Positive Displacement Pump Calculator — help

Overview

Calculates the duty point and suction safety for reciprocating positive displacement pumps. Determines total differential pressure, total dynamic head (TDH), acceleration head loss, and Net Positive Inlet Pressure Available (NPIPA). Compares NPIPA against the required NPIPR to assess cavitation risk, reporting a status of Safe, Marginal, or Critical.

Use this calculator when sizing or verifying a reciprocating pump installation (simplex, duplex, triplex, or quintuplex) and you need to confirm that suction conditions are adequate to prevent cavitation.

Input Parameters

Fluid Properties

Parameter	Type	Default	Range	Description
`density`	Number	998.0	1 – 2000 kg/m³	Mass per unit volume of the fluid
`vapor_pressure`	Number	2.339	0.001 – 500 kPa	Absolute pressure at which fluid vaporizes (at operating temperature)

System Conditions

Parameter	Type	Default	Range	Description
`flowrate`	Number	10.5	0.1 – 10000 m³/h	Required volumetric flowrate
`static_head`	Number	25.15	−100 – 1000 m	Vertical height difference between suction and discharge liquid levels
`suction_static_head`	Number	0.0	−50 – 100 m	Suction liquid level \(Z_s\) above the pump centreline: positive for a flooded suction, negative for a suction lift. Adds \(\rho g Z_s\) to NPIPA
`inlet_pressure`	Number	101.325	0 – 10000 kPa	Pressure on the suction liquid surface (0 kPa gauge for an open tank); the liquid level is entered separately as `suction_static_head`
`discharge_pressure`	Number	500.0	0 – 50000 kPa	Pressure in the discharge vessel
`pressures_are_gauge`	Boolean	True	—	If checked, vessel pressures are treated as gauge and the atmospheric pressure is added to convert to absolute
`atmospheric_pressure`	Number	101.325	50 – 110 kPa	Local atmospheric pressure added to gauge pressures; lower it for altitude (about 89.9 kPa at 1000 m, 84.6 kPa at 1500 m, ISO 2533 standard atmosphere)

Friction Losses

Parameter	Type	Default	Range	Description
`suction_friction`	Number	15.25	0 – 1000 kPa	Total pressure loss due to friction in suction piping
`discharge_friction`	Number	250.8	0 – 5000 kPa	Total pressure loss due to friction in discharge piping

Suction Line & Pump Details

Parameter	Type	Default	Range	Description
`pipe_diameter`	Number	50.8	1 – 5000 mm	Internal diameter of the suction pipe
`suction_length`	Number	10.5	0.1 – 1000 m	Total length of suction pipe from liquid surface to pump
`pump_speed`	Number	150.0	1 – 3600 RPM	Rotational speed of pump crankshaft
`pump_type`	Enum: simplex / duplex / triplex / quintuplex / septuplex / nonuplex	triplex	—	Reciprocating pump configuration (sets the acceleration constant \(C\))
`pump_action`	Enum: single_acting / double_acting	single_acting	—	Single-acting (plunger pumps: one delivery stroke per revolution per cylinder) or double-acting (both strokes deliver). Changes \(C\) for simplex and duplex only

Advanced Parameters

Parameter	Type	Default	Range	Description
`npipr`	Number	35.0	0 – 500 kPa	Net Positive Inlet Pressure Required by the pump (from manufacturer data)
`k_calibration`	Number	1.4	0.1 – 10.0	Hydraulic Institute liquid compressibility factor \(K\): 1.4 deaerated / hot water, 1.5 most liquids (water, amine, glycol), 2.0 most hydrocarbons, 2.5 relatively compressible liquids (hot oil, ethane)

Output Results

Output	Unit	Description
`total_differential_pressure`	kPa	Total differential pressure the pump must overcome
`total_dynamic_head`	m	Total dynamic head (TDH), equivalent head of differential pressure
`velocity`	m/s	Average fluid velocity in the suction pipe
`acceleration_head`	m	Acceleration head loss due to pulsating flow
`acceleration_pressure`	kPa	Acceleration head loss converted to pressure
`suction_static_pressure`	kPa	\(\rho g Z_s\) of the suction liquid level (negative for a lift)
`npipa`	kPa	Net Positive Inlet Pressure Available
`npipa_head`	m	NPIPA expressed as head of fluid
`npipr`	kPa	Net Positive Inlet Pressure Required (echo of input)
`margin`	kPa	Safety margin: NPIPA − NPIPR
`status`	text	"Safe" (≥ 20 kPa margin), "Marginal" (5–20 kPa), or "Critical" (< 5 kPa)
`static_pressure`	kPa	Pressure due to static head
`vessel_pressure_diff`	kPa	Discharge vessel absolute − inlet vessel absolute pressure
`total_friction`	kPa	Sum of suction and discharge friction losses
`inlet_absolute`	kPa	Inlet vessel pressure converted to absolute
`discharge_absolute`	kPa	Discharge vessel pressure converted to absolute

Formulas

Gauge to Absolute Pressure Conversion

\[ P_{abs} = P_{gauge} + P_{atm} \quad (\text{kPa}) \]

Applied to inlet and discharge vessel pressures when pressures_are_gauge is enabled. \(P_{atm}\) is the local atmospheric_pressure (default 101.325 kPa, sea level). At altitude the absolute suction pressure — and so NPIPA — falls by the same amount as the atmosphere; the differential pressure is unchanged because both vessel pressures shift together.

Pipe Cross-Sectional Area & Velocity

\[ A = \frac{\pi \, d^2}{4} \] \[ v = \frac{Q}{A} \]

Where \(d\) is pipe internal diameter in metres (\(d_{mm} / 1000\)) and \(Q\) is flowrate in m³/s (\(Q_{m^3/h} / 3600\)).

Acceleration Head

\[ h_{accel} = \frac{L \times v \times N \times C}{k \times g} \quad (\text{m}) \]

Where \(L\) is suction pipe length (m), \(v\) is average velocity (m/s), \(N\) is pump speed (RPM), \(C\) is the Hydraulic Institute acceleration constant for the pump type and action (table below), \(k\) is the HI liquid compressibility factor (1.4 deaerated hot water, 1.5 water, amine and glycol, 2.0 most hydrocarbons, 2.5 hot oil; default 1.4), and \(g = 9.81\) m/s².

Acceleration Constants \(C\)

Pump Type	Single-acting	Double-acting
Simplex	0.400	0.200
Duplex	0.200	0.115
Triplex	0.066	0.066
Quintuplex	0.040	0.040
Septuplex	0.028	0.028
Nonuplex	0.022	0.022

Hydraulic Institute acceleration-head constants (ANSI/HI 6.1–6.5, reciprocating power pumps; the same table appears in the GPSA Engineering Data Book, Section 12). Only simplex and duplex pumps depend on pump_action; the default is single-acting, the larger (conservative) value.

Head to Pressure Conversion

\[ P = \frac{\rho \times g \times h}{1000} \quad (\text{kPa}) \]

Where \(\rho\) is fluid density (kg/m³), \(g = 9.81\) m/s², and \(h\) is head in metres. Division by 1000 converts Pa to kPa.

Pressure to Head Conversion

\[ h = \frac{P \times 1000}{\rho \times g} \quad (\text{m}) \]

Total Differential Pressure

\[ P_{diff} = P_{static} + P_{\Delta vessel} + P_{friction} \]

Where:

\(P_{static} = \rho \, g \, h_{static} / 1000\) — pressure from elevation difference
\(P_{\Delta vessel} = P_{discharge,abs} - P_{inlet,abs}\) — vessel pressure differential
\(P_{friction} = P_{suction\_friction} + P_{discharge\_friction}\) — total pipe friction

Total Dynamic Head (TDH)

\[ TDH = \frac{P_{diff} \times 1000}{\rho \times g} \quad (\text{m}) \]

NPIPA (Net Positive Inlet Pressure Available)

\[ NPIPA = P_{inlet,abs} + \frac{\rho \, g \, Z_s}{1000} - P_{vapor} - P_{suction\_friction} - P_{accel} \quad (\text{kPa}) \]

Where \(P_{inlet,abs}\) is the absolute pressure on the suction liquid surface, \(Z_s\) the liquid level above the pump centreline (negative for a suction lift) and \(P_{accel}\) the acceleration head converted to pressure using \(P = \rho \, g \, h_{accel} / 1000\) (Hydraulic Institute, ANSI/HI 6.1–6.5; GPSA Engineering Data Book Sec. 12).

NPIP Margin & Status

\[ \text{Margin} = NPIPA - NPIPR \quad (\text{kPa}) \]

Status thresholds:

\(\text{Margin} \geq 20 \text{ kPa} \implies\) Safe
\(5 \leq \text{Margin} < 20 \text{ kPa} \implies\) Marginal
\(\text{Margin} < 5 \text{ kPa} \implies\) Critical

Worked Examples

The 19 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_pump; worked examples for every calculation).

#	Case	Type	ΔP (kPa)	h_a (m)	NPIPA (kPa)	Margin (kPa)	Status	Result
1	Triplex, 150 rpm, 10.5 m³/h water (calculator defaults)	triplex	911.0	10.89	78.4	43.4	Safe	PASS
2	Same triplex at half speed	triplex	718.9	2.72	169.7	134.7	Safe	PASS
3	Simplex pump on light oil — negative NPIPA	simplex (DA)	403.4	24.14	-130.0	-165.0	Critical	FAIL
4	Single-acting simplex plunger pump	simplex (SA)	1,566.2	5.34	64.3	34.3	Safe	PASS
5	Duplex pump with a marginal NPIP	duplex (DA)	992.9	5.38	59.9	11.9	Marginal	PASS
6	Single-acting duplex at the same duty as the double-acting example	duplex (SA)	992.9	9.36	20.9	-27.1	Critical	FAIL
7	Quintuplex from a pressurised vessel, absolute pressures	quintuplex	1,457.0	5.79	182.9	147.9	Safe	PASS
8	Nonuplex pump on a high-flow water duty	nonuplex	7,403.9	6.53	58.5	18.5	Marginal	PASS
9	Triplex on hot oil (K = 2.5)	triplex	1,313.3	4.28	76.9	46.9	Safe	PASS
10	Triplex on diesel (K = 2.0)	triplex	2,625.2	4.96	72.0	32.0	Safe	PASS
11	Glycol (K = 1.5) with the maker's NPIPR	triplex	3,096.6	3.43	81.8	31.8	Safe	PASS
12	Suction from a vessel under vacuum	triplex	430.3	0.82	57.7	2.7	Critical	FAIL
13	Open tank 4 m above the pump inlet	triplex	2,242.0	8.96	45.9	10.9	Marginal	PASS
14	Same pump drawing from a sump 3 m below	triplex	2,242.0	8.96	-22.6	-57.6	Critical	FAIL
15	Slow triplex with a 2.5 m suction lift	triplex	1,110.3	0.64	66.3	31.3	Safe	PASS
16	Pressurised vessel with 2.5 m of liquid above the pump	triplex	3,114.7	9.65	72.9	27.9	Safe	PASS
17	Triplex from an open tank at 1 500 m altitude	triplex	760.8	5.07	47.2	12.2	Marginal	PASS
18	Discharge below the suction level	triplex	249.1	1.15	144.9	110.0	Safe	PASS
19	High-speed triplex with a short suction line	triplex	6,189.4	10.01	41.0	21.0	Safe	PASS

Example 1 — Triplex, 150 rpm, 10.5 m³/h water (calculator defaults)

The calculator's default duty: a triplex plunger pump with a 10.5 m suction line; the acceleration loss is the largest suction loss but the NPIP margin is safe.

Given: Single-acting triplex reciprocating pump at 150 rpm delivering 10.5 m³/h; suction line 10.5 m of 50.8 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 101.325 kPa, discharge vessel 500 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 25.15 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 15.25 kPa, discharge 250.8 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.0508² / 4 = 0.002027 m²; v = (10.5 / 3600) / 0.002027 = 1.439 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 10.5 × 1.4390 × 150 × 0.066 / (1.4 × 9.81) = 10.892 m; P_a = ρ g h_a = 998 × 9.81 × 10.892 / 1000 = 106.63 kPa
Absolute pressures	P_s,abs = 101.325 + 101.325 = 202.650 kPa abs; P_d,abs = 500 + 101.325 = 601.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 25.15 / 1000 + (601.325 − 202.650) + 15.25 + 250.8 = 246.23 + 398.68 + 266.05 = 910.95 kPa
Total dynamic head	TDH = ΔP / (ρg) = 910.95 × 1000 / (998 × 9.81) = 93.046 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 202.650 + 0.00 − 2.339 − 15.25 − 106.63 = 78.43 kPa
NPIP margin	NPIPA − NPIPR = 78.43 − 35 (placeholder — use the maker's value) = 43.43 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 43.43 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 911.0 kPa; NPIPA 78.4 kPa vs NPIPR 35 kPa (Safe); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (10.5/3600)/(π × 0.0508²/4) = 1.439 m/s; h_a = 10.5 × 1.4390 × 150 × 0.066/(1.4 × 9.81) = 10.892 m; P_a = 998 × 9.81 × 10.892/1000 = 106.63 kPa; P_s,abs = 101.325 + 101.325 = 202.650 kPa, P_d,abs = 500 + 101.325 = 601.325 kPa; ΔP = 246.23 + 398.68 + 15.25 + 250.8 = 910.95 kPa (TDH 93.046 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 202.650 + 0.000 − 2.339 − 15.25 − 106.63 = 78.43 kPa; margin = 78.43 − 35 = 43.43 kPa (Safe) (validation case `c0010-triplex-150rpm-npip`)

Example 2 — Same triplex at half speed

Halving the crank speed (and flow) halves the velocity and the speed term, so the acceleration head falls to a quarter — the strongest lever on NPIPA.

Given: Single-acting triplex reciprocating pump at 75 rpm delivering 5.25 m³/h; suction line 10.5 m of 50.8 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 101.325 kPa, discharge vessel 500 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 25.15 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 4 kPa, discharge 70 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.0508² / 4 = 0.002027 m²; v = (5.25 / 3600) / 0.002027 = 0.720 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 10.5 × 0.7195 × 75 × 0.066 / (1.4 × 9.81) = 2.723 m; P_a = ρ g h_a = 998 × 9.81 × 2.723 / 1000 = 26.66 kPa
Absolute pressures	P_s,abs = 101.325 + 101.325 = 202.650 kPa abs; P_d,abs = 500 + 101.325 = 601.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 25.15 / 1000 + (601.325 − 202.650) + 4 + 70 = 246.23 + 398.68 + 74.00 = 718.90 kPa
Total dynamic head	TDH = ΔP / (ρg) = 718.90 × 1000 / (998 × 9.81) = 73.430 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 202.650 + 0.00 − 2.339 − 4 − 26.66 = 169.65 kPa
NPIP margin	NPIPA − NPIPR = 169.65 − 35 (placeholder — use the maker's value) = 134.65 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 134.65 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 718.9 kPa; NPIPA 169.7 kPa vs NPIPR 35 kPa (Safe); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (5.25/3600)/(π × 0.0508²/4) = 0.720 m/s; h_a = 10.5 × 0.7195 × 75 × 0.066/(1.4 × 9.81) = 2.723 m; P_a = 998 × 9.81 × 2.723/1000 = 26.66 kPa; P_s,abs = 101.325 + 101.325 = 202.650 kPa, P_d,abs = 500 + 101.325 = 601.325 kPa; ΔP = 246.23 + 398.68 + 4 + 70 = 718.90 kPa (TDH 73.430 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 202.650 + 0.000 − 2.339 − 4 − 26.66 = 169.65 kPa; margin = 169.65 − 35 = 134.65 kPa (Safe) (validation case `c0010-triplex-75rpm-half-speed`)

Example 3 — Simplex pump on light oil — negative NPIPA

A simplex pump (HI C = 0.200, double-acting) on a long suction line: the acceleration head exceeds the whole atmospheric pressure, NPIPA is negative and the check fails.

Given: Double-acting simplex reciprocating pump at 100 rpm delivering 5 m³/h; suction line 15 m of 40 mm ID. Liquid ρ = 850 kg/m³, P_v = 10 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 200 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 10 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 20 kPa, discharge 100 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.04² / 4 = 0.001257 m²; v = (5 / 3600) / 0.001257 = 1.105 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.200 (simplex, double-acting): 15 × 1.1052 × 100 × 0.200 / (1.4 × 9.81) = 24.142 m; P_a = ρ g h_a = 850 × 9.81 × 24.142 / 1000 = 201.31 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 200 + 101.325 = 301.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 850 × 9.81 × 10 / 1000 + (301.325 − 101.325) + 20 + 100 = 83.39 + 200.00 + 120.00 = 403.38 kPa
Total dynamic head	TDH = ΔP / (ρg) = 403.38 × 1000 / (850 × 9.81) = 48.376 m
Suction static pressure	P_Zs = ρ g Z_s = 850 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 0.00 − 10 − 20 − 201.31 = -129.99 kPa
NPIP margin	NPIPA − NPIPR = -129.99 − 35 (placeholder — use the maker's value) = -164.99 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Critical') → -164.99 vs limit 5.00 kPa FAIL
Result	0/1 checks pass → FAIL; ΔP 403.4 kPa; NPIPA -130.0 kPa vs NPIPR 35 kPa (Critical); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.200 (double-acting simplex): v = (5/3600)/(π × 0.04²/4) = 1.105 m/s; h_a = 15 × 1.1052 × 100 × 0.200/(1.4 × 9.81) = 24.142 m; P_a = 850 × 9.81 × 24.142/1000 = 201.31 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 200 + 101.325 = 301.325 kPa; ΔP = 83.39 + 200.00 + 20 + 100 = 403.38 kPa (TDH 48.376 m); P_Zs = 850 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 101.325 + 0.000 − 10 − 20 − 201.31 = -129.99 kPa; margin = -129.99 − 35 = -164.99 kPa (Critical) (validation case `c0010-simplex-light-oil-critical`)

Example 4 — Single-acting simplex plunger pump

A single-acting simplex plunger (metering-type) pump takes the HI constant C = 0.4 — twice the double-acting 0.2 — so its 3 m suction line costs 52.3 kPa of acceleration loss (26.1 kPa if it were double-acting); the short line keeps the margin safe.

Given: Single-acting simplex reciprocating pump at 90 rpm delivering 1.2 m³/h; suction line 3 m of 25 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 1,500 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 4 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 2 kPa, discharge 25 kPa. NPIPR 30 kPa from the pump maker.

Suction velocity	A = π × 0.025² / 4 = 0.000491 m²; v = (1.2 / 3600) / 0.000491 = 0.679 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.400 (simplex, single-acting): 3 × 0.6791 × 90 × 0.400 / (1.4 × 9.81) = 5.340 m; P_a = ρ g h_a = 998 × 9.81 × 5.340 / 1000 = 52.28 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 1,500 + 101.325 = 1,601.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 4 / 1000 + (1,601.325 − 101.325) + 2 + 25 = 39.16 + 1,500.00 + 27.00 = 1,566.16 kPa
Total dynamic head	TDH = ΔP / (ρg) = 1,566.16 × 1000 / (998 × 9.81) = 159.969 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 2 / 1000 = 19.58 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 19.58 − 2.339 − 2 − 52.28 = 64.29 kPa
NPIP margin	NPIPA − NPIPR = 64.29 − 30 (pump maker) = 34.29 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 34.29 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 1,566.2 kPa; NPIPA 64.3 kPa vs NPIPR 30 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.400 (single-acting simplex): v = (1.2/3600)/(π × 0.025²/4) = 0.679 m/s; h_a = 3 × 0.6791 × 90 × 0.400/(1.4 × 9.81) = 5.340 m; P_a = 998 × 9.81 × 5.340/1000 = 52.28 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 1500 + 101.325 = 1 601.325 kPa; ΔP = 39.16 + 1 500.00 + 2 + 25 = 1 566.16 kPa (TDH 159.969 m); P_Zs = 998 × 9.81 × 2/1000 = 19.581 kPa; NPIPA = 101.325 + 19.581 − 2.339 − 2 − 52.28 = 64.29 kPa; margin = 64.29 − 30 = 34.29 kPa (Safe) (validation case `c0010-simplex-single-acting-plunger`)

Example 5 — Duplex pump with a marginal NPIP

A duplex pump (HI C = 0.115, double-acting) from a flooded tank: the margin is between 5 and 20 kPa — the check passes but the engine reports 'Marginal'.

Given: Double-acting duplex reciprocating pump at 120 rpm delivering 8 m³/h; suction line 8 m of 65 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 800 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 15 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 6 kPa, discharge 40 kPa. NPIPR 48 kPa from the pump maker.

Suction velocity	A = π × 0.065² / 4 = 0.003318 m²; v = (8 / 3600) / 0.003318 = 0.670 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.115 (duplex, double-acting): 8 × 0.6697 × 120 × 0.115 / (1.4 × 9.81) = 5.383 m; P_a = ρ g h_a = 998 × 9.81 × 5.383 / 1000 = 52.70 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 800 + 101.325 = 901.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 15 / 1000 + (901.325 − 101.325) + 6 + 40 = 146.86 + 800.00 + 46.00 = 992.86 kPa
Total dynamic head	TDH = ΔP / (ρg) = 992.86 × 1000 / (998 × 9.81) = 101.411 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 2 / 1000 = 19.58 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 19.58 − 2.339 − 6 − 52.70 = 59.86 kPa
NPIP margin	NPIPA − NPIPR = 59.86 − 48 (pump maker) = 11.86 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Marginal') → 11.86 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 992.9 kPa; NPIPA 59.9 kPa vs NPIPR 48 kPa (Marginal); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.115 (double-acting duplex): v = (8/3600)/(π × 0.065²/4) = 0.670 m/s; h_a = 8 × 0.6697 × 120 × 0.115/(1.4 × 9.81) = 5.383 m; P_a = 998 × 9.81 × 5.383/1000 = 52.70 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 800 + 101.325 = 901.325 kPa; ΔP = 146.86 + 800.00 + 6 + 40 = 992.86 kPa (TDH 101.411 m); P_Zs = 998 × 9.81 × 2/1000 = 19.581 kPa; NPIPA = 101.325 + 19.581 − 2.339 − 6 − 52.70 = 59.86 kPa; margin = 59.86 − 48 = 11.86 kPa (Marginal) (validation case `c0010-duplex-marginal`)

Example 6 — Single-acting duplex at the same duty as the double-acting example

The duplex-marginal duty with a single-acting pump: HI C rises from 0.115 to 0.2, the acceleration loss grows by 74 % and the NPIP check fails.

Given: Single-acting duplex reciprocating pump at 120 rpm delivering 8 m³/h; suction line 8 m of 65 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 800 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 15 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 6 kPa, discharge 40 kPa. NPIPR 48 kPa from the pump maker.

Suction velocity	A = π × 0.065² / 4 = 0.003318 m²; v = (8 / 3600) / 0.003318 = 0.670 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.200 (duplex, single-acting): 8 × 0.6697 × 120 × 0.200 / (1.4 × 9.81) = 9.362 m; P_a = ρ g h_a = 998 × 9.81 × 9.362 / 1000 = 91.66 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 800 + 101.325 = 901.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 15 / 1000 + (901.325 − 101.325) + 6 + 40 = 146.86 + 800.00 + 46.00 = 992.86 kPa
Total dynamic head	TDH = ΔP / (ρg) = 992.86 × 1000 / (998 × 9.81) = 101.411 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 2 / 1000 = 19.58 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 19.58 − 2.339 − 6 − 91.66 = 20.91 kPa
NPIP margin	NPIPA − NPIPR = 20.91 − 48 (pump maker) = -27.09 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Critical') → -27.09 vs limit 5.00 kPa FAIL
Result	0/1 checks pass → FAIL; ΔP 992.9 kPa; NPIPA 20.9 kPa vs NPIPR 48 kPa (Critical); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.200 (single-acting duplex): v = (8/3600)/(π × 0.065²/4) = 0.670 m/s; h_a = 8 × 0.6697 × 120 × 0.200/(1.4 × 9.81) = 9.362 m; P_a = 998 × 9.81 × 9.362/1000 = 91.66 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 800 + 101.325 = 901.325 kPa; ΔP = 146.86 + 800.00 + 6 + 40 = 992.86 kPa (TDH 101.411 m); P_Zs = 998 × 9.81 × 2/1000 = 19.581 kPa; NPIPA = 101.325 + 19.581 − 2.339 − 6 − 91.66 = 20.91 kPa; margin = 20.91 − 48 = -27.09 kPa (Critical) (validation case `c0010-duplex-single-acting`)

Example 7 — Quintuplex from a pressurised vessel, absolute pressures

A quintuplex (HI C = 0.040) fed from a vessel at 250 kPa abs: low pulsation and a pressurised suction give a large margin; absolute pressures are used as given.

Given: Single-acting quintuplex reciprocating pump at 300 rpm delivering 20 m³/h; suction line 6 m of 80 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 250 kPa, discharge vessel 1,500 kPa (absolute). Static head 5 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 8 kPa, discharge 150 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.08² / 4 = 0.005027 m²; v = (20 / 3600) / 0.005027 = 1.105 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.040 (quintuplex): 6 × 1.1052 × 300 × 0.040 / (1.4 × 9.81) = 5.794 m; P_a = ρ g h_a = 998 × 9.81 × 5.794 / 1000 = 56.73 kPa
Absolute pressures	P_s,abs = 250 kPa abs (given as absolute); P_d,abs = 1,500 kPa abs (given as absolute)
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 5 / 1000 + (1,500.000 − 250.000) + 8 + 150 = 48.95 + 1,250.00 + 158.00 = 1,456.95 kPa
Total dynamic head	TDH = ΔP / (ρg) = 1,456.95 × 1000 / (998 × 9.81) = 148.815 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 250.000 + 0.00 − 2.339 − 8 − 56.73 = 182.93 kPa
NPIP margin	NPIPA − NPIPR = 182.93 − 35 (placeholder — use the maker's value) = 147.93 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 147.93 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 1,457.0 kPa; NPIPA 182.9 kPa vs NPIPR 35 kPa (Safe); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.040 (single-acting quintuplex): v = (20/3600)/(π × 0.08²/4) = 1.105 m/s; h_a = 6 × 1.1052 × 300 × 0.040/(1.4 × 9.81) = 5.794 m; P_a = 998 × 9.81 × 5.794/1000 = 56.73 kPa; P_s,abs = 250.000 kPa, P_d,abs = 1 500.000 kPa (given); ΔP = 48.95 + 1 250.00 + 8 + 150 = 1 456.95 kPa (TDH 148.815 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 250.000 + 0.000 − 2.339 − 8 − 56.73 = 182.93 kPa; margin = 182.93 − 35 = 147.93 kPa (Safe) (validation case `c0010-quintuplex-absolute`)

Example 8 — Nonuplex pump on a high-flow water duty

Nine plungers smooth the flow (HI C = 0.022, against 0.4 for a single-acting simplex): at 60 m³/h and 300 rpm a 10 m suction line still costs 63.9 kPa and the margin is only 'Marginal'.

Given: Single-acting nonuplex reciprocating pump at 300 rpm delivering 60 m³/h; suction line 10 m of 125 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 7,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 10 m, suction level Z_s = 3 m (3 m above the pump centreline); friction: suction 6 kPa, discharge 300 kPa. NPIPR 40 kPa from the pump maker.

Suction velocity	A = π × 0.125² / 4 = 0.012272 m²; v = (60 / 3600) / 0.012272 = 1.358 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.022 (nonuplex): 10 × 1.3581 × 300 × 0.022 / (1.4 × 9.81) = 6.527 m; P_a = ρ g h_a = 998 × 9.81 × 6.527 / 1000 = 63.90 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 7,000 + 101.325 = 7,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 10 / 1000 + (7,101.325 − 101.325) + 6 + 300 = 97.90 + 7,000.00 + 306.00 = 7,403.90 kPa
Total dynamic head	TDH = ΔP / (ρg) = 7,403.90 × 1000 / (998 × 9.81) = 756.243 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 3 / 1000 = 29.37 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 29.37 − 2.339 − 6 − 63.90 = 58.46 kPa
NPIP margin	NPIPA − NPIPR = 58.46 − 40 (pump maker) = 18.46 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Marginal') → 18.46 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 7,403.9 kPa; NPIPA 58.5 kPa vs NPIPR 40 kPa (Marginal); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.022 (single-acting nonuplex): v = (60/3600)/(π × 0.125²/4) = 1.358 m/s; h_a = 10 × 1.3581 × 300 × 0.022/(1.4 × 9.81) = 6.527 m; P_a = 998 × 9.81 × 6.527/1000 = 63.90 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 7000 + 101.325 = 7 101.325 kPa; ΔP = 97.90 + 7 000.00 + 6 + 300 = 7 403.90 kPa (TDH 756.243 m); P_Zs = 998 × 9.81 × 3/1000 = 29.371 kPa; NPIPA = 101.325 + 29.371 − 2.339 − 6 − 63.90 = 58.46 kPa; margin = 58.46 − 40 = 18.46 kPa (Marginal) (validation case `c0010-nonuplex-high-flow`)

Example 9 — Triplex on hot oil (K = 2.5)

A compressible liquid (HI K = 2.5 for hot oil) reduces the acceleration head compared with the default K = 1.4.

Given: Single-acting triplex reciprocating pump at 200 rpm delivering 12 m³/h; suction line 12 m of 80 mm ID. Liquid ρ = 820 kg/m³, P_v = 15 kPa abs, compressibility factor K = 2.5. Suction vessel 30 kPa, discharge vessel 1,200 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 6 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 5 kPa, discharge 90 kPa. NPIPR 30 kPa from the pump maker.

Suction velocity	A = π × 0.08² / 4 = 0.005027 m²; v = (12 / 3600) / 0.005027 = 0.663 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 12 × 0.6631 × 200 × 0.066 / (2.5 × 9.81) = 4.283 m; P_a = ρ g h_a = 820 × 9.81 × 4.283 / 1000 = 34.45 kPa
Absolute pressures	P_s,abs = 30 + 101.325 = 131.325 kPa abs; P_d,abs = 1,200 + 101.325 = 1,301.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 820 × 9.81 × 6 / 1000 + (1,301.325 − 131.325) + 5 + 90 = 48.27 + 1,170.00 + 95.00 = 1,313.27 kPa
Total dynamic head	TDH = ΔP / (ρg) = 1,313.27 × 1000 / (820 × 9.81) = 163.256 m
Suction static pressure	P_Zs = ρ g Z_s = 820 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 131.325 + 0.00 − 15 − 5 − 34.45 = 76.87 kPa
NPIP margin	NPIPA − NPIPR = 76.87 − 30 (pump maker) = 46.87 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 46.87 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 1,313.3 kPa; NPIPA 76.9 kPa vs NPIPR 30 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (12/3600)/(π × 0.08²/4) = 0.663 m/s; h_a = 12 × 0.6631 × 200 × 0.066/(2.5 × 9.81) = 4.283 m; P_a = 820 × 9.81 × 4.283/1000 = 34.45 kPa; P_s,abs = 30 + 101.325 = 131.325 kPa, P_d,abs = 1200 + 101.325 = 1 301.325 kPa; ΔP = 48.27 + 1 170.00 + 5 + 90 = 1 313.27 kPa (TDH 163.256 m); P_Zs = 820 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 131.325 + 0.000 − 15 − 5 − 34.45 = 76.87 kPa; margin = 76.87 − 30 = 46.87 kPa (Safe) (validation case `c0010-hot-oil-k2p5`)

Example 10 — Triplex on diesel (K = 2.0)

Most hydrocarbons take the HI compressibility factor K = 2.0: the acceleration head is 1.4/2.0 = 70 % of the default-K value.

Given: Single-acting triplex reciprocating pump at 220 rpm delivering 10 m³/h; suction line 8 m of 65 mm ID. Liquid ρ = 840 kg/m³, P_v = 1 kPa abs, compressibility factor K = 2. Suction vessel 0 kPa, discharge vessel 2,500 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 5 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 4 kPa, discharge 80 kPa. NPIPR 40 kPa from the pump maker.

Suction velocity	A = π × 0.065² / 4 = 0.003318 m²; v = (10 / 3600) / 0.003318 = 0.837 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 8 × 0.8371 × 220 × 0.066 / (2 × 9.81) = 4.956 m; P_a = ρ g h_a = 840 × 9.81 × 4.956 / 1000 = 40.84 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 2,500 + 101.325 = 2,601.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 840 × 9.81 × 5 / 1000 + (2,601.325 − 101.325) + 4 + 80 = 41.20 + 2,500.00 + 84.00 = 2,625.20 kPa
Total dynamic head	TDH = ΔP / (ρg) = 2,625.20 × 1000 / (840 × 9.81) = 318.577 m
Suction static pressure	P_Zs = ρ g Z_s = 840 × 9.81 × 2 / 1000 = 16.48 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 16.48 − 1 − 4 − 40.84 = 71.97 kPa
NPIP margin	NPIPA − NPIPR = 71.97 − 40 (pump maker) = 31.97 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 31.97 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 2,625.2 kPa; NPIPA 72.0 kPa vs NPIPR 40 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (10/3600)/(π × 0.065²/4) = 0.837 m/s; h_a = 8 × 0.8371 × 220 × 0.066/(2 × 9.81) = 4.956 m; P_a = 840 × 9.81 × 4.956/1000 = 40.84 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 2500 + 101.325 = 2 601.325 kPa; ΔP = 41.20 + 2 500.00 + 4 + 80 = 2 625.20 kPa (TDH 318.577 m); P_Zs = 840 × 9.81 × 2/1000 = 16.481 kPa; NPIPA = 101.325 + 16.481 − 1 − 4 − 40.84 = 71.97 kPa; margin = 71.97 − 40 = 31.97 kPa (Safe) (validation case `c0010-hydrocarbon-k2p0`)

Example 11 — Glycol (K = 1.5) with the maker's NPIPR

Glycol (HI K = 1.5) with the pump maker's NPIPR of 50 kPa in place of the 35 kPa placeholder.

Given: Single-acting triplex reciprocating pump at 180 rpm delivering 6 m³/h; suction line 5 m of 50 mm ID. Liquid ρ = 1,110 kg/m³, P_v = 1 kPa abs, compressibility factor K = 1.5. Suction vessel 0 kPa, discharge vessel 3,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 4 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 3 kPa, discharge 50 kPa. NPIPR 50 kPa from the pump maker.

Suction velocity	A = π × 0.05² / 4 = 0.001963 m²; v = (6 / 3600) / 0.001963 = 0.849 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 5 × 0.8488 × 180 × 0.066 / (1.5 × 9.81) = 3.426 m; P_a = ρ g h_a = 1,110 × 9.81 × 3.426 / 1000 = 37.31 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 3,000 + 101.325 = 3,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 1,110 × 9.81 × 4 / 1000 + (3,101.325 − 101.325) + 3 + 50 = 43.56 + 3,000.00 + 53.00 = 3,096.56 kPa
Total dynamic head	TDH = ΔP / (ρg) = 3,096.56 × 1000 / (1,110 × 9.81) = 284.372 m
Suction static pressure	P_Zs = ρ g Z_s = 1,110 × 9.81 × 2 / 1000 = 21.78 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 21.78 − 1 − 3 − 37.31 = 81.79 kPa
NPIP margin	NPIPA − NPIPR = 81.79 − 50 (pump maker) = 31.79 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 31.79 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 3,096.6 kPa; NPIPA 81.8 kPa vs NPIPR 50 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (6/3600)/(π × 0.05²/4) = 0.849 m/s; h_a = 5 × 0.8488 × 180 × 0.066/(1.5 × 9.81) = 3.426 m; P_a = 1110 × 9.81 × 3.426/1000 = 37.31 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 3000 + 101.325 = 3 101.325 kPa; ΔP = 43.56 + 3 000.00 + 3 + 50 = 3 096.56 kPa (TDH 284.372 m); P_Zs = 1110 × 9.81 × 2/1000 = 21.778 kPa; NPIPA = 101.325 + 21.778 − 1 − 3 − 37.31 = 81.79 kPa; margin = 81.79 − 50 = 31.79 kPa (Safe) (validation case `c0010-glycol-k1p5-manufacturer-npipr`)

Example 12 — Suction from a vessel under vacuum

A vessel at 70 kPa abs with an NPIPR of 55 kPa: NPIPA stays positive but the margin over NPIPR is under 5 kPa, so the check fails with status 'Critical'.

Given: Single-acting triplex reciprocating pump at 100 rpm delivering 4 m³/h; suction line 3 m of 50 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 70 kPa, discharge vessel 400 kPa (absolute). Static head 8 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 2 kPa, discharge 20 kPa. NPIPR 55 kPa from the pump maker.

Suction velocity	A = π × 0.05² / 4 = 0.001963 m²; v = (4 / 3600) / 0.001963 = 0.566 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 3 × 0.5659 × 100 × 0.066 / (1.4 × 9.81) = 0.816 m; P_a = ρ g h_a = 998 × 9.81 × 0.816 / 1000 = 7.99 kPa
Absolute pressures	P_s,abs = 70 kPa abs (given as absolute); P_d,abs = 400 kPa abs (given as absolute)
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 8 / 1000 + (400.000 − 70.000) + 2 + 20 = 78.32 + 330.00 + 22.00 = 430.32 kPa
Total dynamic head	TDH = ΔP / (ρg) = 430.32 × 1000 / (998 × 9.81) = 43.954 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 70.000 + 0.00 − 2.339 − 2 − 7.99 = 57.67 kPa
NPIP margin	NPIPA − NPIPR = 57.67 − 55 (pump maker) = 2.67 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Critical') → 2.67 vs limit 5.00 kPa FAIL
Result	0/1 checks pass → FAIL; ΔP 430.3 kPa; NPIPA 57.7 kPa vs NPIPR 55 kPa (Critical); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (4/3600)/(π × 0.05²/4) = 0.566 m/s; h_a = 3 × 0.5659 × 100 × 0.066/(1.4 × 9.81) = 0.816 m; P_a = 998 × 9.81 × 0.816/1000 = 7.99 kPa; P_s,abs = 70.000 kPa, P_d,abs = 400.000 kPa (given); ΔP = 78.32 + 330.00 + 2 + 20 = 430.32 kPa (TDH 43.954 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 70.000 + 0.000 − 2.339 − 2 − 7.99 = 57.67 kPa; margin = 57.67 − 55 = 2.67 kPa (Critical) (validation case `c0010-vacuum-vessel-critical`)

Example 13 — Open tank 4 m above the pump inlet

A flooded suction: the 4 m liquid level above the pump centreline adds ρ·g·Z_s = 998 × 9.81 × 4 = 39.16 kPa to NPIPA on top of the atmosphere acting on the open tank.

Given: Single-acting triplex reciprocating pump at 250 rpm delivering 15 m³/h; suction line 9 m of 80 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 2,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 12 m, suction level Z_s = 4 m (4 m above the pump centreline); friction: suction 4.5 kPa, discharge 120 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.08² / 4 = 0.005027 m²; v = (15 / 3600) / 0.005027 = 0.829 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 9 × 0.8289 × 250 × 0.066 / (1.4 × 9.81) = 8.963 m; P_a = ρ g h_a = 998 × 9.81 × 8.963 / 1000 = 87.75 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 2,000 + 101.325 = 2,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 12 / 1000 + (2,101.325 − 101.325) + 4.5 + 120 = 117.48 + 2,000.00 + 124.50 = 2,241.98 kPa
Total dynamic head	TDH = ΔP / (ρg) = 2,241.98 × 1000 / (998 × 9.81) = 228.999 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 4 / 1000 = 39.16 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 + 39.16 − 2.339 − 4.5 − 87.75 = 45.90 kPa
NPIP margin	NPIPA − NPIPR = 45.90 − 35 (placeholder — use the maker's value) = 10.90 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Marginal') → 10.90 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 2,242.0 kPa; NPIPA 45.9 kPa vs NPIPR 35 kPa (Marginal); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (15/3600)/(π × 0.08²/4) = 0.829 m/s; h_a = 9 × 0.8289 × 250 × 0.066/(1.4 × 9.81) = 8.963 m; P_a = 998 × 9.81 × 8.963/1000 = 87.75 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 2000 + 101.325 = 2 101.325 kPa; ΔP = 117.48 + 2 000.00 + 4.5 + 120 = 2 241.98 kPa (TDH 228.999 m); P_Zs = 998 × 9.81 × 4/1000 = 39.162 kPa; NPIPA = 101.325 + 39.162 − 2.339 − 4.5 − 87.75 = 45.90 kPa; margin = 45.90 − 35 = 10.90 kPa (Marginal) (validation case `c0010-flooded-tank-level`)

Example 14 — Same pump drawing from a sump 3 m below

The flooded-tank duty with the liquid 3 m BELOW the pump centreline: the 7 m change of level costs 998 × 9.81 × 7 = 68.5 kPa, NPIPA turns negative and the check fails — reciprocating pumps with long suction lines need a flooded suction.

Given: Single-acting triplex reciprocating pump at 250 rpm delivering 15 m³/h; suction line 9 m of 80 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 2,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 12 m, suction level Z_s = -3 m (3 m below the pump centreline); friction: suction 4.5 kPa, discharge 120 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.08² / 4 = 0.005027 m²; v = (15 / 3600) / 0.005027 = 0.829 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 9 × 0.8289 × 250 × 0.066 / (1.4 × 9.81) = 8.963 m; P_a = ρ g h_a = 998 × 9.81 × 8.963 / 1000 = 87.75 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 2,000 + 101.325 = 2,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 12 / 1000 + (2,101.325 − 101.325) + 4.5 + 120 = 117.48 + 2,000.00 + 124.50 = 2,241.98 kPa
Total dynamic head	TDH = ΔP / (ρg) = 2,241.98 × 1000 / (998 × 9.81) = 228.999 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × (−3) / 1000 = -29.37 kPa (suction lift)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 − 29.37 − 2.339 − 4.5 − 87.75 = -22.64 kPa
NPIP margin	NPIPA − NPIPR = -22.64 − 35 (placeholder — use the maker's value) = -57.64 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Critical') → -57.64 vs limit 5.00 kPa FAIL
Result	0/1 checks pass → FAIL; ΔP 2,242.0 kPa; NPIPA -22.6 kPa vs NPIPR 35 kPa (Critical); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (15/3600)/(π × 0.08²/4) = 0.829 m/s; h_a = 9 × 0.8289 × 250 × 0.066/(1.4 × 9.81) = 8.963 m; P_a = 998 × 9.81 × 8.963/1000 = 87.75 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 2000 + 101.325 = 2 101.325 kPa; ΔP = 117.48 + 2 000.00 + 4.5 + 120 = 2 241.98 kPa (TDH 228.999 m); P_Zs = 998 × 9.81 × -3/1000 = -29.371 kPa; NPIPA = 101.325 − 29.371 − 2.339 − 4.5 − 87.75 = -22.64 kPa; margin = -22.64 − 35 = -57.64 kPa (Critical) (validation case `c0010-suction-lift-3m-cavitates`)

Example 15 — Slow triplex with a 2.5 m suction lift

A slow triplex on a short, large suction line can lift: the 2.5 m lift takes 24.5 kPa, the acceleration loss is only 6.2 kPa and the margin stays 'Safe'.

Given: Single-acting triplex reciprocating pump at 100 rpm delivering 6 m³/h; suction line 4 m of 80 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 1,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 8 m, suction level Z_s = -2.5 m (2.5 m below the pump centreline); friction: suction 2 kPa, discharge 30 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.08² / 4 = 0.005027 m²; v = (6 / 3600) / 0.005027 = 0.332 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 4 × 0.3316 × 100 × 0.066 / (1.4 × 9.81) = 0.637 m; P_a = ρ g h_a = 998 × 9.81 × 0.637 / 1000 = 6.24 kPa
Absolute pressures	P_s,abs = 0 + 101.325 = 101.325 kPa abs; P_d,abs = 1,000 + 101.325 = 1,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 8 / 1000 + (1,101.325 − 101.325) + 2 + 30 = 78.32 + 1,000.00 + 32.00 = 1,110.32 kPa
Total dynamic head	TDH = ΔP / (ρg) = 1,110.32 × 1000 / (998 × 9.81) = 113.410 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × (−2.5) / 1000 = -24.48 kPa (suction lift)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 101.325 − 24.48 − 2.339 − 2 − 6.24 = 66.27 kPa
NPIP margin	NPIPA − NPIPR = 66.27 − 35 (placeholder — use the maker's value) = 31.27 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 31.27 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 1,110.3 kPa; NPIPA 66.3 kPa vs NPIPR 35 kPa (Safe); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (6/3600)/(π × 0.08²/4) = 0.332 m/s; h_a = 4 × 0.3316 × 100 × 0.066/(1.4 × 9.81) = 0.637 m; P_a = 998 × 9.81 × 0.637/1000 = 6.24 kPa; P_s,abs = 0 + 101.325 = 101.325 kPa, P_d,abs = 1000 + 101.325 = 1 101.325 kPa; ΔP = 78.32 + 1 000.00 + 2 + 30 = 1 110.32 kPa (TDH 113.410 m); P_Zs = 998 × 9.81 × -2.5/1000 = -24.476 kPa; NPIPA = 101.325 − 24.476 − 2.339 − 2 − 6.24 = 66.27 kPa; margin = 66.27 − 35 = 31.27 kPa (Safe) (validation case `c0010-suction-lift-slow-triplex`)

Example 16 — Pressurised vessel with 2.5 m of liquid above the pump

Both suction terms together: 50 kPa gauge on the liquid surface plus a 2.5 m level (998 × 9.81 × 2.5 = 24.48 kPa) above the pump centreline.

Given: Single-acting triplex reciprocating pump at 200 rpm delivering 12 m³/h; suction line 10 m of 65 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 50 kPa, discharge vessel 3,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 6 m, suction level Z_s = 2.5 m (2.5 m above the pump centreline); friction: suction 6 kPa, discharge 100 kPa. NPIPR 45 kPa from the pump maker.

Suction velocity	A = π × 0.065² / 4 = 0.003318 m²; v = (12 / 3600) / 0.003318 = 1.005 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 10 × 1.0045 × 200 × 0.066 / (1.4 × 9.81) = 9.655 m; P_a = ρ g h_a = 998 × 9.81 × 9.655 / 1000 = 94.52 kPa
Absolute pressures	P_s,abs = 50 + 101.325 = 151.325 kPa abs; P_d,abs = 3,000 + 101.325 = 3,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 6 / 1000 + (3,101.325 − 151.325) + 6 + 100 = 58.74 + 2,950.00 + 106.00 = 3,114.74 kPa
Total dynamic head	TDH = ΔP / (ρg) = 3,114.74 × 1000 / (998 × 9.81) = 318.143 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 2.5 / 1000 = 24.48 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 151.325 + 24.48 − 2.339 − 6 − 94.52 = 72.94 kPa
NPIP margin	NPIPA − NPIPR = 72.94 − 45 (pump maker) = 27.94 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 27.94 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 3,114.7 kPa; NPIPA 72.9 kPa vs NPIPR 45 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (12/3600)/(π × 0.065²/4) = 1.005 m/s; h_a = 10 × 1.0045 × 200 × 0.066/(1.4 × 9.81) = 9.655 m; P_a = 998 × 9.81 × 9.655/1000 = 94.52 kPa; P_s,abs = 50 + 101.325 = 151.325 kPa, P_d,abs = 3000 + 101.325 = 3 101.325 kPa; ΔP = 58.74 + 2 950.00 + 6 + 100 = 3 114.74 kPa (TDH 318.143 m); P_Zs = 998 × 9.81 × 2.5/1000 = 24.476 kPa; NPIPA = 151.325 + 24.476 − 2.339 − 6 − 94.52 = 72.94 kPa; margin = 72.94 − 45 = 27.94 kPa (Safe) (validation case `c0010-flooded-pressurised-vessel`)

Example 17 — Triplex from an open tank at 1 500 m altitude

Gauge pressures at 1 500 m use the local atmosphere (84.56 kPa, standard atmosphere): NPIPA is 16.77 kPa lower than at sea level and the margin falls from 'Safe' into 'Marginal'; the differential pressure is unchanged.

Given: Single-acting triplex reciprocating pump at 150 rpm delivering 10.5 m³/h; suction line 8 m of 65 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 0 kPa, discharge vessel 500 kPa (gauge, + 84.56 kPa atmospheric to absolute). Static head 20 m, suction level Z_s = 2 m (2 m above the pump centreline); friction: suction 5 kPa, discharge 60 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.065² / 4 = 0.003318 m²; v = (10.5 / 3600) / 0.003318 = 0.879 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 8 × 0.8790 × 150 × 0.066 / (1.4 × 9.81) = 5.069 m; P_a = ρ g h_a = 998 × 9.81 × 5.069 / 1000 = 49.62 kPa
Absolute pressures	P_s,abs = 0 + 84.56 = 84.560 kPa abs; P_d,abs = 500 + 84.56 = 584.560 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 20 / 1000 + (584.560 − 84.560) + 5 + 60 = 195.81 + 500.00 + 65.00 = 760.81 kPa
Total dynamic head	TDH = ΔP / (ρg) = 760.81 × 1000 / (998 × 9.81) = 77.710 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 2 / 1000 = 19.58 kPa (flooded suction)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 84.560 + 19.58 − 2.339 − 5 − 49.62 = 47.18 kPa
NPIP margin	NPIPA − NPIPR = 47.18 − 35 (placeholder — use the maker's value) = 12.18 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Marginal') → 12.18 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 760.8 kPa; NPIPA 47.2 kPa vs NPIPR 35 kPa (Marginal); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (10.5/3600)/(π × 0.065²/4) = 0.879 m/s; h_a = 8 × 0.8790 × 150 × 0.066/(1.4 × 9.81) = 5.069 m; P_a = 998 × 9.81 × 5.069/1000 = 49.62 kPa; P_s,abs = 0 + 84.56 = 84.560 kPa, P_d,abs = 500 + 84.56 = 584.560 kPa; ΔP = 195.81 + 500.00 + 5 + 60 = 760.81 kPa (TDH 77.710 m); P_Zs = 998 × 9.81 × 2/1000 = 19.581 kPa; NPIPA = 84.560 + 19.581 − 2.339 − 5 − 49.62 = 47.18 kPa; margin = 47.18 − 35 = 12.18 kPa (Marginal) (validation case `c0010-altitude-1500m`)

Example 18 — Discharge below the suction level

A negative static head (discharge 6 m below the suction tank) subtracts from the differential pressure; the suction-side check is unaffected.

Given: Single-acting triplex reciprocating pump at 90 rpm delivering 3 m³/h; suction line 4 m of 40 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 58.7 kPa, discharge vessel 350 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head -6 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 1.5 kPa, discharge 15 kPa. No NPIPR given (35 kPa placeholder).

Suction velocity	A = π × 0.04² / 4 = 0.001257 m²; v = (3 / 3600) / 0.001257 = 0.663 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 4 × 0.6631 × 90 × 0.066 / (1.4 × 9.81) = 1.147 m; P_a = ρ g h_a = 998 × 9.81 × 1.147 / 1000 = 11.23 kPa
Absolute pressures	P_s,abs = 58.7 + 101.325 = 160.025 kPa abs; P_d,abs = 350 + 101.325 = 451.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × -6 / 1000 + (451.325 − 160.025) + 1.5 + 15 = -58.74 + 291.30 + 16.50 = 249.06 kPa
Total dynamic head	TDH = ΔP / (ρg) = 249.06 × 1000 / (998 × 9.81) = 25.439 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 160.025 + 0.00 − 2.339 − 1.5 − 11.23 = 144.95 kPa
NPIP margin	NPIPA − NPIPR = 144.95 − 35 (placeholder — use the maker's value) = 109.95 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 109.95 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 249.1 kPa; NPIPA 144.9 kPa vs NPIPR 35 kPa (Safe); governing: npip margin. NPIPR is a 35 kPa placeholder; use the pump maker's value.
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (3/3600)/(π × 0.04²/4) = 0.663 m/s; h_a = 4 × 0.6631 × 90 × 0.066/(1.4 × 9.81) = 1.147 m; P_a = 998 × 9.81 × 1.147/1000 = 11.23 kPa; P_s,abs = 58.7 + 101.325 = 160.025 kPa, P_d,abs = 350 + 101.325 = 451.325 kPa; ΔP = -58.74 + 291.30 + 1.5 + 15 = 249.06 kPa (TDH 25.439 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 160.025 + 0.000 − 2.339 − 1.5 − 11.23 = 144.95 kPa; margin = 144.95 − 35 = 109.95 kPa (Safe) (validation case `c0010-negative-static-head`)

Example 19 — High-speed triplex with a short suction line

A fast (400 rpm) triplex shows why the suction line must be short: even 2 m of pipe at 2.6 m/s costs ~98 kPa of acceleration loss; the margin lands just above the 20 kPa 'Safe' band edge.

Given: Single-acting triplex reciprocating pump at 400 rpm delivering 18.4 m³/h; suction line 2 m of 50 mm ID. Liquid ρ = 998 kg/m³, P_v = 2.339 kPa abs, compressibility factor K = 1.4. Suction vessel 49 kPa, discharge vessel 6,000 kPa (gauge, + 101.325 kPa atmospheric to absolute). Static head 3 m, suction level Z_s = 0 m (0 m above the pump centreline); friction: suction 9 kPa, discharge 200 kPa. NPIPR 20 kPa from the pump maker.

Suction velocity	A = π × 0.05² / 4 = 0.001963 m²; v = (18.4 / 3600) / 0.001963 = 2.603 m/s
Acceleration head	h_a = L·v·N·C / (K·g), HI C = 0.066 (triplex): 2 × 2.6031 × 400 × 0.066 / (1.4 × 9.81) = 10.007 m; P_a = ρ g h_a = 998 × 9.81 × 10.007 / 1000 = 97.98 kPa
Absolute pressures	P_s,abs = 49 + 101.325 = 150.325 kPa abs; P_d,abs = 6,000 + 101.325 = 6,101.325 kPa abs
Differential pressure	ΔP = ρ g H_static + (P_d,abs − P_s,abs) + P_f,s + P_f,d = 998 × 9.81 × 3 / 1000 + (6,101.325 − 150.325) + 9 + 200 = 29.37 + 5,951.00 + 209.00 = 6,189.37 kPa
Total dynamic head	TDH = ΔP / (ρg) = 6,189.37 × 1000 / (998 × 9.81) = 632.189 m
Suction static pressure	P_Zs = ρ g Z_s = 998 × 9.81 × 0 / 1000 = 0.00 kPa (level at the centreline)
NPIP available	NPIPA = P_s,abs + P_Zs − P_v − P_f,s − P_a = 150.325 + 0.00 − 2.339 − 9 − 97.98 = 41.01 kPa
NPIP margin	NPIPA − NPIPR = 41.01 − 20 (pump maker) = 21.01 kPa, required ≥ 5 kPa (engine bands: ≥ 20 safe, 5–20 marginal, < 5 critical → 'Safe') → 21.01 vs limit 5.00 kPa PASS
Result	1/1 checks pass → PASS; ΔP 6,189.4 kPa; NPIPA 41.0 kPa vs NPIPR 20 kPa (Safe); governing: npip margin
Reference	Hand calculation, acceleration head per ANSI/HI 6.1–6.5 h_a = L·v·N·C/(K·g) with HI C = 0.066 (single-acting triplex): v = (18.4/3600)/(π × 0.05²/4) = 2.603 m/s; h_a = 2 × 2.6031 × 400 × 0.066/(1.4 × 9.81) = 10.007 m; P_a = 998 × 9.81 × 10.007/1000 = 97.98 kPa; P_s,abs = 49 + 101.325 = 150.325 kPa, P_d,abs = 6000 + 101.325 = 6 101.325 kPa; ΔP = 29.37 + 5 951.00 + 9 + 200 = 6 189.37 kPa (TDH 632.189 m); P_Zs = 998 × 9.81 × 0/1000 = 0.000 kPa; NPIPA = 150.325 + 0.000 − 2.339 − 9 − 97.98 = 41.01 kPa; margin = 41.01 − 20 = 21.01 kPa (Safe) (validation case `c0010-high-speed-short-line`)

Standards & References

Hydraulic Institute Standards — ANSI/HI 6.1–6.5 Reciprocating Power Pumps — acceleration head formula, NPIP definitions, and pump type coefficients
API 674 — Positive Displacement Pumps — Reciprocating — design requirements, pulsation analysis, and suction system design guidance
API 675 — Positive Displacement Pumps — Controlled Volume Metering — applicable for metering pump variants
Pump manufacturer datasheets — always use manufacturer-supplied NPIPR values when available; the default 35 kPa is a conservative estimate only

Tips & Limitations

Tips

Always use the manufacturer-supplied NPIPR. The default value of 35 kPa is a general conservative estimate and may not be appropriate for all pumps.
Triplex and quintuplex pumps produce much lower pulsation than simplex or duplex, significantly reducing acceleration head loss.
Suction velocity should be kept below 3 m/s. The calculator warns when this limit is exceeded.
Shorter, larger-diameter suction lines reduce both friction losses and acceleration head.
Reducing pump speed lowers acceleration head proportionally — consider a slower pump or a VFD for marginal NPIP conditions.
When pressures_are_gauge is enabled, the calculator adds atmospheric_pressure (101.325 kPa at sea level) to convert to absolute. Enter the local value at altitude, or uncheck gauge if you already have absolute pressure readings.
Negative static head (pump above liquid source) is supported and increases the system difficulty — enter negative values carefully.

Limitations

Steady-state only — the calculator does not model transient pulsation damping, suction stabiliser effects, or dynamic surge analysis.
Empirical acceleration head formula — the \(h_{accel}\) calculation is an industry-standard approximation. For critical applications, perform a full pulsation study per API 674 Annex A.
Single fluid phase assumed — the calculator does not account for two-phase flow, entrained gas, or compressible fluids.
Friction losses are user-supplied — the calculator does not compute pipe friction from pipe roughness, fittings, or equivalent lengths. Calculate friction separately and enter as inputs.
No slurry or non-Newtonian fluid corrections — density and vapor pressure assume a simple Newtonian liquid.
Liquid compressibility factor — the default \(K = 1.4\) is the Hydraulic Institute value for an almost incompressible liquid (deaerated water); use 1.5 for most liquids, 2.0 for hydrocarbons and 2.5 for hot oil.

Developer Guide

Architecture

File layout:

components/c0010_positive_displacement_pump/component.py — Component registration, parameter schema, calculator class, equation builder, and summary cards builder
components/c0010_positive_displacement_pump/calculations.py — Pure math functions and constants (no Django dependencies)
components/c0010_positive_displacement_pump/equations.py — MathJax equation builder for PDF report generation
components/c0010_positive_displacement_pump/excel_generator.py — Excel report generator (openpyxl workbook with inputs, results, equations, and safety)

The calculator class is PositiveDisplacementPumpCalculator, extending BaseCalculator. It is registered with calc type 'positive_displacement_pump' via the register_component(registry) function.

Constants defined in calculations.py:

GRAVITY = 9.81 m/s²
ATMOSPHERIC_PRESSURE = 101.325 kPa
DEFAULT_K_CALIBRATION = 1.4 (HI liquid compressibility factor)
DEFAULT_NPIPR = 35.0 kPa
ACCELERATION_CONSTANTS — dict mapping (pump type, action) to the HI constant C; acceleration_coefficient(pump_type, pump_action) looks it up
MARGIN_SAFE = 20.0 kPa, MARGIN_MARGINAL = 5.0 kPa

Code Paths

Key functions in calculations.py:

Function	Purpose
`convert_gauge_to_absolute(pressure_gauge, atmospheric_pressure)`	Add atmospheric pressure to gauge reading
`convert_head_to_pressure(head, density)`	Convert fluid head (m) to pressure (kPa)
`convert_pressure_to_head(pressure, density)`	Convert pressure (kPa) to fluid head (m)
`calculate_pipe_velocity(flowrate_m3h, diameter_mm)`	Average velocity from flowrate and pipe area
`calculate_acceleration_head(L, v, N, C, k)`	Empirical acceleration head loss for reciprocating pumps
`calculate_total_differential_pressure(...)`	Sum of static, vessel differential, and friction pressures
`calculate_npipa(...)`	Net Positive Inlet Pressure Available
`assess_npip_status(npipa, npipr)`	Classify margin as Safe / Marginal / Critical
`calculate_positive_displacement_pump(data)`	Main orchestrator — calls all above and returns results dict

Request flow:

PositiveDisplacementPumpCalculator.__init__(parameters) — stores parameters via BaseCalculator
validate_parameters() — checks physical consistency (positive density, valid pressures, speed range)
calculate() — assembles data dict and delegates to calculate_positive_displacement_pump(data)
equation_builder(results) — produces MathJax article list for report rendering
summary_cards_builder(results) — produces dashboard cards with status-based colour coding

Testing

Running tests:

pytest calcs/components/c0010_positive_displacement_pump/ -v
pytest calcs/test_c0010* -v
pytest -m validation mcp_public/tests/test_validation_corpus.py -k c0010 -q
pytest calcs/test_help_examples.py -k pump -q

Worked examples: the examples above are generated from the validation corpus (mcp_public/validation/cases/fe_calc_pump/, ids c0010-*) by python manage.py generate_help_examples --tool fe_calc_pump, which writes _positive_displacement_pump_examples.html. Add or change a case there, then regenerate; the fragment is never edited by hand.

How to extend:

Add new pump types by extending the PUMP_TYPE_COEFFICIENTS dict in calculations.py and updating the pump_type enum in the parameter schema.
To add pipe friction calculation (currently user-supplied), create a new helper function for Darcy-Weisbach or equivalent and call it from the main orchestrator.
For non-Newtonian fluid support, introduce a viscosity parameter and apply correction factors to the acceleration head formula.
Write tests covering edge cases: zero friction, negative static head, absolute vs gauge pressure toggle, very high pump speed.