This page documents key calculation paths used by Frictionless Calc so results can be independently checked.
Pipe pressure-drop calculator
1. Geometry and velocity
For inside diameter D and volumetric flow rate Q:
2. Reynolds number
Using density ρ and dynamic viscosity μ:
3. Straight-pipe friction factor
The calculator uses the Darcy friction factor and normally selects the method by Reynolds number. An optional custom mode lets the user enter a Darcy friction factor directly; Reynolds number is still calculated and displayed, but the entered value is used for straight-pipe pressure loss.
Laminar flow: Re ≤ 2300
Transition region: 2300 < Re < 4000
The Churchill correlation is used as a continuous estimate through the transition region. Because transition flow can be unstable and sensitive to disturbances, the calculator displays a warning for results in this range.
Turbulent flow: Re ≥ 4000
The Colebrook-White equation is solved iteratively using relative roughness ε/D.
4. Straight-pipe pressure loss
Here L is straight-pipe length. The calculator performs the calculation internally in SI units and converts the displayed result afterward.
5. Fitting losses
Fittings are represented by dimensionless loss coefficients K. Depending on fitting type, the coefficient may use a complete-turbulence reference factor, diameter ratio, bend radius ratio, junction flow split, or fitting angle.
For fitting rules expressed as a multiple of a complete-turbulence reference factor, the calculator uses a fixed reference roughness of 0.0018 in (0.04572 mm). This fitting reference factor is intentionally separate from the actual pipe roughness entered for the straight-pipe calculation.
Long-radius elbow options are included explicitly. The 90° long-radius elbow uses r/d ≈ 1.5, and the 45° long-radius elbow is evaluated from the non-90° bend relation at the same radius ratio.
The fitting list also supports user-defined loss methods: a direct K, a multiplier K = n fT, or an equivalent-length ratio Le/D converted with K = f(Le/D). These options are intended for vendor-specific strainers, filters, meters, backflow preventers, proprietary fittings, partly open valves, and other inline equipment when project or manufacturer data are available.
Tee and wye junctions
Converging and diverging junctions are calculated separately for the branch path and run path. The correlations use the branch diameter ratio β = dbranch/dcombined, the branch flow fraction x = Qbranch/Qcombined, and, where applicable, the branch angle. Standard 30°, 45°, 60°, and 90° junction angles are supported.
Because a junction can redistribute momentum and static pressure, a path-specific junction coefficient can be negative. This is not automatically an error. The main calculator still represents one constant-flow straight-pipe section, so split or merged downstream sections with different flows should be calculated separately.
Tilting-disc check valves
Tilting-disc check-valve options are provided for 5° and 15° seat angles in the listed 2–8 in, 10–14 in, and 16–48 in size groups. As with other check-valve entries, the listed coefficients assume sufficient velocity for full disc lift.
6. Total pressure drop
The results panel also reports straight-pipe loss and fitting loss separately so the total can be audited.
Important applicability notes
- The current calculator assumes one constant pipe diameter for the modeled section.
- Flow in the transition region is less predictable than fully laminar or turbulent flow.
- Some check-valve, tilting-disc, stop-check, and foot-valve coefficients assume sufficient velocity for full disc lift. The calculator displays an applicability warning for those fittings.
- Tee/wye coefficients are path-specific and referenced to combined-leg velocity and diameter; systems with different flows in downstream branches should be separated into appropriate calculation sections.
- Actual systems may require additional losses, equipment data, elevation terms, compressibility treatment, or project-specific design standards.
Multi-layer heat-transfer calculator
The heat-transfer tool models steady-state, one-dimensional heat flow through a series of area-normalized thermal resistances. All elements are assumed to have the same heat-transfer area.
For convection, the user may enter h directly or compute it from a known Nusselt number using h = Nu·k/Lc. Fluid velocity is not converted directly into a convection coefficient because velocity alone is insufficient; the applicable geometry, fluid properties, flow regime, and correlation are also required.
When solving for one unknown layer property from a known heat flux or heat rate, the required total resistance is first calculated from R''total = (TA − TB)/q''. The resistance of all known elements is subtracted, and the remaining resistance is converted to the selected unknown conductivity, thickness, convection coefficient, or contact resistance.
Interface temperatures are calculated sequentially from Side A using ΔT = q''R'' for each resistance element.
Related calculators
Focused calculators are available for pipe velocity, Reynolds number, friction factor, K factor and equivalent length, liquid valve Cv, pump power, NPSH available, and liquid orifice flow, plus multi-layer heat transfer. Each page documents its equation and limitations.