Hydraulic network glossary
A working glossary of the terms and equations behind steady-state pipe-network analysis, written for practising engineers and anyone learning the field. Each entry is short on purpose: enough to define the term correctly and place it in context, with links to the worked examples and application guides where it shows up in practice.
These are the same methods Fluid Network Studio uses internally, stated openly. Where a term names a correlation or algorithm we actually solve with, we say which one. The tool is built to support a qualified engineer's judgement, not to replace it, so treat these definitions as a grounding rather than design advice.
Darcy-Weisbach equation
The standard relation for friction head loss in a full pipe flowing steadily: h_f = f (L/D) (V^2 / 2g), where f is the Darcy friction factor, L the length, D the internal diameter, V the mean velocity and g gravity. It is physically based and valid across laminar and turbulent flow for any Newtonian fluid, which is why Fluid Network Studio uses Darcy-Weisbach rather than the empirical, water-only Hazen-Williams formula. The whole method rests on getting the friction factor f right (see below).
Head loss
The mechanical energy lost per unit weight of fluid as it moves through a pipe, expressed as a height of fluid column in metres. It splits into friction loss along the pipe wall (the Darcy-Weisbach term) and minor losses at fittings and changes of section. Head loss is what makes pressure fall along a real pipe run, and balancing it around every loop and path is the core of network analysis. See the supply line with a fitting example for friction and a fitting loss side by side.
Hydraulic grade line (HGL)
The height to which fluid would rise in an open standpipe tapped into the pipe at each point: H = z + p / (rho g), where z is elevation, p is gauge pressure, rho is density and g is gravity. The HGL is total head minus the velocity head, and its slope along a pipe is the friction gradient. Fluid Network Studio solves the incompressible network in head and reports nodal pressure back from the HGL, so an HGL profile is the most natural way to read where pressure is being spent. Trace it along any run in the branched distribution example.
Reynolds number
A dimensionless number, Re = rho V D / mu (or V D / nu with kinematic viscosity nu), that compares inertial to viscous forces and so predicts the flow regime. Below roughly 2300 the flow is laminar and friction is independent of roughness; above about 4000 it is turbulent and roughness matters. The Reynolds number is the input that sets the friction factor at every iteration of a solve. For non-Newtonian fluids the plain definition no longer applies and a generalised Reynolds number is used instead (see Metzner-Reed below).
Friction factor (Churchill and Colebrook-White)
The dimensionless coefficient f in the Darcy-Weisbach equation, set by the Reynolds number and the relative roughness. The Colebrook-White equation is the classical implicit correlation for turbulent flow and is the reference most handbooks quote. Fluid Network Studio evaluates friction with the Churchill (1977) correlation, which is explicit, spans laminar, transitional and turbulent flow in one continuous expression, and agrees closely with Colebrook-White in the turbulent range - so there is no regime-switching discontinuity inside the solver. See how it works for where this sits in a solve.
Relative roughness
The internal wall roughness height divided by the pipe diameter, epsilon/D. It is dimensionless and is one of the two inputs (with Reynolds number) to the turbulent friction factor: a rougher or narrower pipe loses more head. Fluid Network Studio carries material roughness presets (commercial steel, PVC, drawn copper and so on) so you set a material and diameter rather than guessing epsilon. Note roughness only influences friction once flow is turbulent.
Minor (fitting) losses and the K factor
The localised head losses at bends, tees, valves, entrances, exits and changes of section, lumped as h = K (V^2 / 2g) where K is a dimensionless loss coefficient for the fitting. They are called "minor" by convention, not because they are always small - in short, fitting-heavy runs they can dominate. Fluid Network Studio uses the fixed-K method with a Crane TP-410 fitting library, and node types such as elbows, tees and crosses prefill their own K. See the supply line with a fitting example.
Pump curve
The relationship between the head a pump adds and the flow it passes, falling as flow rises; it is the pump's signature, usually given as a few catalogue points. Fluid Network Studio fits a least-squares head-flow curve through the points you enter and, for variable-speed pumps, scales it with the affinity laws. The pump curve is one half of finding the duty point; the system curve is the other. The pump and system example shows the fit and the resulting chart.
System curve
The head the network demands as a function of flow: the static lift (elevation and pressure difference) plus the friction and minor losses, which grow roughly with the square of flow. It is a property of the piping, not the pump. Plotting it against the pump curve is the classic way to size a pump, and changing pipe diameter or length moves the whole curve. See pump system design.
Operating point
The single flow and head at which a pump actually runs in a given system: the intersection of the pump curve and the system curve, where supply equals demand. Move either curve - throttle a valve, change speed, alter the pipework - and the operating point shifts. Fluid Network Studio solves for it directly and marks it on the pump chart. The pump and system example is the canonical case.
Best efficiency point (BEP)
The flow at which a pump converts the most shaft power into useful hydraulic power; efficiency falls away on either side. Running far from BEP wastes energy and, at low flow, can shorten pump life through recirculation and vibration. When you give a pump an efficiency curve, Fluid Network Studio reports its BEP and flags whether the duty point sits in a sensible operating region around it. This is covered in pump system design.
NPSH and NPSHa
Net Positive Suction Head is the margin between the absolute head at a pump suction and the fluid's vapour pressure, expressed as a height of fluid. NPSH available (NPSHa) is what the system provides; NPSH required (NPSHr) is what the pump needs to avoid cavitating, and safe operation needs NPSHa above NPSHr with margin. Fluid Network Studio computes NPSHa using the Antoine equation for vapour pressure and raises a cavitation-risk flag when the margin is thin. See cavitation and pump system design.
Cavitation
The formation and violent collapse of vapour bubbles when the local pressure in a liquid drops to its vapour pressure, typically at a pump suction or a sharp restriction. The collapsing bubbles erode metal, cut performance and make a characteristic gravelly noise. It is avoided by keeping NPSHa comfortably above NPSHr. Fluid Network Studio derives vapour pressure from the Antoine equation and warns when a pump is at risk; it does not predict the resulting damage, which remains an engineering judgement.
Affinity laws
The scaling relations that predict how a centrifugal pump or fan behaves at a new speed: flow scales with speed, head with speed squared, and absorbed power with speed cubed (at constant impeller diameter). They let one measured curve cover a whole range of variable-speed-drive operation. Fluid Network Studio applies the affinity laws to shift a pump's fitted curve when you set its speed, and to scale a fan's pressure-rise curve to the working density.
Compressible vs incompressible flow
Incompressible flow treats density as constant, which is accurate for liquids and for gases at low velocity and small pressure drop; the network can then be solved in head. Compressible flow lets density vary with pressure, which matters for gases over a meaningful pressure ratio - the velocity rises and density falls as pressure drops along the line. Fluid Network Studio solves liquids incompressibly in head, and gases compressibly in absolute pressure with mass-flow balances (isothermally, or with a temperature march when heat transfer is on). See the compressed-air line example and compressed air system design.
Bingham plastic
A non-Newtonian fluid model for materials that behave as a solid until a yield stress is exceeded, then flow with a constant plastic viscosity - many sludges, drilling muds and concentrated suspensions approximate this. Below the yield stress nothing moves; above it, the relation between shear stress and shear rate is linear but offset. Fluid Network Studio models homogeneous (non-settling) Bingham-plastic fluids using the Buckingham-Reiner relation in laminar flow and the Darby-Melson and Hanks methods for the transition and turbulent regimes. Settling slurries are out of scope. See the Bingham sludge line example.
Power-law (shear-thinning and shear-thickening) fluid
A non-Newtonian model where apparent viscosity changes with shear rate, set by a consistency index K and a behaviour index n. With n below 1 the fluid is shear-thinning (thins as it is sheared - many polymer solutions, pulps and pastes); with n above 1 it is shear-thickening; n equal to 1 recovers a Newtonian fluid. Fluid Network Studio handles homogeneous power-law fluids via the Metzner-Reed generalised Reynolds number and the Dodge-Metzner friction correlation. See the power-law fluid network example.
Metzner-Reed generalised Reynolds number
A redefinition of the Reynolds number for non-Newtonian fluids so that the familiar laminar friction relation (f = 16/Re, Fanning) still holds. It absorbs the consistency and behaviour indices into an effective viscosity at the wall shear rate, giving a single number that predicts the laminar-turbulent transition for power-law fluids. Fluid Network Studio uses it to choose the flow regime and friction model on every non-Newtonian pipe, and reports it per pipe so you can see the regime. See the power-law fluid network example.
Where these methods come from
Fluid Network Studio assembles the network with the Global Gradient Algorithm (Todini and Pilati, 1988) - the same incidence-matrix formulation behind EPANET - and solves it by Newton iterations. Incompressible results are cross-checked against an independent EPANET implementation, within the published verification cases spanning liquid, gas, heat and non-Newtonian flow. The named correlations above (Churchill, Crane TP-410, Antoine, the affinity laws, Metzner-Reed, Dodge-Metzner, Buckingham-Reiner, Darby-Melson and Hanks) are stated so the method is auditable. The tool does not claim compliance with any particular standard, and every result should be checked by a qualified engineer before it is relied upon.
For a step-by-step of how a network goes from sketch to solved result, see how it works. To see how the same physics meets a real design task, read the application guides for compressed air, pipe heat loss and pump systems.
Put a term to work
The fastest way to understand any of these is to solve a network that uses it. Open a built-in example or draw your own.
Launch the Studio - free to build and to run the 14 built-in examples.