 3.7D + 5.74 ÷ Re^0.9)]² for Re > 4,000; Dunlop’s cubic between (EPANET).",
  "assumptions": [
    "Steady flow of a liquid (incompressible) filling a straight round pipe; fittings, valves and height changes are not included.",
    "Between Re = 2,000 and 4,000 the flow is unstable and f is uncertain (Hydraulic Institute); the page interpolates as EPANET does."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "by": {
        "title": "Flow given as",
        "description": "Give the flow as a volume rate or as the mean velocity in the pipe.",
        "type": "string",
        "enum": [
          "flow",
          "velocity"
        ]
      },
      "q": {
        "title": "Flow rate (Q)",
        "description": "The volume of fluid per unit time, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-9,
        "maximum": 1000000000
      },
      "qu": {
        "title": "Flow unit",
        "description": "The unit of the flow rate you type.",
        "type": "string",
        "enum": [
          "gpm",
          "lps",
          "lpm",
          "m3h",
          "cfs"
        ]
      },
      "v": {
        "title": "Velocity (v)",
        "description": "The mean velocity of the fluid in the pipe.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0.000001,
        "maximum": 100
      },
      "D": {
        "title": "Inside diameter (D)",
        "description": "The inside diameter of the pipe.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0001,
        "maximum": 10
      },
      "L": {
        "title": "Pipe length (L)",
        "description": "The length of straight pipe.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.001,
        "maximum": 10000000
      },
      "mat": {
        "title": "Pipe material",
        "description": "The pipe material, which sets the absolute roughness ε (Hydraulic Institute Table 3.A.1).",
        "type": "string",
        "enum": [
          "drawn",
          "copper",
          "fiberglass",
          "rubber",
          "stainless",
          "steel",
          "asphalted",
          "galvanized",
          "castIron",
          "concreteSmooth",
          "concreteRough",
          "custom"
        ]
      },
      "e": {
        "title": "Roughness (ε)",
        "description": "The absolute roughness of the pipe wall.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0,
        "maximum": 0.1
      },
      "fl": {
        "title": "Fluid",
        "description": "The fluid, which sets its density and viscosity (NIST Chemistry WebBook for water).",
        "type": "string",
        "enum": [
          "water10",
          "water20",
          "water40",
          "water60",
          "water80",
          "custom"
        ]
      },
      "rho": {
        "title": "Density (ρ)",
        "description": "The density of the fluid.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "minimum": 0.01,
        "maximum": 30000
      },
      "mu": {
        "title": "Viscosity (μ)",
        "description": "The dynamic viscosity of the fluid, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-7,
        "maximum": 1000000
      },
      "muu": {
        "title": "Viscosity unit",
        "description": "The unit of the viscosity you type.",
        "type": "string",
        "enum": [
          "Pa-s",
          "mPa-s",
          "P"
        ]
      }
    }
  },
  "outputs": {
    "dp": {
      "label": "Pressure drop",
      "description": "Δp = f × (L ÷ D) × ρ × v² ÷ 2 over the length of pipe.",
      "format": "quantity",
      "unit": "psi"
    },
    "pa": {
      "label": "Pressure drop (Pa)",
      "description": "The pressure drop in pascals.",
      "format": "number"
    },
    "psi": {
      "label": "Pressure drop (psi)",
      "description": "The pressure drop in pounds per square inch.",
      "format": "number"
    },
    "headM": {
      "label": "Head loss (m)",
      "description": "h = Δp ÷ (ρg): the same loss as a height of the fluid, in metres.",
      "format": "number"
    },
    "headFt": {
      "label": "Head loss (ft)",
      "description": "The head loss in feet of the fluid.",
      "format": "number"
    },
    "velocity": {
      "label": "Velocity (m/s)",
      "description": "The mean velocity in the pipe.",
      "format": "number"
    },
    "flowLps": {
      "label": "Flow rate (L/s)",
      "description": "The flow rate in litres per second.",
      "format": "number"
    },
    "re": {
      "label": "Reynolds number",
      "description": "Re = ρ × v × D ÷ μ.",
      "format": "number"
    },
    "regime": {
      "label": "Flow",
      "description": "Laminar below Re = 2,000, turbulent above 4,000, transitional between.",
      "format": "text"
    },
    "f": {
      "label": "Friction factor f",
      "description": "The Darcy friction factor used (EPANET method).",
      "format": "number"
    },
    "colebrook": {
      "label": "Colebrook friction factor",
      "description": "The Colebrook-White factor, for turbulent flow only, to compare.",
      "format": "number"
    },
    "relRough": {
      "label": "Relative roughness ε ÷ D",
      "description": "The roughness as a share of the diameter.",
      "format": "number"
    },
    "rho": {
      "label": "Density used (kg/m³)",
      "description": "The fluid density in kilograms per cubic metre.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "by": "flow",
      "q": 30,
      "qu": "gpm",
      "v": 1,
      "D": 0.0508,
      "L": 30.48,
      "mat": "steel",
      "e": 0.000045,
      "fl": "water20",
      "rho": 900,
      "mu": 100,
      "muu": "mPa-s"
    },
    "outputs": {
      "dp": 6287.820042195853,
      "pa": 6287.820042195853,
      "psi": 0.9119711941747553,
      "headM": 0.642328972993125,
      "headFt": 2.1073785203186515,
      "velocity": 0.9338257130973868,
      "flowLps": 1.8927058920000002,
      "re": 47277.787126201954,
      "regime": "Turbulent",
      "f": 0.0240782697940942,
      "colebrook": 0.023935876308155146,
      "relRough": 0.0009,
      "rho": 998.21
    },
    "text": "The pressure drop is 0.91197 psi (2.1074 ft of head), with f = 0.0240783 at Re = 47,277.8."
  },
  "examples": [
    {
      "given": {
        "by": "velocity",
        "v": 1,
        "D": 0.05,
        "L": 10,
        "mat": "drawn",
        "fl": "custom",
        "rho": 900,
        "mu": 0.1,
        "muu": "Pa-s"
      },
      "expect": {
        "re": 450,
        "f": 0.14222222222222222,
        "pa": 12800,
        "regime": "Laminar"
      },
      "source": "Hydraulic Institute, HI Data Tool, Pipe Frictional Losses (Eq. 3.A.1 h_f = f × (L ÷ D) × v² ÷ 2g; Eq. 3.A.2 Colebrook; Eq. 3.A.3 explicit approximation; Eq. 3.A.5 f = 64 ÷ Re below 2,000; Table 3.A.1 roughness), https://datatool.pumps.org/fluid-flow-iii/general (retrieved 2026-10-18) (f = 64 ÷ Re); OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence (Poiseuille’s law, Equation 14.19: Q = (p₂ − p₁)πr⁴ ÷ 8ηl), https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence (retrieved 2026-10-18): Δp = 8ηlv ÷ r² = 8 × 0.1 × 10 × 1 ÷ 0.025² = 12,800 Pa, the same as Darcy-Weisbach with f = 64 ÷ 450",
      "tolerance": 1e-12
    },
    {
      "given": {
        "by": "flow",
        "q": 30,
        "qu": "gpm",
        "D": 0.0508,
        "L": 30.48,
        "mat": "steel",
        "fl": "water20"
      },
      "expect": {
        "v": 0.9338257130973868,
        "re": 47277.787126201954,
        "f": 0.0240782697940942,
        "psi": 0.9119711941747553,
        "colebrook": 0.023935876308155146
      },
      "source": "Hydraulic Institute, HI Data Tool, Pipe Frictional Losses (Eq. 3.A.1 h_f = f × (L ÷ D) × v² ÷ 2g; Eq. 3.A.2 Colebrook; Eq. 3.A.3 explicit approximation; Eq. 3.A.5 f = 64 ÷ Re below 2,000; Table 3.A.1 roughness), https://datatool.pumps.org/fluid-flow-iii/general (retrieved 2026-10-18); US EPA, EPANET Users Manual, 13. Analysis Algorithms, §13.1 (Hagen-Poiseuille below Re = 2,000, Swamee and Jain above 4,000, Dunlop’s cubic interpolation between), https://epanet-manual.readthedocs.io/en/latest/analysis_algorithms.html (retrieved 2026-10-18); NIST Chemistry WebBook, SRD 69, Isobaric Properties for Water at 0.101325 MPa (20 °C: 998.21 kg/m³, 0.0010016 Pa·s), https://webbook.nist.gov/cgi/fluid.cgi?Action=Load&ID=C7732185&Type=IsoBar&Digits=5&P=0.101325&THigh=100&TLow=10&TInc=10&RefState=DEF&TUnit=C&PUnit=MPa&DUnit=kg%2Fm3&HUnit=kJ%2Fkg&WUnit=m%2Fs&VisUnit=Pa*s&STUnit=N%2Fm (retrieved 2026-10-18); hand calculation in content.mdx",
      "tolerance": 1e-9
    },
    {
      "given": {
        "by": "velocity",
        "v": 0.3,
        "D": 0.01,
        "L": 1,
        "mat": "drawn",
        "fl": "water20"
      },
      "expect": {
        "re": 2989.8462460063897,
        "regime": "Transitional (critical zone)",
        "f": 0.03304276025407338
      },
      "source": "US EPA, EPANET Users Manual, 13. Analysis Algorithms, §13.1 (Hagen-Poiseuille below Re = 2,000, Swamee and Jain above 4,000, Dunlop’s cubic interpolation between), https://epanet-manual.readthedocs.io/en/latest/analysis_algorithms.html (retrieved 2026-10-18) (Dunlop cubic interpolation); hand calculation in content.mdx",
      "tolerance": 1e-9
    },
    {
      "given": {
        "by": "velocity",
        "v": 2,
        "D": 0.2,
        "L": 1000,
        "mat": "castIron",
        "fl": "water10"
      },
      "expect": {
        "re": 306210.27643770585,
        "f": 0.021876722657402755,
        "colebrook": 0.02173123161355749
      },
      "source": "Hydraulic Institute, HI Data Tool, Pipe Frictional Losses (Eq. 3.A.1 h_f = f × (L ÷ D) × v² ÷ 2g; Eq. 3.A.2 Colebrook; Eq. 3.A.3 explicit approximation; Eq. 3.A.5 f = 64 ÷ Re below 2,000; Table 3.A.1 roughness), https://datatool.pumps.org/fluid-flow-iii/general (retrieved 2026-10-18) (Colebrook and the explicit form); US EPA, EPANET Users Manual, 13. Analysis Algorithms, §13.1 (Hagen-Poiseuille below Re = 2,000, Swamee and Jain above 4,000, Dunlop’s cubic interpolation between), https://epanet-manual.readthedocs.io/en/latest/analysis_algorithms.html (retrieved 2026-10-18); NIST Chemistry WebBook, SRD 69, Isobaric Properties for Water at 0.101325 MPa (20 °C: 998.21 kg/m³, 0.0010016 Pa·s), https://webbook.nist.gov/cgi/fluid.cgi?Action=Load&ID=C7732185&Type=IsoBar&Digits=5&P=0.101325&THigh=100&TLow=10&TInc=10&RefState=DEF&TUnit=C&PUnit=MPa&DUnit=kg%2Fm3&HUnit=kJ%2Fkg&WUnit=m%2Fs&VisUnit=Pa*s&STUnit=N%2Fm (retrieved 2026-10-18); hand calculation in content.mdx",
      "tolerance": 1e-9
    }
  ],
  "sources": [
    "Hydraulic Institute, HI Data Tool, Pipe Frictional Losses: Eq. 3.A.1, h_f = f × (L ÷ D) × v² ÷ 2g; Eq. 3.A.2, Colebrook; Eq. 3.A.3, the explicit approximation; Eq. 3.A.4, Re = ρvD ÷ μ; Eq. 3.A.5, f = 64 ÷ Re; Table 3.A.1, pipe roughness, retrieved 2026-10-18. https://datatool.pumps.org/fluid-flow-iii/general",
    "US EPA, EPANET Users Manual, 13. Analysis Algorithms, §13.1 Hydraulics: Hagen-Poiseuille below Re = 2,000, Swamee and Jain above 4,000, and Dunlop’s cubic interpolation from the Moody diagram between, retrieved 2026-10-18. https://epanet-manual.readthedocs.io/en/latest/analysis_algorithms.html",
    "OpenWaterAnalytics, EPANET source code, src/hydcoeffs.c, frictionFactor(): the turbulent factor 1 ÷ (−0.8686 ln y)² and the transition terms taken at Re = 4,000, retrieved 2026-10-18. https://github.com/OpenWaterAnalytics/EPANET/blob/dev/src/hydcoeffs.c",
    "NIST Chemistry WebBook, SRD 69, Isobaric Properties for Water at 0.101325 MPa: density and viscosity at 10, 20, 40, 60 and 80 °C, retrieved 2026-10-18. https://webbook.nist.gov/cgi/fluid.cgi?Action=Load&ID=C7732185&Type=IsoBar&Digits=5&P=0.101325&THigh=100&TLow=10&TInc=10&RefState=DEF&TUnit=C&PUnit=MPa&DUnit=kg%2Fm3&HUnit=kJ%2Fkg&WUnit=m%2Fs&VisUnit=Pa*s&STUnit=N%2Fm",
    "OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence: Poiseuille’s law, Equation 14.19, Q = (p₂ − p₁)πr⁴ ÷ 8ηl, retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence",
    "Colebrook, C. F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. Journal of the Institution of Civil Engineers 11(4), 133–156. https://doi.org/10.1680/ijoti.1939.13150",
    "Swamee, P. K., and Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division (ASCE) 102(5), 657–664. https://doi.org/10.1061/JYCEAJ.0004542"
  ],
  "related": [
    "reynolds-number",
    "flow-rate",
    "manning-equation",
    "pressure"
  ],
  "changelog": []
}