Water in a 100 mm pipe
Inputs: water at 20 C, Q = 10 L/s, D = 100 mm, L = 50 m, PVC roughness. The area is 0.00785 m², velocity is 1.27 m/s, Re is about 127,000, turbulent. Swamee-Jain gives f about 0.017 and ΔP about 6.9 kPa.
Pump-loss estimate
Pipe Flow Calculator — Flow Rate, Velocity, Reynolds Number & Pressure Drop
Inputs
Flow
If Q, D, and v are all entered, the calculator checks whether they agree before using the selected solve path.
Pipe or duct
Hydraulic diameter uses \(D_h = 4A/P_{\text{wetted}}\). Circular diameter solve is available only for circular pipe geometry.
Fluid
Presets are typical values near the listed temperature. Edit the properties for design data.
ν is kept in sync from μ/ρ when a preset is applied; edit any property as needed.
Pressure loss
Major losses only: fittings, valves, entrances, elevation change, compressibility, and pump curves are not included.
Results
Solved Variables
Q: – | Dh: – | v: –
Reynolds Number
Re = – (–)
Pressure Loss
f: – | ΔP: – | head: –
Gradient: –
Fluid Properties Used
ρ: – | μ: – | ν: –
Enter the required fields to see an interpretation.
Calculation steps
Results will appear after calculation.
Equations: \( v=\frac{Q}{A} \), \( D_h=\frac{4A}{P} \), \( \mathrm{Re}=\frac{vD_h}{\nu} \), \( \Delta P=f\frac{L}{D_h}\frac{\rho v^2}{2} \).
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What This Calculator Does
This calculator estimates flow rate, velocity, Reynolds number, Darcy friction factor, head loss, and pressure drop for steady, incompressible, single-phase flow in a full pipe or duct. Use circular pipe diameter, rectangular duct dimensions, or a custom hydraulic diameter. The pressure-drop result uses Darcy-Weisbach major loss only, so add separate allowances for fittings, valves, entrances, exits, elevation changes, pumps, and compressible gas effects when those matter.
Methods and Assumptions
Flow area is \(A=\pi D^2/4\) for a circular full pipe and \(A=wh\) for a rectangular duct. Mean velocity is \(v=Q/A\). Non-circular sections use the hydraulic diameter \(D_h=4A/P_{\text{wetted}}\). Reynolds number is \( \mathrm{Re}=vD_h/\nu=\rho vD_h/\mu \).
Regime thresholds follow the common internal-flow convention: laminar below Re 2300, transitional from about 2300 to 4000, and turbulent above about 4000. Laminar Darcy friction factor is \(f=64/\mathrm{Re}\). Turbulent friction factor is estimated with the Swamee-Jain explicit approximation, \(f=0.25/[\log_{10}(\epsilon/(3.7D_h)+5.74/\mathrm{Re}^{0.9})]^2\), which is commonly used as a practical approximation to Colebrook-White for turbulent pipe flow. Transitional friction factor is uncertain; this tool blends the laminar and turbulent estimates only to provide a planning estimate.
Pressure drop is calculated with Darcy-Weisbach: \( \Delta P=f(L/D_h)(\rho v^2/2) \). Head loss is \(h_f=\Delta P/(\rho g)\), with \(g=9.80665\ \mathrm{m/s^2}\). Source notes: Reynolds thresholds, Darcy-Weisbach, hydraulic diameter, Colebrook-White, and Swamee-Jain/Haaland-style explicit approximations are standard topics in fluid mechanics references such as Crane TP-410 and Munson, Young, and Okiishi's Fundamentals of Fluid Mechanics. Use manufacturer data or project standards for final roughness values.
Units & Assumptions
- Supported flow units: m³/s, L/s, L/min, m³/h, gpm, and cfs.
- Supported diameter units: m, mm, cm, in, and ft. Velocity units: m/s and ft/s. Pressure output: Pa, kPa, bar, and psi.
- Assumptions: full pipe or duct, steady incompressible Newtonian fluid, no phase change, no elevation term, and no minor losses.
- Gas flows are treated as incompressible. For high Mach number or large pressure-ratio gas flow, use a compressible-flow method.
Disclaimer: Educational calculator only — not a substitute for detailed engineering design or code compliance.
Worked Examples
Air through a rectangular duct
Inputs: air at 20 C, 300 mm by 150 mm duct, Q = 250 L/s, L = 12 m, galvanized iron roughness. \(D_h=0.2\) m, velocity is 5.56 m/s, Re is about 74,000, turbulent, and ΔP is about 25 Pa before minor losses.
HVAC duct flow
Oil in a small tube
Inputs: light oil, Q = 0.2 L/min, D = 8 mm, L = 2 m, drawn tubing. Velocity is 0.066 m/s and Re is about 9, so the flow is laminar. The calculator uses \(f=64/Re\), giving a pressure drop near 3.3 kPa.
Laminar example
Diameter sizing from flow and velocity
Inputs: water at 20 C, Q = 25 gpm, target velocity = 5 ft/s. Solving for diameter gives about 1.43 in. Re is about 55,000, so a pressure-drop check should use a turbulent friction-factor method and the chosen pipe roughness.
Sizing workflow
FAQ
How do I calculate flow velocity from flow rate?
For a full circular pipe, velocity is \(v=Q/A\), where \(A=\pi D^2/4\). For a non-circular section, use \(v=Q/A\) with the entered flow area.
What Reynolds number is turbulent in a pipe?
This calculator classifies Re below 2300 as laminar, 2300 to 4000 as transitional, and 4000 or above as turbulent for internal pipe flow.
How do I calculate pressure drop in a pipe?
Pressure drop is estimated with Darcy-Weisbach: \(\Delta P=f(L/D)(\rho v^2/2)\). The calculator estimates \(f\) from laminar \(f=64/Re\) or a turbulent explicit approximation using roughness.
What roughness should I use?
Use a material preset when you know the pipe material, such as PVC, copper, commercial steel, galvanized iron, cast iron, concrete, or drawn tubing. For design work, confirm roughness from manufacturer or project standards.
Can this handle non-circular ducts?
Yes. Choose rectangular duct or custom hydraulic diameter. The hydraulic diameter is \(D_h=4A/P_{\text{wetted}}\) and is used for Reynolds number and Darcy-Weisbach pressure loss.
What if my pipe is partly full?
Partly full flow is open-channel flow, not full-pipe pressure flow. Use a method such as Manning or a dedicated open-channel calculator for that case.