How this pressure-drop model maps to textbook fluid mechanics
Use this page as both a working calculator and a short engineering brief. It accepts inner diameter and velocity prefilled from the piping preliminary design scenario (ecDi / ecDo+ecT query keys). All evaluation runs locally in your browser.
Model assumptions (read before quoting results)
- Single-phase, incompressible fluid with uniform density and viscosity along the line.
- Constant pipe inner diameter D, absolute roughness ε, and mean axial velocity v over length L (developed flow; entry lengths not modeled explicitly).
- Straight-pipe loss uses Darcy–Weisbach with Darcy friction factor f from the Churchill (1977) unified correlation across laminar, transitional, and turbulent Reynolds numbers.
- Minor losses use ΣK×ρv²/2 with user-defined K totals (fittings table or manual K). K values and the straight-pipe term use the same reference velocity (mean axial velocity in the stated inner diameter); use K data that matches your actual fitting geometry (including reducers/expansions where applicable).
- Elevation change uses ΔPz = ρgΔz with g = 9.80665 m/s²; interpret sign with your coordinate system (positive Δz upward increases static pressure requirement).
- Heat transfer, compressibility, multiphase flow, non-Newtonian rheology, unsteady/transient effects, pump/system operating-point iteration, and detailed NPSH studies are not modeled.
Standards, correlations & further reading
- Churchill (1977) unified friction factor — see existing correlation notes.
- Piping preliminary design scenario at /tools/scenarios/piping-prelim — step 3 after GB/T 17395 sizing and wall thickness check.
- Steam thermodynamics screening: /tools/steam-calculator (IAPWS-IF97) for density inputs when needed.
Shareable URL (query encodes SI inputs)
Use “Copy shareable link” below the grids. Query keys are lowercase SI tokens: rho (kg/m³), mu (Pa·s), D (m), L (m), eps (m absolute roughness), v (m/s), z (m elevation change), K (total minor-loss coefficient). Opening the link restores inputs; press Calculate again to refresh outputs after hydration. When K is present in the URL, minor-loss rows collapse to a single custom K row so the decoded total is not overwritten by default fitting rows.
Frequently asked questions
- When is Darcy–Weisbach preferred over Hazen–Williams?
- For general liquids and gases where you can supply ρ, μ, ε, and you care about Reynolds-dependent friction, Darcy–Weisbach is the more fundamental route. Hazen–Williams is an empirical water-pipe shortcut with a narrow validity window; it is still common in municipal hydraulics but should not be mixed blindly with steam, hydrocarbons, or non-water fluids.
- Why might my field measurement disagree with this calculator?
- Real installations have fittings not tabulated, partially open valves, pipe aging, deposits, temperature-dependent viscosity, entrance effects, and instrument location differences. Treat this output as an order-of-magnitude or design-check aid, not a certified loss survey.
- How is the friction factor f obtained?
- The tool uses the Churchill unified explicit f(Re, relative roughness) suitable across regimes, then applies ΔPf = f (L/D) (ρv²/2). Laminar Hagen–Poiseuille behavior emerges from the same pipeline at low Re.
- Does the elevation term include pump head?
- No. Only ρgΔz for a single continuous static head difference between endpoints is included. Pumps, control valves with active throttling, and breaks in the hydraulic grade line need separate equipment curves.
- What Reynolds number range does the Churchill (1977) implementation cover?
- The same explicit f(Re, ε/D) form is applied from laminar through transitional to fully turbulent Reynolds numbers for Newtonian flow in round pipes, consistent with the original article’s intent to span regimes without switching formulas.
- How do I combine this tool with the TP-410 style K-factor calculator on the site?
- Build or audit ΣK in the resistance-coefficient tool, then paste the total K here (or use this page’s fitting table, which follows similar catalog practice). Keep velocity bases consistent: both tools reference the pipe ID you enter.
Extended copy on this page (headings, assumptions, references, FAQs) may be drafted or localized with AI assistance; engineering judgment and governing codes still apply. Numerical models run locally in your browser as implemented. For contract-critical work, cite primary standards and qualified review.