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 selects the method by Reynolds number.
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, 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.
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, stop-check, and foot-valve coefficients assume sufficient velocity for full disc lift. The calculator displays an applicability warning for those fittings.
- 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.