Validation

Series pipe + pump lifting water from a 1350 ft reservoir to a 1425 ft reservoir (75 ft static lift) through 6000 ft of 18 in pipe, sand-grain roughness 0.015 in, water ν = 1.14×10⁻⁵ ft²/s (≈ 60 °F), local losses neglected. Ingersoll-Dresser 15H277 pump (largest impeller). Book answer: Q = 3280 gpm = 7.30 ft³/s, pump head = 95.7 ft, f = 0.019546.

Example Problem 2.4's line (6000 ft of 18 in pipe, 1350→1425 ft reservoirs, water ν = 1.14×10⁻⁵ ft²/s (≈ 60 °F), local losses neglected) but driven by two three-stage Ingersoll-Dresser 15H277 pumps in parallel (smallest impeller per stage). Each pump carries half the pipeline flow. Per-stage curve points (6.685 ft³/s, 67 ft), (7.35, 55), (7.80, 45); a 3-stage pump develops 3× that head. Book answer: Q = 6680 gpm = 14.878 ft³/s, pump head = 159.4 ft per pump, f = 0.01917. Modelled as two pump nodes between a split junction and a join junction (passive nodes, no local loss, since local losses are neglected) so it exercises the parallel-pump path.

Three reservoirs (water-surface elevations 100 m, 85 m, 60 m) connected by three pipes to a common junction J that also has an external demand of 0.06 m³/s. Pipe data (D[m] × L[m], roughness 0.0005 m, water ν = 1.31×10⁻⁶ m²/s (≈ 10 °C)): pipe 1 = 0.3 × 2000 (from 100 m), pipe 2 = 0.25 × 1500 (from 85 m), pipe 3 = 0.25 × 3000 (to 60 m). The crux: the flow direction in pipe 2 is not known a priori and must be solved (the middle reservoir turns out to supply the junction). Book answer: Q₁ = 0.1023, Q₂ = 0.0200, Q₃ = 0.0622 m³/s, junction head 83.7 m. Modelled with a single passive junction node at J (the 3 pipes + the demand offtake all meet there, no local loss); local losses neglected.

Flow between two reservoirs with a 15 m surface-elevation difference through 1500 m of 300 mm cast-iron main, Hazen-Williams C = 120. The Hazen-Williams equation (AWWA C-factor method) gives Q = 0.1172 m³/s (117.2 L/s) for this line. This validates SimuPipe's Hazen-Williams friction model — the empirical head-loss method used throughout water-distribution practice and in EPANET — which none of the Darcy-Weisbach cases above exercise. An equation-conformance check, so the match is essentially exact.

Air flowing through 1000 m of 100 mm steel pipe from 700 kPa(g) to 600 kPa(g) (8.0 → 7.0 bar absolute), isothermal at 15 °C. The standard isothermal compressible-flow equation (friction from Colebrook) gives a mass flow of 0.807 kg/s, and SimuPipe's compressible solver reproduces it — the ~0.08% difference is a small flow-acceleration term it additionally accounts for.

A small looped distribution network: a 500 ft reservoir feeds a 6-pipe network (one closed loop) with a water demand drawn at each of the five junction nodes (0.50, 0.35, 0.50, 0.50, 0.25 ft³/s). Cast-iron pipes, ε = 0.005 in, water ν = 1.417×10⁻⁵ ft²/s (≈ 50 °F, NETWEQS1 default), all junctions at 350 ft. Pipe sizes/lengths: 8 in × 1500, 6 in × 1000, 6 in × 1500, 6 in × 1500, 6 in × 1200, 4 in × 1000 ft. The solver must close the loop — i.e. split the flow between the two parallel paths (pipes 2→3 and 4→5) so the head loss around the loop balances. Book answer (NETWEQS1): pipe flows 2.100 / 0.824 / 0.474 / 0.776 / 0.276 / 0.249 ft³/s. Modelled with passive junction nodes at the five network nodes (each carries its pipes + a fixed-flow demand offtake, no local loss); the two 4-way nodes need no tee-chaining.

Fuel oil (ρ = 0.815 g/cm³, ν = 2.7 cSt) flowing at 7 L/s through 30 m of 50 mm steel pipe. Crane's worked example (Darcy-Weisbach with Colebrook friction): head loss 8.95 m, ΔP = 0.715 bar, V = 3.566 m/s, Re = 6.6×10⁴. SimuPipe reproduces it. This exercises the friction path with a viscous non-water fluid — every case above uses water or air — and comes from Crane TP-410.

Two cast-iron (asphalt-lined) pipes in series with an intermediate demand and a pressurised outlet: an 8 in × 3000 ft pipe from a 165 ft reservoir to a joint, then a 6 in × 3500 ft pipe from the joint to an outlet held at 40 psi. An off-take draws 0.5 ft³/s at the joint. The solver finds how the reservoir flow splits between the off-take and the pressurised outlet. Book answer: 8 in pipe = 1.438 ft³/s, 6 in outlet = 0.938 ft³/s (water ν = 1.2×10⁻⁵ ft²/s, ≈ 62 °F). Modelled with a passive junction node at the joint (no local loss) + a fixed-flow demand sink.

Water at 60 °F flows at 400 US gpm through a multi-size piping run: 110 ft of 4 in pipe, a 5 in × 4 in reducing welding elbow, a 75 ft vertical riser and 150 ft of 5 in pipe, plus a 5 in welding elbow, rising 75 ft between the two pressure gauges. Crane's worked answer is P1 − P2 = 38.9 psi, with 10.08 ft/s in the 4 in pipe and 6.41 ft/s in the 5 in pipe. SimuPipe models the welded elbows (auto-K = 14·fT, matching Crane's long-radius elbow); the reducing elbow is a single reducing-elbow fitting (4 in inlet → 5 in outlet) whose loss is the bend plus the area change. It reproduces the gauge differential and both velocities, exercising the K-factor fittings path, a two-diameter run, and the elevation/velocity-head terms together. The small ~1.2% on the differential is Crane's deliberately conservative hand estimate of the reducing-elbow loss vs the solver's bend + area-change K.

A level control valve passes 250 US gpm of condensate (water at 160 °F, SG 0.978) from a 65.86 psig valve inlet to a 56.08 psig header — a measured differential of 9.776 psi. Crane rounds the inlet/outlet to 80.6/70.8 psia (ΔP 9.8 psi) to size the valve, giving a required flow coefficient of Cv ≈ 78.98 (with the piping-geometry factor Fp = 1). Holding that Cv on a globe valve and pushing 250 gpm through it, SimuPipe's IEC 60534 liquid valve model reproduces Crane's 9.8 psi Cv-basis valve drop. This exercises the control-valve Cv → ΔP path.

Natural gas (75% CH₄ / 21% C₂H₆ / 4% C₃H₈, M 20.06, SG 0.693) through 100 miles of 14" Schedule 20 pipe (ID 13.376 in) from 1300 psia to 300 psia at an average 40 °F. Crane's simplified isothermal flow equation gives 107.8 MMscfd ≈ 29.9 kg/s (Weymouth 105.1, Panhandle A 128.2 are alternative correlations, not SimuPipe's method). SimuPipe's isothermal P² solver reproduces it to within 0.2% on a single 100-mi pipe.

Carbon dioxide (M 44.01, k 1.30, Z₁≈0.991 via PR-EOS) through a rotary control valve from 680 kPa to 250 kPa abs at 433 K. The pressure-drop ratio x = 0.632 exceeds the critical value Fk·xT = 0.929×0.60 = 0.557, so the valve is choked and the IEC 60534 expansion factor is floored at Y = 0.667. ISA sizes Kv = 62.6 to pass 3800 std m³/h ≈ 2.088 kg/s. SimuPipe implements this exact standard; holding Kv = 62.6 reproduces that flow to within ~0.8%, confirming the choked-flow clamp is accurate at this (1.13× critical) choke depth.

Carbon dioxide (M 44.01, k 1.30, Z₁≈0.991 via PR-EOS) through a rotary control valve from 680 kPa to 450 kPa abs at 433 K. The pressure-drop ratio x = 0.338 is below the critical value Fk·xT = 0.557, so the flow is sub-critical (expansion factor Y = 0.798). ISA sizes Kv = 67.2 to pass 3800 std m³/h ≈ 2.088 kg/s. Being sub-critical (x below the x_choked = 0.557 threshold), it exercises general gas-valve sizing accuracy rather than the choked-flow clamp.

Water at 363 K (ρ 965.4 kg/m³, Pv 70.1 kPa, Pc 22,120 kPa) through a 150 mm globe valve from 680 kPa to 220 kPa abs. ΔP = 460 kPa is below the choked value FL²(P1 − FF·Pv) = 497 kPa (FL = 0.90), so the flow is non-cavitating. ISA sizes Kv = 165 to pass 360 m³/h. Holding Kv = 165 at the given pressures, SimuPipe's IEC 60534 liquid valve should reproduce 360 m³/h (0.1 m³/s). Clean non-cavitating liquid-valve check (a low-FL ball valve at the same boundaries would cavitate).

Water at 363 K (ρ 965.4 kg/m³, Pv 70.1 kPa, Pc 22,120 kPa) through a 100 mm segmented-ball valve from 680 kPa to 220 kPa abs. The low recovery factor FL = 0.60 drops the choked ΔP to FL²(P1 − FF·Pv) = 221 kPa, well below the available 460 kPa, so the valve cavitates and the flow is choked. ISA sizes Kv = 238 to pass 360 m³/h at the choked ΔP. SimuPipe's IEC 60534 liquid valve flags cavitation and limits the flow to the choked value, reproducing the ISA result to within ~0.2%. A high-FL globe valve at the same boundaries would not cavitate.

A Fisher Design V250 8" ball valve passing natural gas (Gg 0.60, M 17.38, k 1.31, ideal Z=1.0) from 200 psig to 50 psig at 60 °F. With xT = 0.137 the pressure-drop ratio x = 0.70 is ~5.4× the critical value (Fk·xT = 0.129), so the valve is deeply choked and the IEC 60534 expansion factor is clamped to Y = 0.667. At Cv = 1515 the handbook flow is 6.0×10⁶ scfh ≈ 34.62 kg/s. This is the deepest-choke gas-valve benchmark: SimuPipe plateaus the flow near the true choked capacity and reproduces the handbook to within ~2%. At ~5.4× the choke ratio the residual reflects the inherent uncertainty of the IEC 60534 FL/xT sizing model itself.

Air from a reservoir at 293 K through 6 m of 25 mm insulated duct (Darcy f 0.020) discharging to a standard atmosphere — the back-pressure is below the choke pressure, so the flow chokes (Mach 1) at the duct exit. Evett solves the Fanno choke to inlet Mach 0.311, inlet static pressure 353 kPa abs, giving choked flow 0.220 kg/s. The source is set to that inlet static 353 kPa abs at the book's inlet temperature 293 K (Evett applies the reservoir temperature directly as the static inlet — a low-Mach simplification). Roughness back-figured to the book's f 0.020. A clean choked-Fanno case (no lumped entrance/exit K), isolating the adiabatic Mach-1 endpoint choke.

Hydrogen (M 2.016, γ 1.41) flowing adiabatically through 25.6 m of 6 cm duct (Darcy f 0.025) from a static inlet 502 kPa abs, 294 K, 298 m/s; the duct length is exactly the choke length, so the flow reaches Mach 1 at the exit (exit pressure 104 kPa abs). The inlet velocity fixes the mass flow at 0.349 kg/s. A clean choked-Fanno gauge with the static inlet given directly (no reservoir-stagnation conversion), on a different gas (H₂). Roughness back-figured to the book's f 0.025.

Air flowing adiabatically with friction through 19 m of 5 cm stainless duct (ε 0.0015 mm, given) from an inlet at 150 kPa abs, 40 °C, Mach 0.3. A clean forward Fanno case with the roughness given directly (so SimuPipe's Colebrook f is self-consistent, not back-figured). The book's station table gives the duct exit at 19 m as Mach 0.771, 55.76 kPa abs, 284.9 K; the inlet Mach 0.3 corresponds to 0.349 kg/s. Fixing the geometry and both end pressures, SimuPipe solves the flow on the adiabatic solver.

A 2.000 in square-edged orifice plate in a 3 in Schedule 80 steel pipe (ID 2.900 in, so diameter ratio β = 0.690) carries 60 °F water, with a differential of 2.5 psi measured across taps located 1 diameter upstream and ½ diameter downstream (D-and-D/2 taps). Crane iterates the orifice flow coefficient (C ≈ 0.695, Re ≈ 131,000) to a flow rate of 131 US gpm. This exercises SimuPipe's ISO 5167 orifice-plate component (Reader-Harris/Gallagher discharge coefficient, D-D/2 tap type): holding a 2.5 psi differential across the orifice, the solver returns the flow. Incompressible liquid service, so the ISO 5167-2 expansibility factor ε = 1 — this case isolates the discharge coefficient Cd from any compressibility correction. (SimuPipe applies the ISO 5167-2 expansibility factor ε for compressible-gas orifices, validated separately.)

A 4" Schedule 40 equal-leg tee carries 300 US gpm of 60 °F water into the straight run and 100 gpm converging in from the 90° branch (400 gpm combined; branch flow ratio Q_b/Q_c = 0.25). Crane TP-410's converging-tee equations give the straight-leg resistance K_run = 1.55·(Q_b/Q_c) − (Q_b/Q_c)² = 0.325 and the branch-leg resistance K_branch = −0.0422 — the branch K is negative, a genuine kinetic-energy recovery, not an error. SimuPipe's auto-mode tee uses the same Crane TP-410 correlation (referenced to the combined-leg velocity) and reproduces both to the digit, exercising the converging regime + the negative-K physics that the per-leg K clamp protects.

A 50 mi NPS 16 (0.250 in wall, ID 15.5 in) natural-gas pipeline (SG 0.60) flowing 100 MMSCFD at 60 °F isothermal, General Flow + Colebrook (roughness 0.0007 in), delivery 870 psig. The line rises from inlet elevation 100 ft to delivery 450 ft (350 ft net), so the AGA NB-13 static-head term raises the required inlet from 985.66 psig (flat, Case A) to 993.64 psig — an ~8 psig elevation effect. Menon uses CNGA Z = 0.866 at this ~1000 psia. This case validates two solver pieces at once: (1) the compressibility factor Z in the P² flow equation — without it the flow is ~7% low — using SimuPipe's PR-EOS Z (natural_gas pseudo-criticals); and (2) the static-head elevation term, since the +8 psig inlet exactly offsets the 350 ft rise to hold 100 MMSCFD. SimuPipe reproduces 100 MMSCFD (24.05 kg/s) to ~1% — the residual is the PR-EOS-vs-CNGA Z-correlation difference.

A 50 mi NPS 16 (ID 15.5 in) natural-gas pipeline (SG 0.60) flowing 100 MMSCFD at 60 °F isothermal, General Flow + Colebrook (roughness 0.0007 in), delivery 870 psig, flat profile. Menon's required inlet pressure is 985.66 psig, using CNGA Z = 0.866 at ~1000 psia. This isolates the compressibility factor Z in the P² flow equation: with ideal-gas (Z=1) the flow is ~7% low; with SimuPipe's PR-EOS Z (natural_gas pseudo-criticals) it reproduces 100 MMSCFD (24.05 kg/s) to ~1% — the residual is the PR-EOS-vs-CNGA Z-correlation difference.

Air flowing adiabatically with friction through 19 ft of 1" cast-iron duct (ε 0.00085 ft) from 39 psia to 29.4 psia at an inlet 521 °R (61 °F). A clean forward Fanno case — exact geometry and both end pressures given (no rounded sizing diameter, no nozzle/stagnation conversion, no lumped K) — so the delta is purely the adiabatic solver. The textbook flow is 0.006852 slug/s ≈ 0.1 kg/s (exit Mach 0.237, sub-sonic). Roughness is the book's stated value, so SimuPipe's Colebrook f should land on the book's 0.0384.