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.

Crane's control-valve sizing example: a level control valve must pass 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, and the example asks for the required flow coefficient. Crane rounds the inlet and outlet to 80.6 and 70.8 psia (ΔP 9.8 psi) and sizes the valve at Cv = 78.98 with a piping-geometry factor Fp = 1. Modelled with the inlet and header at Crane's exact pressures and a flow control valve holding 250 gpm between them, SimuPipe solves the valve's operating point and reports the IEC 60534 flow coefficient a valve needs there: Cv 79.16, 0.2% above Crane — the difference is Crane's rounding of the differential (9.776 psi measured, 9.8 psi used).

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.

ISA-75.01.01 Annex E, Example 4: the same carbon dioxide service (M 44.01, k 1.30, 433 K, 3,800 std m³/h from 680 kPa abs) but discharging to 250 kPa abs, and the standard asks for the required Kv. 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; the standard sizes the valve at Kv = 62.6. Modelled with both pressures pinned and a flow control valve holding 2.088 kg/s, SimuPipe solves the operating point and reports the IEC 60534 flow coefficient with the choke limit honoured: Kv 63.3, 1.1% above the standard, confirming the choked-flow sizing basis at this 1.13× choke depth.

ISA-75.01.01 Annex E, Example 3: carbon dioxide (M 44.01, k 1.30, Z₁ ≈ 0.991 via PR-EOS) must flow at 3,800 std m³/h through a rotary control valve from 680 kPa to 450 kPa abs at 433 K, and the standard asks for the required Kv. 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) and the standard sizes the valve at Kv = 67.2. Modelled with both pressures pinned and a flow control valve holding the standard's flow (2.088 kg/s), SimuPipe solves the operating point and reports the IEC 60534 flow coefficient a valve needs there: Kv 67.9, 1.0% above the standard — the residual is the compressibility factor and the short pipe stubs.

ISA-75.01.01 Annex E, Example 1: water at 363 K (ρ 965.4 kg/m³, Pv 70.1 kPa, Pc 22,120 kPa) must flow at 360 m³/h through a 150 mm globe valve (FL = 0.90) from 680 kPa to 220 kPa abs, and the standard asks for the required Kv. ΔP = 460 kPa is below the choked value FL²(P1 − FF·Pv) = 497 kPa, so the flow is non-cavitating and the standard sizes the valve at Kv = 165. Modelled with both pressures pinned and a flow control valve holding 360 m³/h, SimuPipe solves the operating point and reports the IEC 60534 flow coefficient a valve needs there: Kv 165.3, within 0.2% of the standard.

ISA-75.01.01 Annex E, Example 2: the same water service (363 K, ρ 965.4 kg/m³, Pv 70.1 kPa, Pc 22,120 kPa; 360 m³/h from 680 kPa to 220 kPa abs) through a 100 mm segmented-ball valve whose 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; the standard asks for the required Kv and sizes it at the choked ΔP: Kv = 238. Modelled with both pressures pinned and a flow control valve holding 360 m³/h, SimuPipe flags the cavitation and reports the IEC 60534 flow coefficient at the choked drop, not the available one: Kv 238.1, matching the standard to 0.03%. A high-FL globe valve at the same boundaries would not cavitate (Example 1).

The Fisher handbook's first compressible sizing problem: a Design V250 8″ ball valve must pass 6.0×10⁶ scfh of natural gas (Gg 0.60, M 17.38, k 1.31, ideal Z = 1.0) from 200 psig to 50 psig at 60 °F, and the handbook asks for the required Cv. With xT = 0.137 the pressure-drop ratio x = 0.70 is about 5.4× the critical value Fk·xT = 0.129, so the valve is deeply choked and the IEC 60534 expansion factor sits at its Y = 0.667 floor; the handbook sizes it at Cv = 1515. Modelled with both pressures pinned and a flow control valve holding the handbook's flow (34.62 kg/s), SimuPipe solves the operating point and reports the IEC 60534 flow coefficient a valve needs there, choke honoured: Cv 1516, within 0.1% of the handbook. This is the deepest-choke gas-valve benchmark on the page.

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.

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.

The same 50 mi NPS 16 (0.250 in wall, ID 15.5 in) natural-gas pipeline (SG 0.60) delivering 100 MMSCFD at 60 °F isothermal to 870 psig, now rising from an inlet elevation of 100 ft to 450 ft at delivery (350 ft net). Menon asks for the required inlet pressure and finds 993.64 psig — about 8 psi more than the flat case, the AGA NB-13 static-head term working against the climb — using CNGA Z = 0.866. Modelled as a fixed 100 MMSCFD source at 100 ft feeding the 870 psig delivery at 450 ft, SimuPipe solves the required inlet pressure directly and returns 991.4 psig, 0.2% below the book, and reproduces the 8 psi elevation increment over the flat case. Two solver pieces are checked at once: the compressibility factor Z in the P² flow equation and the elevation static-head term; the residual is the Peng-Robinson vs CNGA Z difference.

A 50 mi NPS 16 (ID 15.5 in) natural-gas pipeline (SG 0.60) must deliver 100 MMSCFD at 60 °F isothermal to a delivery point held at 870 psig, flat profile, General Flow equation with Colebrook friction (roughness 0.0007 in). Menon asks for the inlet pressure required to do it and finds 985.66 psig, using the CNGA compressibility Z = 0.866 at about 1,000 psia. Modelled as a fixed 100 MMSCFD source feeding the 870 psig delivery, SimuPipe solves the required inlet pressure directly and returns 983.5 psig, 0.2% below the book. The case isolates the compressibility factor in the P² flow equation — with ideal-gas Z = 1 the required inlet pressure would be materially lower — and the small residual is the difference between SimuPipe's Peng-Robinson Z (natural-gas pseudo-critical properties) and Menon's CNGA correlation.

The same 50 mi NPS 16 (ID 15.5 in) natural-gas line (SG 0.60) and pressures as the General Flow case — 985.66 psig inlet, 870 psig delivery, 60 °F isothermal — but solved with the Weymouth equation at pipeline efficiency E = 1.0. Weymouth fixes the friction from diameter alone (transmission factor F = 6.521·D^(1/6)) rather than from Colebrook, and is the more conservative correlation: for these pressures it passes ≈93 MMSCFD versus ≈100 MMSCFD on General Flow. Menon's Weymouth flow equation gives 22.36 kg/s, and SimuPipe's Weymouth model reproduces it — the ~0.06% difference is the explicit flow-equation form versus SimuPipe's equivalent friction-term form. This validates the Weymouth correlation and the pipeline-efficiency factor E.

The same 50 mi NPS 16 (ID 15.5 in) natural-gas line (SG 0.60) and pressures as the General Flow case — 985.66 psig inlet, 870 psig delivery, 60 °F isothermal — solved with the Panhandle A equation at pipeline efficiency E = 1.0. Panhandle A uses a flow-dependent transmission factor F = 11.85·E·(Q·G/D)^0.07305 and is less conservative than General Flow: for these pressures it passes ≈116 MMSCFD versus ≈100 on General Flow (and ≈93 on Weymouth). Menon's Panhandle A flow equation gives 27.93 kg/s, and SimuPipe reproduces it to +0.03% — validating the correlation and the flow-dependent transmission factor.

The same 50 mi NPS 16 (ID 15.5 in) natural-gas line (SG 0.60) and pressures as the General Flow case — 985.66 psig inlet, 870 psig delivery, 60 °F isothermal — solved with the Panhandle B (revised Panhandle) equation at pipeline efficiency E = 1.0. Panhandle B is the least conservative of the transmission correlations, used for large-diameter high-pressure lines: for these pressures it passes ≈119 MMSCFD, the highest of the four flow equations (Weymouth ≈93, General Flow ≈100, Panhandle A ≈116). Menon's Panhandle B flow equation gives 28.55 kg/s, and SimuPipe reproduces it to +0.02%.

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.

Air at 200 °C flows at about 2.24 kg/s through 200 m of bare 150 mm steel pipe (overall heat-transfer coefficient U = 12 W/m²·K) into 15 °C surroundings. The steady-flow energy balance, ṁ·Cp·(T_in − T_out) = U·πDL·(T_avg − T_amb), predicts the gas leaves at 398.8 K (125.6 °C) — a 74 K drop. SimuPipe's diabatic solver reproduces the outlet temperature to within 0.02%; the small residual is the fraction of enthalpy converted to kinetic energy as the gas accelerates down the pressure gradient, which the full compressible solve accounts for.

A 100-mile, 12.09 in ID natural-gas transmission line (SG 0.60) flowing from 400 psia to 200 psia at 520 °R (60 °F), solved with the Weymouth equation (transmission factor from diameter alone). Ikoku's Weymouth flow rate is 989,859 std ft³/h. This is an independent low-pressure check on SimuPipe's Weymouth correlation — the line averages ~300 psia (Z ≈ 0.95), well below the high-pressure transmission cases — and SimuPipe reproduces the textbook flow to ~0.2%.

Mohitpour asks: what is the downstream pressure of a 200-mile NPS 20 (ID 19.5 in) natural-gas transmission line (G = 0.65) transporting 200,000 Sm³/h from a 1,000 psia inlet at a flowing temperature of 520 °R, with Z = 1.0 and the Panhandle A flow equation at pipeline efficiency E = 1.0? The book's answer is 522 psia. Modelled with the inlet pinned at 1,000 psia and a fixed 200,000 Sm³/h withdrawal at delivery, SimuPipe's Panhandle A transmission-factor form solves the delivery pressure directly and returns 523.5 psia, 0.3% above the book. The 200-mi line is split into two 100-mi segments at a passive junction because a single pipe exceeds the 200 km length limit.

The second half of Mohitpour's Example 3.5: the same 200-mile NPS 20 (ID 19.5 in) line (G = 0.65, 1,000 psia inlet, 520 °R, Z = 1.0) is looped over its whole length with a parallel NPS 16 (ID 15.5 in) pipe, and the book asks for the new downstream pressure at the same 200,000 Sm³/h. Panhandle A parallel-resistance gives 823 psia (against 522 psia unlooped). Modelled with the inlet pinned at 1,000 psia and a fixed 200,000 Sm³/h withdrawal at delivery, SimuPipe splits the flow between the two legs (about 65% through the larger line) and solves the delivery pressure directly, returning 822.8 psia — within 0.1% of the book — which validates loop closure in compressible flow. Each 200-mi leg is two 100-mi segments meeting at a passive junction; a short inlet manifold splits the flow at a third junction.

150,000 lb/hr of methane through 10-in Schedule 40 pipe (ID 10.02 in) at 750 psia and 60 °F. Using the simplified compressible Darcy formula (ΔP₁₀₀ = 0.000336·fₘ·W²/(d⁵·ρ)) with density 2.38 lb/ft³ (compressibility Z = 0.905 from its charts), GPSA gets a pressure drop of 0.423 psi per 100 ft. Holding the 750 psia inlet and the 150,000 lb/hr flow, SimuPipe's isothermal solver returns the drop over a 100-ft run and reproduces GPSA's 0.423 psi to within ~1.5%. SimuPipe's Colebrook friction factor sits within ~1% of GPSA's clean-steel chart value, so the residual is essentially the PR-EOS-vs-chart compressibility-Z difference for methane at 750 psia.

Natural gas (SG 0.75) through a 3.500 in orifice in a 6.065 in meter tube (β = 0.577), flange taps, at 90 psia and 70 °F with a 60 in-water differential. GPSA's simplified orifice equation (Qh = Keyg·Ftf·Fg·√(hw·Pf)) with a chart-read coefficient (Fig. 3-3) gives 222,387 cu ft/hr at 14.73 psia / 60 °F. SimuPipe solves the same meter with the rigorous ISO 5167-2 discharge coefficient (Reader-Harris/Gallagher, Cd ≈ 0.605) plus the compressible expansibility factor, reproducing GPSA's flow to ~0.3%. GPSA notes its chart method is approximate and defers to AGA Report No. 3 for custody-transfer precision, so the close agreement confirms SimuPipe's ISO 5167 orifice is consistent with the GPSA industry chart — an independent-textbook check on a gas orifice meter.

75,000 lb/hr of methane at 400 psia and 100 °F (compressibility Z = 0.96, density 1.11 lb/ft³). GPSA sizes the Schedule 40 line for ΔP₁₀₀ ≤ 1 psi with its simplified compressible Darcy formula and selects 8-in pipe (ID 7.981 in), for which the actual drop works out to 0.74 psi per 100 ft. Holding the 400 psia inlet and the 75,000 lb/hr flow through 100 ft of 8-in Sch 40, SimuPipe's isothermal solver returns the drop and reproduces GPSA's 0.74 psi to ~0.1%. At 400 psia the PR-EOS and chart compressibility factors nearly coincide, and SimuPipe's Colebrook friction matches GPSA's clean-steel chart value, so the two methods agree closely.

A seven-pipe water network fed by two independent supplies — a curve pump (1.0 ft³/s → 60 ft, 1.5 → 55, 2.0 → 48; suction at 90 ft) and a 100 ft reservoir — delivering 1.0 ft³/s at node 2 and 1.0 ft³/s at node 4. All pipes are 6″ except the 1″ × 1500 ft pipe 7; ε = 0.02 in throughout, Darcy-Weisbach, water at NETWK's default ν = 1.417×10⁻⁵ ft²/s. A pressure-reducing valve sits halfway along the 1000 ft pipe 6 (modelled here as two 500 ft segments with the PRV node between them) and holds an HGL of 55 ft on its downstream side. The regulator is what sets the flow split: it throttles pipe 6 down to 0.04 ft³/s so node 4's 1.0 ft³/s demand is met almost entirely through pipe 5, and it dissipates ~67 ft of head. Pipe 3 also settles into reverse flow. Book answer (NETWK): pipe flows 1.11 / 1.07 / 0.07 / 0.89 / 0.96 / 0.04 / 0.01 ft³/s, node HGLs 121.81 / 96.55 / 96.45 / 54.98 ft, pump head 59.1 ft, PRV 121.79 ft upstream → 55.00 ft downstream. The three near-stagnant legs are printed to a single significant figure, so they are quoted rather than scored: SimuPipe returns 0.0653 ft³/s in pipe 3 (book 0.07), 0.0358 through the PRV in pipe 6 (book 0.04) and 0.0072 in the 1″ pipe 7 (book 0.01) — each rounds to the printed value, but a percentage against a one-digit reference would measure the rounding, not the solver.

A nine-pipe, six-node water network with three supplies — a curve pump (0.10 m³/s → 35 m, 0.15 → 32, 0.20 → 28; suction at 180 m) and reservoirs at 200 m and 135 m — serving demands of 15, 20, 15, 20, 20 and 30 L/s. Pipes are 150–300 mm, ε = 0.02 mm, Darcy-Weisbach. Without a regulator the 135 m reservoir would be overfilled from the high side, so a back-pressure valve 1200 m along the 2000 m pipe 4 (modelled here as 1200 m + 800 m segments with the BPV node between) holds an HGL of 195 m on its own upstream side, dissipating 65.88 m of head. That single constraint fixes the whole flow pattern: pipe 4 passes only 6 L/s while pipe 8 carries 65 L/s the long way round, and pipes 5 and 6 settle into reverse flow. Book answer (NETWK): pipe flows 0.102 / 0.004 / 0.091 / 0.006 / 0.009 / 0.015 / 0.035 / 0.065 / 0.014 m³/s, node HGLs 199.25 / 195.02 / 129.08 / 130.97 / 136.66 / 169.78 m, pump head 34.88 m, BPV 195.00 m upstream → 129.12 m downstream. Pipes 2, 4 and 5 carry 4–9 L/s, printed to a single significant figure, so they are quoted rather than scored: SimuPipe returns 3.56, 5.63 (through the BPV) and 9.37 L/s against the book's 4, 6 and 9. This is a deep-throttle case — the regulator burns 65.88 m of head at 6 L/s, a throttling K of ~2×10⁵ — and two pipes reverse direction relative to the state the network would settle into with the valve wide open.

An eight-pipe water network with two supply reservoirs (170 m and 200 m), two curve pumps, two globe valves (K = 10), an in-line meter (K = 2), two closed loops and one open loop, delivering 30, 80, 50 and 100 L/s at four junctions. A pressure-reducing valve sits 200 m along the 600 m pipe 5 (modelled here as 200 m + 400 m segments with the PRV node between) and holds an HGL of 149 m on its downstream side. This is the regulator working in its normal band rather than at a limit: the head just upstream of it (156.5 m) stays below node 2's 157.5 m so it is not wide open, and node 5 downstream sits at 147.0 m, below the 149 m setting, so it has not shut. Book answer (Example Problem 4.9 at the 0.100 m³/s demand): pipe flows 0.1125 / -0.0018 / 0.1175 / 0.0792 / 0.0343 / 0.0657 / 0.0633 / 0.1967 m³/s, pump heads 6.18 m and 3.58 m, nodal heads 175.3 / 157.5 / 155.1 / 179.7 / 147.0 m. Pipe 2 is near-stagnant (under 2 L/s, and the printed value does not satisfy continuity at either end unless its sign is flipped), so it is quoted rather than scored: SimuPipe returns 0.34 L/s. The remaining spread is the friction basis — the book solves this network with an exponential formula h = K·Qⁿ fitted per pipe (n ≈ 1.77–1.83), while SimuPipe uses Darcy-Weisbach with Colebrook (n = 2), which moves the loop split by one to two percent.

Air at 500 → 450 kPa abs (p₂/p₁ = 0.90, well within the ISO 5167-2 ε validity floor of 0.75) through a 50 mm square-edged orifice in a 100 mm meter tube (β = 0.50), flange taps, 20 °C. This validates SimuPipe's compressible orifice path — the ISO 5167-2 mass-flow equation ṁ = Cd·ε·(π/4)d²·√(2ρ₁ΔP/(1−β⁴)) with the expansibility factor ε. The solver reproduces the ISO 5167-2 closed-form flow (0.918 kg/s) to ~0.1%. The expansibility itself is cross-validated against an independent standard: SimuPipe's ISO 5167-2 ε = 0.9731 agrees with the AGA Report No. 3 flange-tap factor Y₁ = 1 − (0.41 + 0.35β⁴)·x/k = 0.9692 to 0.4%. No clean compressible-orifice worked example exists in the reference set (Crane TP-410 / Evett are liquid; Menon / Oosthuizen use AGA-3 / isentropic), so this is tracked as a standard self-consistency + cross-standard ε check rather than a single-textbook reproduction. The liquid-orifice equivalent has ε = 1 (no expansibility).

Nitrogen flows adiabatically with friction through a 4″ schedule 40 duct (flow area 0.08840 ft²) at 20 lb/s from an inlet at 200 psia and 70 °F, against a stated pipe-section loss coefficient of K = 10, and the reference asks for the outlet pressure and temperature. It gives K directly and no length or roughness — K is the friction parameter f·L/D inside the exact Fanno relations, not a lumped fitting loss — so the duct modelled here is 62.68 m of 4″ pipe, the length at which SimuPipe's own Colebrook friction factor returns f·L/D = 10.000. The inlet is pinned at 200 psia and 70 °F and the outlet withdraws the given 20 lb/s, so the solver returns the outlet pressure and temperature. Book answer: 125.621 psia at 63.78 °F (290.80 K), obtained three independent ways — Shapiro's, Binder's and Turton's adiabatic equations — which agree with one another and close back on K = 10.00. SimuPipe returns 125.08 psia and 290.74 K: the outlet temperature, the quantity that tests the adiabatic solver's per-node energy balance most directly, lands within 0.06 K, and the pressure lands 0.5% low. That residual is the compressibility factor: the reference applies z = 0.99472 at the inlet where SimuPipe treats nitrogen as an ideal gas, so the ideal gas is slightly denser, moves slower at the same mass flow, and loses slightly less pressure.

Air flowing adiabatically with friction through a 3″ schedule 40 duct (flow area 0.05134 ft²) from an inlet at 50 psia and 70 °F, discharging to atmosphere at 14.70 psia against a stated pipe-section loss coefficient of K = 8. The pressure ratio is severe — the duct loses 70.6% of its inlet pressure — and the flow leaves at Mach 0.82, near sonic but not choked, which is the hardest regime for a compressible solver to get right. As in the reference's other adiabatic examples, K is the friction parameter f·L/D inside the exact Fanno relations rather than a lumped fitting loss, so the duct modelled here is 35.54 m (116.6 ft) of 3″ pipe — the length at which SimuPipe's own Colebrook friction factor returns f·L/D = 8.000. Both ends are pinned at the reference's pressures, so the solver returns the mass flow and the outlet temperature. Book answer: 3.7699 lb/s (1.7100 kg/s) leaving at 13.26 °F (262.74 K), obtained three independent ways — Shapiro's, Binder's and Turton's adiabatic equations — which agree with one another to six figures and close back on K = 8.000. SimuPipe holds the outlet temperature to 0.34 K across a 31.5 K adiabatic expansion and the mass flow to 0.60%. Of that 0.60%, roughly a tenth is the compressibility factor: the reference applies z = 0.998286 at the inlet where SimuPipe treats air as an ideal gas.

Oosthuizen's Example 9.3: air enters a 5 cm stainless-steel pipe (ε 0.0015 mm) at Mach 0.3, 150 kPa abs and 40 °C, and the book asks for the Mach number, temperature and pressure at 4, 8, 12, 16, 18 and 19 m from the inlet, tabulating them in TABLE E9.3 down to the exit at M 0.771, 55.76 kPa abs and 284.9 K. The given inlet state fixes the mass flow at ρ₁·A·V₁ = 0.3487 kg/s, so the model pins the inlet at the book's state, withdraws that flow at the exit and splits the duct at the book's own stations: every station pressure and temperature, and the exit state, is solved rather than given. SimuPipe's Colebrook friction factor lands on the book's 0.01372 (Darcy) at the inlet to 0.02%, and — because an adiabatic duct cools as it expands — its viscosity follows the falling temperature, so the Reynolds number rises along the duct exactly as the book's table shows (466,904 → 500,597). The solver reproduces every station within 1% in pressure and 0.5 K in temperature, and the exit at Mach 0.77 within 1% and 1 K: the exit is the sensitive end of a Fanno duct (0.1% in mass flow moves the exit pressure by about 2%), and the remaining difference is the book's Swamee-Jain friction correlation against Colebrook-White.

Coke-oven gas (SG 0.42, M 12.17, k 1.4) from a 125 psig (139.7 psia), 140 °F header through 20 ft of 3" Schedule 40 pipe discharging to atmosphere. Crane totals the resistance as K = 2.87 — pipe friction 1.369, entrance 0.5, exit 1.0 — and the required pressure-drop ratio 0.895 exceeds the critical 0.657, so the flow chokes at the pipe exit (Y = 0.637) at q = 1,028,000 scfh ≈ 4.15 kg/s. Modelled at the book's own geometry, with the sharp entrance and the exit carried as fittings ON the pipe — Crane's lumped-resistance basis, folded into the pipe's friction as f·L/D + ΣK. SimuPipe reports the pipe choked at Mach 1 at its outlet, exactly as the book concludes, and returns 4.27 kg/s. An independent closed-form Fanno integration of the same duct and ΣK gives 4.25 kg/s — itself 2.3% above the printed answer — so the small residual is Crane's Y-factor approximation to the Fanno line at choking, not the network solution: SimuPipe sits within 0.5% of the rigorous reference.

Air at 19.3 psig (34.0 psia), 100 °F, measured 10 ft from the outlet of a 1/2" Schedule 80 pipe (ID 0.546 in) discharging to atmosphere. With K = 7.04 (pipe friction 6.04 + exit 1.0) the pressure-drop ratio 0.568 stays below the critical 0.657, so the flow is sub-sonic (Y = 0.76) at q = 3762 scfh ≈ 0.0362 kg/s. Modelled at the book's own geometry with the exit carried as a fitting ON the pipe — Crane's lumped-resistance basis, folded into the pipe's friction as f·L/D + ΣK. SimuPipe stays sub-sonic end to end exactly as Crane's sub-critical pressure-drop ratio predicts and returns 0.0367 kg/s. Crane's Y-factor method is itself an approximation to the Fanno line, which accounts for most of the small residual difference.

Natural gas (modelled as methane, M 16.04, γ 1.3) flows isothermally at 15 °C through 750 m of 75 mm pipe from an inlet at 900 kPa abs and Mach 0.09, and the book asks for the exit pressure. It states its friction basis as an input — Fanning f = 0.002 (Darcy 0.008), visible in its own 4fL/D = 4 × 0.002 × 750/0.075 = 80 step — and works through the isothermal relations to an exit Mach number of 0.2435 and an exit pressure of 332.7 kPa abs. The inlet state fixes the mass flow at ρ₁·A·M₁·a₁ = 1.0557 kg/s (the book prints 1.06), so the model pins the inlet at 900 kPa abs, withdraws that flow at the outlet, and carries the book's stated friction factor on the pipe exactly as the reference does. SimuPipe solves the exit pressure directly and returns 332.7 kPa abs — every step of the book's solution was independently recomputed and confirmed (4fl*/D = 89.41 at M 0.09, M₂ = 0.2435). Worth knowing when comparing against real pipe: the book's assumed factor sits below the smooth-pipe Colebrook floor at this Reynolds number (about 0.0107 at Re 1.64×10⁶), so on computed friction the same duct would deliver a materially lower exit pressure — the specified-f input is what lets the model state the reference's basis rather than argue with it.

Air released at 72,000 lbm/h (9.07 kg/s) from a high-pressure vessel at 120 °F through 90 ft of 4.026″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.2 (the base case). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 128.46 psia, with the line choked at its exit. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (315.9 K at the book's inlet Mach 0.317). SimuPipe reports the pipe choked at Mach 1 at its exit, exactly as the book concludes, and returns p₁ = 126.2 psia. An independent closed-form Fanno integration of the same duct with Colebrook friction gives 126.7 psia — itself 1.3% below the printed answer, because the book fixes the friction factor at its fully-turbulent 0.017 where Colebrook at Re ≈ 6×10⁶ gives 0.0164 — so the residual is the friction-factor basis, not the network solution: SimuPipe sits within 0.5% of the rigorous reference.

Air released at 144,000 lbm/h (18.14 kg/s) from a high-pressure vessel at 120 °F through 90 ft of 4.026″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.3 (twice the released flow). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 256.93 psia, with the line choked at its exit. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (315.9 K at the book's inlet Mach 0.317). The required source pressure sits at a 17:1 absolute pressure ratio to the outlet. SimuPipe reports the pipe choked at Mach 1 at its exit, exactly as the book concludes, and returns p₁ = 252.1 psia; the residual is the friction-factor basis (the book fixes f at its fully-turbulent value where Colebrook at this Reynolds number sits slightly lower), as in the base case.

Air released at 72,000 lbm/h (9.07 kg/s) from a high-pressure vessel at 120 °F through 90 ft of 2.067″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.6 (an undersized 2″ line). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 661.96 psia, with the line choked at its exit. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (318.7 K at the book's inlet Mach 0.235). The required source pressure sits at a 45:1 absolute pressure ratio to the outlet. SimuPipe reports the pipe choked at Mach 1 at its exit, exactly as the book concludes, and returns p₁ = 658.6 psia; the residual is the friction-factor basis (the book fixes f at its fully-turbulent value where Colebrook at this Reynolds number sits slightly lower), as in the base case.

Air released at 72,000 lbm/h (9.07 kg/s) from a high-pressure vessel at 120 °F through 180 ft of 4.026″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.4 (twice the line length). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 168.52 psia, with the line choked at its exit. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (318.5 K at the book's inlet Mach 0.243). SimuPipe reports the pipe choked at its exit and returns p₁ = 165.1 psia. An independent closed-form Fanno integration with Colebrook friction gives 166.0 psia — itself 1.5% below the printed answer (the book's fixed fully-turbulent 0.017 vs Colebrook 0.0164) — so SimuPipe sits within 0.5% of the rigorous reference.

Air released at 72,000 lbm/h (9.07 kg/s) from a high-pressure vessel at 500 °F through 90 ft of 4.026″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.5 (vessel at 500 °F). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 165.29 psia, with the line choked at its exit. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (522.8 K at the book's inlet Mach 0.317). SimuPipe reports the pipe choked at its exit and returns p₁ = 162.4 psia. An independent closed-form Fanno integration with Colebrook friction gives 163.1 psia — itself 1.4% below the printed answer (the book's fixed fully-turbulent friction factor vs Colebrook) — so SimuPipe sits within 0.5% of the rigorous reference.

Air released at 72,000 lbm/h (9.07 kg/s) from a high-pressure vessel at 120 °F through 90 ft of 7.981″-bore Schedule 40 commercial steel vent line discharging to atmosphere — the handbook's safety-valve vent line sizing family, Sample Problem B8.7 (an 8″ line, sub-sonic). The book runs an adiabatic Fanno analysis with a fixed fully-turbulent friction factor and finds the valve-discharge pressure p₁ = 25.15 psia, with the line sub-sonic throughout. Modelled as a fixed-flow source at the valve discharge; the book's vessel temperature is a stagnation value, so the source static temperature is the corresponding pipe-inlet static temperature (311.8 K at the book's inlet Mach 0.41). SimuPipe stays sub-sonic end to end, exactly as the book's sub-critical exit pressure predicts — no false choke — and returns p₁ = 25.32 psia; an independent Fanno integration with Colebrook friction gives 25.34 psia, so SimuPipe sits within 0.1% of the rigorous reference and 0.7% of the printed answer.

Water pumped uphill at 0.001 m³/s through 70 m of 2-nominal Schedule 40 pipe inclined 30° (35 m rise); the book states the friction factor (f = 0.03) and solves the inlet-to-outlet pressure drop: 347.1 kPa, of which 343.0 kPa is elevation head and only 4.1 kPa friction. Modelled as a fixed-flow source into the pipe with the outlet at atmosphere. Gravity dominates, so the difference between the book's stated friction factor and the solver's Colebrook f(Re) moves the total by well under 1%. SimuPipe returns 347.0 kPa — within 0.05% of the book.

Water at 22 °C flowing at 0.02 m³/s through 350 m of horizontal 8-nominal Schedule 40 cast iron pipe (ID 20.27 cm, ε = 0.025 cm). The book reads f = 0.022 from the Moody chart at Re = 1.31×10⁵ and finds a head loss of 0.744 m = 7.279 kPa(g). Modelled as a fixed-flow source with the outlet at atmosphere; the solver computes Colebrook friction directly (0.0224) rather than a chart reading. SimuPipe returns 7.42 kPa(g) (+2.0%) — the gap is exactly the book's chart-read f = 0.022 vs the solver's Colebrook 0.0224 on a pure-friction line.

Benzene (SG 0.876) in a horizontal 12-nominal Schedule 80 wrought iron pipe; gauges 1,200 ft apart read a 15 psi drop, and the flow rate is the unknown. The book iterates the Moody chart to f = 0.0139 and finds Q = 8.51 ft³/s (V = 12.06 ft/s). Modelled with the measured drop as the boundary pressures so the solver finds the flow itself. SimuPipe returns 8.49 ft³/s, 0.2% from the book's answer.

A water tank drains to a pond through 82 ft of 1½-nominal Schedule 40 cast iron pipe (ε/D = 0.0063) with a sharp entrance, a return bend, an elbow and a fully-open globe valve — the book's threaded regular K values total 13.4 plus the exit. The free surface sits 23 ft above the discharge. The book iterates to f = 0.034 and Q = 5.51 ft³/min. Modelled with the surface as a 0 psig boundary at +23 ft, the book's K values carried on the pipe (ΣK = 14.4 with the exit), and the discharge at atmosphere. SimuPipe returns 5.53 ft³/min, within 0.4% of the book.

0.3 ft³/s of water reaches junction A and splits between two 4,500 ft wrought iron legs to junction B: the Schedule 40 10-nominal main and a Schedule 40 8-nominal loop. Minor losses are neglected. Equal head loss across the legs gives the printed split Q(10″) = 0.19 and Q(8″) = 0.11 ft³/s (rounded to two figures). Modelled as a fixed-flow source feeding a passive junction, both legs closing on an atmospheric boundary — the network analogue of the book's equal-Δp condition. SimuPipe returns 0.1947 and 0.1053 ft³/s — a 64.9/35.1 split that the book's two-figure rounding (0.19/0.11) brackets.