Theory & Method

Pump Network Simulator · AntraSIM-0020 · version 1.0.1 · build 2026-09-22. This document describes the model as implemented in the application. Numbers that depend on the model are generated from the same code that runs in the page.

Model status. The hydraulic model is numerically verified (Table 7.1: independent references, transcribed v4.0.2 solver, invariants, IC/CSV tests). It is not validated against pump test data. The default pump characteristics are reconstructed from KSB datasheet anchor values (§10); the shapes between the anchors, the NPSHR curve and the efficiency curve are model assumptions, not KSB curve data. Do not use the results for guarantees or purchase decisions.

How to read this document. Each topic follows Intuition → Physical mechanism → Mathematical formulation → Engineering interpretation → Assumptions and limitations. Evidence classes: externally sourced derived assumption not verified.

1. Physical Background

Intuition A centrifugal pump lifts the pressure of a liquid; the pipe system it feeds resists the flow. The pump settles where the pressure it can deliver equals the pressure the system demands — the operating point. If the liquid arrives at the pump with too little pressure reserve, vapour bubbles form and collapse (cavitation), the head falls and the pump is damaged. The reserve is called NPSH.

Physical mechanism

Speed, curve, density→pump head H(Q)→intersection with system head→flow, pressures, power→NPSHA vs NPSHR

Engineering interpretation The operating point tells how much flow a network delivers; the power curve tells what it costs; the NPSH curves tell how far the suction side is from cavitation and up to which flow the arrangement is safe. Assumptions and limitations Steady state, single-phase liquid water, incompressible flow; no transients, water hammer, two-phase flow or motor/VFD model (§9).

2. Assessment of the Source Model (v4.0.2)

Rule The supplied v4.0.2 application (executable code) and its documentation were read completely and compared. The executable model was implemented unless physics or the request said otherwise. Findings and resolutions:

ID	Finding	Resolution
A-1	Documentation names the density correlation of Kell (1975); the code implements a different, Tanaka-type formula. Deviation from steam-table values: see Table 5.2.	Executable formula kept (behaviour preserved); deviation quantified; warning above 200 °C.
A-2	Documentation states that the density correction applies to table pumps only; the code also applies ρ_ref/ρ_sim to the analytic curve.	Code behaviour kept (basis “ΔP const.”), now selectable against “H const.” (finding A-9).
A-3	Documentation: table curves are extrapolated beyond the last point with the last-segment slope; code holds the last value constant.	Documented behaviour implemented (slope extrapolation, head floored at 0 for pumps); advisory when the operating flow lies outside the table.
A-4	v4.0.2 default system table: negative differential heads are clamped to 0 and the mid-group pipe is omitted, so the table initialiser did not reproduce the calculated curve (hand calculation for the v4 3+3 default: ≈ 1.3 bar at Q = 0; not re-run).	New initialiser samples the calculated curve without clamping and including the mid-group pipe; operating points agree (Table 5.1, T9).
A-5	“ρ ref (table)” of the system table has no numerical effect in v4.0.2 (the documentation admits this).	Kept as an informational field with the same reporting; semantics unchanged.
A-6	“Q nominal” of the analytic pump is the flow at which H = 0.85·H₀, not a design flow; the derived a = 0.15·H₀/Q²_nom.	Re-parametrised by the physically meaningful BEP point: a = (H₀ − H_BEP)/Q_BEP². The v4 rule is the special case H_BEP = 0.85·H₀. Same quadratic model.
A-7	v4.0.2 uses one constant efficiency η per pump; no power curve, no NPSH.	Replaced by η(Q) derived from the shaft-power characteristic (required for the power curves); NPSHA/NPSHR added.
A-8	v4.0.2 defaults of the 3+3 tabs (200 °C, P_in = 3 bar) lie below the saturation pressure of water at 200 °C (15.5 bar): the inlet state is vapour, the single-phase model is invalid, NPSHA would be negative. All pumps differed between tabs (45 m … 530 m).	New reference cases: water 20 °C, all pumps identical (§8, §10), system curves aligned to the pump. An advisory is issued whenever P_in ≤ p_v.
A-9	The pump-curve density correction H_sim = H_ref·ρ_ref/ρ_sim (constant pressure rise) contradicts pump similarity, where head in metres is independent of density and pressure rise and power scale with ρ. At 150 °C the two bases differ by a factor 1.090 in head.	Open point for the owner. v4.0.2 behaviour is the default (“ΔP const.”); “H const.” is offered. No effect at ρ_sim = ρ_ref (all reference cases).
A-10	A running pump behind a closed check valve had zero power in v4.0.2.	Shut-off power P(0) is reported and a warning issued (dead-heading).
A-12	The v4.0.2 side-branch pipe model solved h_loss(q) − ΔH = 0 with a bisection written for decreasing functions; for the increasing h_loss it converges to ≈ 0 or to the bracket limit (10·A·2·ρ).	Corrected (sign of the residual); test T18 against the closed-form minor-loss pipe. The manual method is unchanged and identical to v4.0.2 (T4).
A-13	v1.0.0 stored the system-curve table as ΔP above the current P_out input (H_bar = row value + P_out, reconstructed at solve time). Editing P_out after defining a table therefore silently changed the head the table represented, without changing its displayed rows — a canonical-model-state defect (the table depended on a second, mutable input instead of being a self-contained definition), and the source of a reported ergonomics complaint about the column's meaning.	Corrected: the table now stores the absolute required pressure rise directly (ΔP = H in bar); P_in + ΔP(Q) is the pressure delivered at the pump outlet, independent of P_out. IC schema incremented to 2 with a registered, tested migration (T15); regression values unchanged (the two conventions were numerically equivalent by construction, so no physical result changes — test T16, T19). The pump- and system-curve table editors were moved into a wider pop-out dialog after a reported readability complaint, and the network schematic now animates pump rotation (rate ∝ N/N_ref) and flow direction (rate ∝ Q) in every configuration.
A-11	v4.0.2 trend plot sampled by timer; Freeze/Run button.	The model is fast (410 solves/s in Node): automatic recalculation after each valid input change, history sampled per calculation, no Run/Freeze.

3. Governing Equations

3.1 System curve and piping

Intuition The pump has to lift the liquid by the static head, raise its pressure to the outlet boundary and overcome friction, which grows roughly with the square of the flow.

H_{s y s} (Q) = H_{z} + \frac{P_{o u t} - P_{i n}}{ρ g} + h_{s u c} (Q) + h_{d i s} (Q)

h = (f \frac{L}{D} + K) \frac{v^{2}}{2 g}, v = \frac{4 Q}{π D^{2}}, f = \frac{64}{R e} (R e < 2300), f = \frac{0.3164}{R e^{0.25}} (R e \geq 2300)

with H_z [m] the level difference outlet − inlet, P [Pa] absolute boundary pressures, ρ [kg/m³], g = 9.81 m/s², L [m], D [m], K [–], v [m/s], Re = ρvD/μ with μ = 1 mPa·s (constant, v4.0.2). Blasius friction is valid for smooth pipes, 4000 ≤ Re ≤ 10⁵ (externally sourced). In the 3+3 tabs the mid-group pipe adds h_mid between the groups. A Table system curve replaces the formula: rows (ΔP above P_out [bar], ṁ [kg/s]) are converted at the simulation density, Q = ṁ/ρ_sim, H = ΔP·10⁵/(ρ_simg) + P_out·10⁵/(ρ_simg), and interpolated linearly. For the 3+3 tabs the table represents the whole pump train including the mid-group pipe.

3.2 Pump characteristics (reference speed N_ref, reference density ρ_ref)

Intuition Head falls with flow; shaft power rises with flow; the pressure reserve the pump needs (NPSHR) rises with flow. Efficiency is the ratio of hydraulic to shaft power.

Analytic definition Quadratic head (v4.0.2 form) anchored at the shut-off head and the BEP; linear shaft power whose intercept places the efficiency maximum at Q_BEP; quadratic NPSHR:

H_{r} (q) = H_{0} - a q^{2}, a = \frac{H_{0} - H_{B E P}}{Q_{B E P}^{2}}

P_{r} (q) = P_{B E P} [p_{0} + (1 - p_{0}) \frac{q}{Q_{B E P}}], p_{0} = min (1, \frac{2 (H_{0} - H_{B E P})}{H_{B E P}}), P_{B E P} = \frac{ρ_{r e f} g Q_{B E P} H_{B E P}}{η_{B E P}}

N P S H R_{r} (q) = N P S H R_{B E P} [ν_{0} + (1 - ν_{0}) {(\frac{q}{Q_{B E P}})}^{2}]

The choice of p₀ follows from d(η)/dq = 0 at Q_BEP for η = ρ_refgqH_r/P_r (derived); for the default pump it gives P(0) = 5.77 kW = 45 % of P_BEP. Hence the efficiency curve is derived, not independent. Table definition rows (Q, H, P, NPSHR) at N_ref, ρ_ref, interpolated linearly; η = ρ_refgQH/P is derived. Tables need strictly increasing Q and non-increasing H (unique inversion Q(H)).

3.3 Operating conditions: affinity laws and density basis

H = n^{2} k H_{r} (\frac{Q}{n}), P = \frac{ρ}{ρ_{r e f}} k n^{3} P_{r} (\frac{Q}{n}), N P S H R = n^{2} N P S H R_{r} (\frac{Q}{n}), n = \frac{N}{N_{r e f}}

k = ρ_ref/ρ_sim for the basis “ΔP const.” (v4.0.2: constant pressure rise) and k = 1 for “H const.” (pump similarity, finding A-9). Shaft power then equals ρ_sim·g·Q·H/η with η(Q/n) taken at the similar point. Speed 0 or “off” gives no head, closed check valve and zero power. A pump that is on with a closed check valve is dead-heading: it consumes the shut-off power (warning).

3.4 Networks

Stages in series contain pumps in parallel. Series: the flow is common, heads add, H_tot(Q) = Σ H_i(Q). Parallel: the head is common, flows add; the group head H_g(Q) is the inverse of Q_g(H) = Σ Q_i(H):

\sum_{i} Q_{i} (H_{g}) = Q, H_{A} (Q) + H_{B} (Q_{m a i n}) - h_{m i d} (Q_{m a i n}) = H_{r e q} (Q, Q_{m a i n}), Q_{m a i n} = Q - \frac{{\dot{m}}_{s i d e}}{ρ}

Modes: 1 pump; series (2); parallel (2); 3+3 Complex (group A in series with group B via the mid-group pipe); 3+3 CF Flow (as 3+3 with a side branch at the outlet of group A: manual mass flow or a Darcy–Weisbach pipe driven by P_outA − P_side; Q_side = 0 reproduces 3+3 Complex exactly, test T6).

4. Inputs and Operating Conditions

Semantics P_in and P_out are absolute boundary pressures at the inlet and outlet vessel surfaces. H_z is the level difference outlet − inlet. The new input z_s is the height of the inlet liquid level above the pump suction (positive = flooded, negative = suction lift); it affects only suction pressure, NPSHA and the pressure labels, not the operating point (for z_s = 0 the pressure nodes equal v4.0.2). Percent in the interface (efficiency), fractions internally; flows in m³/h and kg/s, heads in m and bar (H[bar] = H·ρ_simg/10⁵).

Tabs Five configurations, each with its own complete input set; switching tabs keeps all of them. Input Configuration (IC) and CSV The IC is one JSON file (format “AntraSIM-input-configuration”, schemaVersion 1) with units in the key names, storing all five configurations, inactive alternatives (tables and analytic parameters of every pump, system table) and the active tab. Loading is transactional; v4.0.2 export files are rejected with a message (different schema). Table CSV: Q_m3h,H_m,P_kW,NPSHR_m and dP_bar,mdot_kgs, comma or semicolon (decimal comma), # comments, header names in any order, whole file rejected on any error.

5. Calculated Quantities

Operating point (Q, H), pump results (flow, head, hydraulic and shaft power, η, NPSHR), pressure nodes, NPSHA per suction node and margins, cavitation-limit flow (first flow at which NPSHA falls below the NPSHR of the pumps fed by the node), specific energy, side flow.

N P S H A = \frac{p_{s} - p_{v} (T)}{ρ g} + \frac{v_{s}^{2}}{2 g}, p_{s} = P_{i n} + ρ g z_{s} - ρ g h_{s u c} (Q) (group A, single, parallel)

p_v from the Wagner–Pruss saturation equation (externally sourced; Table 5.2), v_s in the suction pipe D_s (group B: mid-group pipe). Downstream stages use their own suction pressure (previous stage pressure rise less mid-pipe loss). NPSHR is the 3 % head-drop value; the operating point itself is computed on the non-cavitating curve, so with NPSHA < NPSHR the reported point is not attainable. The suction pipe always defines the suction pressure, also with a system table.

Table 5.1 — Reference results (generated from the code): default of each tab, and equivalence of the table initialisers (relative difference of the operating flow when all pumps use their table, or the system curve its table).

Tab	Q [m³/h]	H [m]	P_shaft [kW]	η [%]	min NPSHA [m]	NPSHR [m]	ΔQ pump tables	ΔQ system table
1 Pump	150.1	24.99	12.85	79.4	11.87	2.1	1.4e-05	6.3e-04
Series	149.9	50	25.68	79.4	11.87	2.1	1.9e-05	4.1e-04
Parallel	299.46	25.01	25.66	79.4	11.94	2.1	5.3e-05	4.2e-04
3+3 Complex	299.54	49.42	51.33	79.4	11.94	2.1	5.1e-05	2.9e-04
3+3 CF Flow	299.54	49.42	51.33	79.4	11.94	2.1	5.1e-05	2.9e-04

Table 5.2 — Fluid properties: implemented formulas vs steam-table values (values typed by the implementer from common steam tables; not machine-verified against IAPWS-IF97 output).

T [°C]	ρ formula [kg/m³]	ρ steam table	Δρ [%]	p_v Wagner–Pruss [kPa]	p_v steam table [kPa]	Δp_v [%]
20	998.234	998.21	+0.00	2.33919	2.3392	-0.0003
50	988.063	988.03	+0.00	12.3525	12.352	+0.0039
100	958.097	958.35	-0.03	101.418	101.42	-0.0020
150	915.701	916.75	-0.11	476.159	476.16	-0.0003
200	862.334	864.7	-0.27	1554.94	1554.9	+0.0025
300	724.553	712.1	+1.75	8587.87	8587.9	-0.0004

6. Numerical Method

Approach Operating points by bisection on the balance residual (100 iterations, 120 for the 3+3 tabs; the bracket is expanded until the sign changes). Group heads are obtained by bisection on the common head; pump inversions Q(H) are exact (closed form for the analytic curve, segment scan for tables), so no nested bisection is needed. Robustness: zero flow when H(0) ≤ H_sys(0); no active pump; group overload redistribution in 3+3 CF Flow (as v4.0.2); non-finite results stop the calculation with a message. Speed: a full 3+3 evaluation (solve + curves) takes about 1/50 s in Node (410 pure solves per second). The result is independent of the previous state (stateless).

7. Verification and Numerical Accuracy

Scope Verification shows that the equations are solved correctly and reference values are reproduced; it is not validation. The suite runs in the application (footer → Verification) and in Node with identical code. T4 compares with the v4.0.2 solver (transcribed from the executable code, analytic pumps, calculated system curve) on 60 random cases.

Table 7.1 — Release verification suite (19 of 19 passed; generated from an actual run).

ID	Test	Criterion	Result	Measured
T1	Vapour pressure (Wagner–Pruss) vs steam-table values at 20, 50, 100, 150, 200 °C; density correlation vs steam tables up to 150 °C	p_v ≤ 5e-4, ρ ≤ 5e-3 relative	PASS	p_v 3.88e-5, ρ 1.14e-3
T2	Vapour pressure at 20 °C vs the value printed in the KSB datasheet (0.02337 bar)	relative difference ≤ 3e-3	PASS	9.39e-4
T3	Single pump, quadratic pump curve and pure minor-loss system: closed-form intersection Q = √((H₀−H_st)/(a+k))	relative difference ≤ 1e-9	PASS	5.23e-12
T4	Solver vs the v4.0.2 reference solver (transcribed): 5 configurations × 12 random cases (temperature, pressures, pipes, speeds, on/off, ρ_ref, manual side flow); Q, H, Q_main, Q_side	max relative difference ≤ 1e-8 (49 converged cases)	PASS	1.55e-15
T5	Default cases: flows of the pumps of each stage sum to the stage flow; series heads add; P_hyd = η·P_shaft	max relative residual ≤ 1e-9	PASS	3.34e-16
T6	3+3 CF Flow with zero side flow equals 3+3 Complex; with a side flow Q_tot = Q_main + Q_side/ρ and Q_main decreases	≤ 1e-9; Q_main < Q_tot	PASS	3.68e-17
T7	Affinity laws at similar points: Q ∝ N, H ∝ N², P ∝ N³, NPSHR ∝ N² (N = 0.8·N_ref)	max relative difference ≤ 1e-12	PASS	2.22e-16
T8	Default pump reproduces the KSB anchor values: H(0) = 30.62 m, H(150 m³/h) = 25 m, P = 12.84 kW, NPSHR = 2.10 m, shut-off pressure 2.997 bar	max relative difference ≤ 2e-3	PASS	2.55e-4
T9	Initialisers are identical: pump table vs analytic definition (curves, operating point, power) and system table vs calculated system curve (operating point) in all five configurations	curves ≤ 1e-3 of H₀/P_BEP/NPSHR_BEP; operating points ≤ 1e-3	PASS	curve 9.62e-4, pump table 5.26e-5, system table 6.32e-4
T10	Power curve: P_shaft finite and increasing with Q, η ≤ 1, efficiency maximum at Q_BEP (150 m³/h); P at the curve end (202.5 m³/h) vs KSB P_max/curve 15.32 kW	η_max at 150 ± 1 m³/h; \|ΔP_max\| ≤ 3e-2	PASS	η_max at 150.6 m³/h, ΔP_max 1.21e-4
T11	NPSHA equals the suction-side pressure balance (closed form); NPSHA = NPSHR at the reported cavitation-limit flow; hot suction-lift case gives a reduced margin	≤ 1e-9; ≤ 1e-6 m; margin < 2×NPSHR	PASS	1.11e-16 / 0
T12	Density basis: 'pressure' (v4.0.2) scales the pump head by ρ_ref/ρ_sim, 'head' leaves it unchanged; both bases coincide when ρ_sim = ρ_ref	≤ 1e-12	PASS	0
T13	Off pump ≡ zero-speed pump (no flow, closed check valve, zero power); parallel with one pump off equals the single-pump result of the same system	b.ok = c.ok = false; results identical ≤ 1e-12	PASS	ok
T14	Invariants on 60 random cases: finite, non-negative Q, H, power; pump and group heads non-increasing with flow	all cases	PASS	pass
T15	IC round trip restores every input exactly (all five configurations, inactive alternatives); 7 malformed files rejected; the registered schema 1→2 migration (system-curve ΔP rebasing, finding A-13) reproduces the case exactly	exact; 7 of 7 rejected; migratedFrom = 1, exact	PASS	round trip exact
T16	System-curve table result is unaffected by a subsequent change of P_out (the table stores the absolute required pressure rise, not an amount relative to P_out)	Q, H identical ≤ 1e-12	PASS	0
T17	Table CSV (pump 4 columns, system 2 columns): exact round trip; ';' delimiter with decimal comma; header names recognised in any column order; 6 malformed files rejected (rising head, non-increasing flow, non-numeric, header)	exact; 6 of 6 rejected	PASS	ok
T18	Side-flow pipe model: closed-form flow of a minor-loss pipe, ṁ = ρA√(2gΔH/K) at the converged group-A outlet pressure; no side flow when P_side,out exceeds P_outA	relative difference ≤ 1e-9; zero side flow	PASS	6.50e-11
T19	Default-case regression values (Q, H, P_shaft, minimum NPSH margin; 5 configurations)	max relative difference ≤ 1e-9 to the stored values	PASS	0

Table 7.2 — Default-case regression values (stored in the suite and printed from the same run).

Tab	Q [m³/h]	H [m]	P_shaft [kW]	min NPSH margin [m]
1 Pump	150.097119889	24.9868705919	12.8487995266	9.76773443485
Series	149.903309807	50.0027800983	25.6793306184	9.7709074225
Parallel	299.455235206	25.0145359777	25.6627699651	9.84605431772
3+3 Complex	299.54400987	49.4241610771	51.3339077826	9.84536906434
3+3 CF Flow	299.54400987	49.4241610771	51.3339077826	9.84536906434

8. Model Parameters and Constants

Evidence classes: externally sourced derived assumption not verified.

Parameter	Default	Unit	Class	Basis	Editable
H₀ (shut-off head)	30.62	m	externally sourced	KSB datasheet, 1480 rpm (§10); consistent with the stated 2.997 bar	yes
Q_BEP, H_BEP	150, 25.0	m³/h, m	externally sourced / assumption	KSB duty point; assumption: duty point = BEP	yes
η_BEP	79.4	%	externally sourced	KSB datasheet at the duty point	yes
NPSHR_BEP	2.10	m	externally sourced	KSB datasheet (6.89 ft), 3 % head drop	yes
ν₀ = NPSHR(0)/NPSHR(BEP)	0.45	–	assumption	Typical shape; KSB states NPSH below 0.3·Q_BEP is not determined	yes
P(0)/P_BEP	0.4496	–	derived	Efficiency maximum at Q_BEP (§3.2)	via H₀, H_BEP
Q_min	25.17	m³/h	externally sourced	KSB “minimum permissible flow rate”	yes
Q_max (end of curve)	202.5	m³/h	derived	Flow at which the model power equals the KSB “maximum power input / curve” (15.32 kW); model value at 202.5 m³/h: 15.32 kW	yes
N, N_ref	1480	rpm	externally sourced	KSB datasheet speed	yes
ρ_ref	998	kg/m³	externally sourced	KSB datasheet (water 20 °C)	yes
Table rows (pump / system)	29 / 18–22	–	derived	Analytic definition sampled at Q_BEP/12 to the runout (350.1 m³/h); system curve sampled at 2·Q_op	yes
T, P_in, z_s	20 °C, 1 bar, +2 m	–	assumption	Water at KSB reference temperature, open inlet vessel, flooded suction	yes
Piping and static head of each tab	see inputs	–	assumption	DN150/125 (1 pump, series), DN200 (parallel, 3+3); H_z and P_out chosen so that the duty point lies at Q_BEP per pump (Table 5.1)	yes
Design margin NPSHA/NPSHR	1.3	–	assumption	Advisory threshold only; not taken from a standard	no

Reasonableness check: alignment of the reference cases. All five defaults reach the KSB duty point (150 m³/h per pump at 25 m head; Table 5.1); the minimum NPSH margin is about 9.8 m against NPSHR = 2.1 m (ratio ≈ 5), i.e. no cavitation risk by design. Previous v4.0.2 defaults (45 m / 530 m pumps, 200 °C at 3 bar) were replaced for the reasons in A-8.

9. Model Scope and Limitations

Represented Steady-state single-phase hydraulics of five pump arrangements, affinity scaling, speed variation, density and vapour pressure of water 0–300 °C, pump power, NPSHA/NPSHR. Not represented Transients and inertia; two-phase flow; the head break-down caused by cavitation; Reynolds/viscosity corrections and the thermodynamic NPSH benefit of hot water; motor, coupling and VFD losses (shaft power only); pipe roughness (smooth-pipe Blasius); viscosity variation with temperature (μ = 1 mPa·s); ideal check valves (no cracking pressure); equal-share pump start behaviour; unstable (humped) H–Q curves; dynamic suction losses inside the pump. The pump-curve density basis is an open point (A-9). The plotted NPSHR curves of pumps in a group use the actual split of the group flow; NPSHA of group B in the CF Flow tab is drawn with the side flow held at its operating value.

10. Data Provenance and Open Points

Selected pump KSB Etanorm 125-100-315 GG (cast-iron volute casing pump to EN 733; suction DN125, discharge DN100, nominal impeller 315 mm; 1480 rpm, 50 Hz), duty point 1 of a KSB technical datasheet, water 20 °C. The datasheet impeller diameter was not visible in the consulted excerpt (the impeller is trimmed for the duty point).

What was found From excerpts of the datasheet (hosted by a third party): flow 150 m³/h, head 25 m, efficiency 79.4 %, NPSH required 6.89 ft (2.10 m), power at the duty point 17.22 hp (12.84 kW), maximum power on the curve 20.54 hp (15.32 kW), minimum permissible flow 25.17 m³/h, shut-off head 30.62 m, speed 1480 rpm, fluid density 998 kg/m³, vapour pressure 0.02337 bar, shut-off (maximum discharge) pressure 2.997 bar. From KSB Etanorm type-series statements: curves to ISO 9906 class 3B, NPSH values at 3 % head drop, catalogue values for ρ = 1.0 kg/dm³ and ν ≤ 20 mm²/s, NPSH for Q < 0.3·Q_BEP not determined. The KSB lexicon article on characteristic curves and selection charts defines the terms; its figures are images without numerical data.

Table 10.1 — Internal consistency of the datasheet values (computed: P = ρ·g·Q·H/η with ρ = 998 kg/m³; shut-off pressure = ρ·g·H₀). Agreement supports the transcription; it is not an independent verification.

Datasheet	n [rpm]	Q [m³/h]	H [m]	η [%]	P stated [kW]	P = ρgQH/η [kW]	H₀ [m]	p₀ stated [bar]	ρgH₀ [bar]
Etanorm 125-100-315 GG	1480	150	25	79.4	12.841	12.844	30.62	2.997	2.998
Etanorm 065-050-200 GG	1457	50.01	10	62.6	2.17	2.1726	15.28	—	1.496
Etanorm 100-080-250 GB	2965	100	72.01	69.6	28.14	28.14	—	—	—
Etanorm 100-080-250 GB	2148	—	35.7	76.5	12.68	—	39.25	3.84	3.843

What was not found The numerical H–Q, P–Q and NPSH–Q curve points of this pump (the type-series booklet and datasheet curves are graphics; bash access to KSB hosts was not available). Unverified: (1) shape of H(Q) between the anchors (quadratic through H₀ and the duty point; runout 350.1 m³/h); (2) duty point = BEP; (3) linear power shape (checked against one independent value: the KSB “maximum power on curve” implies Q_max = 202.5 m³/h ≈ 1.35·Q_BEP, a typical end of curve, but this is one number used for fitting, not a test); (4) NPSHR shape (ν₀ = 0.45); (5) η at off-design flows. To replace them, paste or import the KSB curve points into the pump table (CSV, or edit the rows); analytic and table definitions then diverge deliberately.

Equivalence of the initialisers The default pump table is the analytic definition sampled every Q_BEP/12 (29 rows); interpolation error ≤ 0.010 m (0.032 % of H₀). The system table is the calculated curve sampled at 2·Q_op. Table 5.1 and test T9 show operating-point differences ≤ 1 × 10⁻³ in all five tabs; the pump card displays the live deviation.

11. References

External standards, reports and data (evidence grade stated per entry)

[1] KSB SE & Co. KGaA, Technical datasheet, Etanorm 125-100-315 GG (operating point 1, 1480 rpm), third-party hosted copy, excerpts as returned by web search. Consulted at excerpt level; not verified against KSB's own selection software.
[2] KSB SE & Co. KGaA, Etanorm type-series booklet (statements on ISO 9906 class 3B, NPSH at 3 % head drop, ρ = 1.0 kg/dm³), excerpts. Consulted at excerpt level.
[3] KSB, Centrifugal Pump Lexicon — Characteristic curves and selection chart, ksb.com. Consulted in full (text); figures not numerical.
[4] Wagner, W., Pruss, A., “International equations for the saturation properties of ordinary water substance”, J. Phys. Chem. Ref. Data 22 (1993) 783 (coefficients as used in IAPWS-95). Further reading — the paper was not consulted; coefficients reproduce steam-table values (Table 5.2, T1, T2).
[5] Blasius, H., Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, Heft 131 (1913); White, F. M., Fluid Mechanics, 7th ed., McGraw-Hill (2011). Further reading — not consulted; cited as in the v4.0.2 documentation.
[6] Gülich, J. F., Centrifugal Pumps, 2nd ed., Springer (2008). Further reading — not consulted (affinity laws, NPSH concepts).

Antranova model basis

[A1] Antranova Engineering AB, Pump Network Simulator v4.0.2 (application and Technical Documentation Rev 0.2, June 2026).

Pump Network Simulator

Theory & Method

Theory & Method

1. Physical Background

2. Assessment of the Source Model (v4.0.2)

3. Governing Equations

3.1 System curve and piping

3.2 Pump characteristics (reference speed N_ref, reference density ρ_ref)

3.3 Operating conditions: affinity laws and density basis

3.4 Networks

4. Inputs and Operating Conditions

5. Calculated Quantities

6. Numerical Method

7. Verification and Numerical Accuracy

8. Model Parameters and Constants

9. Model Scope and Limitations

10. Data Provenance and Open Points

11. References

About & Licence

Pump Network Simulator

Table

Verification suite