Pipe Flow Calculator - Darcy-Weisbach Head Loss and Pressure Drop

Pipe flow describes how a fluid moves through a closed conduit. This calculator turns a pipe's inner diameter, length, flow rate, and fluid properties into flow velocity, Reynolds number, friction factor, head loss, and pressure drop, so you can size a pump or check a gravity drain.

• • Pump and pipe sizing: check the head loss a pump must overcome for a given flow rate.
• • Gravity drain and stormwater checks: see whether a sloped drain can carry a design rainfall.
• • Compare pipe materials: swap drawn tubing, commercial steel, and concrete to compare pressure drop.
• • Compare working fluids: switch between water, air, and oil for the same physical run of pipe.

If the diameter is still open, the pipe size calculator helps you back-solve the diameter that holds a given flow rate at a target velocity.

The calculator implements Darcy-Weisbach end to end: diameter, length, and flow rate become velocity; density and viscosity give a Reynolds number; the Reynolds number picks the friction factor model; the friction factor and velocity give head loss and pressure drop. Fluid presets fill the density and viscosity.

• D, L: pipe inner diameter and straight-run length in metres.
• Q, A, V: flow rate, cross-section (pi D squared over 4), and average velocity (Q / A).
• rho, mu: fluid density and dynamic viscosity, preset or custom.
• f: Darcy friction factor, 64 over Re for laminar, Swamee-Jain for turbulent.
• eps: pipe wall roughness in metres, from the millimetres you enter.
• g: gravitational acceleration, 9.80665 m/s^2.

Swamee-Jain approximates the Colebrook-White implicit friction factor to within 1 percent for typical engineering Reynolds numbers and roughnesses, which is why spreadsheets use it. Between Re 2300 and 4000 the calculator still uses Swamee-Jain but flags the regime as transitional.

According to Wikipedia - Darcy-Weisbach equation, head loss h_f equals f L/D V^2/(2g), and pressure drop is that head loss times fluid density times gravity.

According to Wikipedia - Darcy friction factor formulae, Swamee-Jain approximates the Colebrook-White implicit friction factor to within 1 percent.

For a quick Reynolds number sanity check, the Reynolds number calculator does the same density times velocity times diameter divided by viscosity product in one step.

Four ideas drive the result. None dominates on its own; the pressure drop depends on how pipe geometry, fluid properties, and flow speed interact.

These four ideas together decide the entire pressure drop. The Reynolds number and the friction-factor model show up as the intermediate outputs, so the user can see which regime the pipe is operating in before trusting the head loss number.

If the friction factor is the only number you need, the friction factor calculator takes the same Reynolds number and relative roughness and returns f in isolation, which is useful when the pipe is shared between two different flow rates.

The default values reproduce a 50 mm commercial steel pipe carrying 5 L/s of water at 20 deg C over 10 m, so the workflow can be verified against the worked example above before you plug in your own numbers.

1. 1 Enter diameter and length: Type the inner diameter in millimetres and the straight-run length in metres.
2. 2 Enter the flow rate: Type the volumetric flow rate in litres per second (multiply GPM by 0.0631 to convert).
3. 3 Pick a fluid preset or enter custom values: Choose water, water at 4 deg C, air, SAE 30 oil, or custom with your own density and viscosity.
4. 4 Set the pipe roughness: Type the wall roughness in millimetres. Use 0.0015 for drawn tubing, 0.045 for commercial steel, 0.15 for galvanized iron.
5. 5 Read the results: Velocity tells you the flow speed, the Reynolds number and regime label tell you which friction-factor model was used, and the head loss and pressure drop are the headline numbers.

An engineer sizing a 100 m run of 100 mm commercial steel pipe that needs to carry 10 L/s of water at 20 deg C sets D = 100, L = 100, Q = 10, fluidPreset = water20C, roughness = 0.045. The result is V = 1.27 m/s, Re = 126,841 (turbulent), f = 0.0215, head loss = 1.42 m, pressure drop = 13.92 kPa.

If the pipe is not horizontal, the Bernoulli equation calculator combines this head loss with the elevation and velocity heads into the full Bernoulli energy balance.

A single Darcy-Weisbach evaluation per click replaces the multi-step Moody chart lookup and the multi-iteration Colebrook solver.

• • Settle pump head in one pass: Plug in the design flow rate and pipe geometry, read the head loss, and add the elevation head to get the total dynamic head.
• • Pick the right pipe material: Swap drawn tubing, commercial steel, and concrete roughnesses to see which one keeps the pressure drop under budget.
• • Compare fluids without re-deriving viscosity: Pick water at 4 deg C versus 20 deg C, air, oil, or a custom fluid, and the same pipe geometry returns the new head loss and pressure drop.
• • See which regime the pipe is in: The Reynolds number and regime label tell you at a glance whether the friction factor came from the laminar or turbulent model.
• • Use both metric and imperial units: Inputs are metric, while the pressure drop is also returned in psi for cross-checking with US plumbing and pump ratings.
• • Audit every step: Velocity, Reynolds number, friction factor, head loss, and pressure drop are all visible, so the calculation can be checked field by field.

The tool solves one straight-run Darcy-Weisbach problem at a time. For networks with branches, loops, or pumps, the per-pipe head loss is the right building block and the rest of the network has to be balanced with a Hardy-Cross or linear solver on top.

When the straight run is part of a reactor or clarifier circuit, the hydraulic retention time calculator turns the flow velocity and the pipe volume into the residence time.

The head loss and pressure drop printed by the calculator assume a single straight run of pipe, a single homogeneous fluid, and a fully developed flow profile. Common reasons the real number differs:

• • It assumes fully developed flow. The first 10-50 diameters after a sharp entrance, a pump, or a valve carry an entrance or developing length that adds extra loss.
• • It assumes a single fluid temperature. For long pipe runs with a strong ambient temperature gradient, the density and viscosity change along the pipe.

According to Wikipedia - Reynolds number, pipe flow is laminar below Re 2300, transitional between 2300 and 4000, and fully turbulent above 4000.

For the stored-volume side of the same pipe, the pipe volume calculator takes the same inner diameter and length and returns the area times length in litres and gallons.