Pipe Pressure Drop and Pump Sizing Calculator

The calculation follows a steady mechanical-energy balance between large supply and receiving vessels. Every head is measured in metres of the pumped liquid. SI is used internally; displayed physical quantities support the platform's metric/US conversion.

With $A=\pi D^2/4$, $v=Q/A$ and $Re=\rho vD/\mu$, the Darcy friction factor is $64/Re$ for $0<Re\leq2000$, including $Re<1$; no positive Reynolds number is clamped. The Colebrook–White turbulent equation is

Fourteen fixed-point iterations start from the Swamee–Jain estimate. The explicit alternative is $f=0.25/[\log_{10}(\epsilon/(3.7D)+5.74/Re^{0.9})]^2$. These are Darcy factors, four times the Fanning factor. At zero flow the displayed factor is set to zero so all losses vanish; a physical friction factor is not defined there.

For $2000<Re<4000$, the tool linearly blends $f=0.032$ at Re=2000 with the selected turbulent value at Re=4000. This is a continuity aid, not a validated transition correlation. EPA EPANET 2.2, attached pp. 31–33 and 125, supports the regime distinction and minor-loss method; EPANET uses a different, cubic transition interpolation.

The reported friction pressure drop is $\Delta p_{loss}=\rho g(h_f+h_K)$. Total required pump head is $H=\Delta z+\Delta p_{vessels}/(\rho g)+h_f+h_K$. Hydraulic power is $\rho gQ\max(H,0)$; divide by pump efficiency for shaft power and by motor/drive efficiency for electrical input. The positive-head limit makes power zero for gravity-driven duties.

The user-entered curve is $H_p(Q)=H_0-(H_0-H_e)(Q/Q_e)^2$, valid only for $0\leq Q\leq Q_e$. Brent's method solves $H_p-H_{system}=0$ only with a bracket in that interval. A constant head ($H_0=H_e$) is also supported. The chart stays within the entered range. The evaluated flow is either the specified flow or that root.

For a negligible-velocity supply surface,

The same diameter, roughness and friction method apply to the suction subset. Suction losses are already included in total losses. Reported NPSH margin is $NPSH_a-NPSH_r$; reserve also subtracts the entered extra allowance. The published NPSH check uses equivalent stagnation head, not a static pressure tap.

• Steady, single-phase, incompressible Newtonian liquid in a completely full, rigid circular pipe; constant properties and one inside diameter/roughness throughout.
• End-vessel velocities are negligible. Positive Δz and Δp mean the receiving vessel is higher or at higher pressure. Positive suction elevation means the liquid surface is above the manufacturer's pump datum.
• All K values refer to the same mean pipe velocity. Add entrance, exit, valve, elbow and strainer losses as appropriate; actual fitting data take precedence over generic examples. EPA EPANET Table 3.3 gives illustrative K=0.5 for a square entrance, 1.0 for an exit and 0.9 for a short-radius elbow.
• The default roughness is EPA's new-steel value, 0.15 millifeet = 0.04572 mm. Default fluid inputs approximate water at 20 °C; they are editable values, not a temperature-property model.
• The default pump curve, efficiencies, NPSHr and 1 m allowance are illustrative design inputs, not catalogue data or universal selection rules. Update NPSHr and efficiency at the evaluated flow. The two-point quadratic does not establish a best-efficiency point or preferred operating range.
• The metric/US switch converts supported length, pressure, density and power displays. Flow fields accept unit-tagged US entries such as 44.03 gal/min; both m³/h and US gal/min duty readouts are provided. The schematic's labels and flow-chart axis retain their marked SI units.
• Liquid-surface elevations set hydrostatic energy terms; they are not pipe endpoint elevations. Enter actual pipe run lengths between vessel connections and pump. A short horizontal connection can serve a submerged tank nozzle even when the liquid surface is well above it; pipe lengths are not compared with liquid-surface elevations.

Use for preliminary sizing and teaching of full liquid lines. Fully developed laminar flow is represented below Re=2000; turbulent sizing is intended for Re≥4000 with Colebrook, or preferably Re≥5000 with Swamee–Jain, up to Re=10⁸ and ε/D≤0.05. A transition estimate is flagged. Short entrance regions and laminar fitting coefficients may need more detailed treatment.

Only the manufacturer-supported flow interval entered for the pump is solved; no pump-curve extrapolation is used for the operating point. If a bracket is absent, operating-point mode holds the result cards and identifies what to change. A zero helper intersection in specified-flow mode means no supported intersection, not a prediction of no flow. A flat pump curve with a loss-free line does not define a unique operating point and is rejected in operating-point mode. The duty readout always identifies the chosen evaluated flow.

NPSHa is an energy margin above vapor pressure, not gauge pressure. NPSHr often means NPSH3, a specified head-drop test criterion; exceeding it alone does not guarantee cavitation-free operation. Set the additional allowance using manufacturer and application guidance. Verify worst-case liquid level, temperature, atmospheric pressure, strainer fouling and flow.

Not a network, transient, water-hammer, compressible, non-Newtonian, two-phase or slurry model. Separate suction and discharge diameters, detailed measured pump curves, viscous pump corrections and speed variation are outside scope. Electrical power is an estimate at the entered efficiencies, not a motor nameplate rating. Installation and commissioning require qualified personnel.