Introduction & Context

A reciprocating pump converts rotational crank motion into a fixed volume displacement per stroke. Knowing the delivered flow rate is essential for sizing piping, setting control-valve Cv, and verifying that the pump can meet a process duty point. The calculation is routinely performed in Process Engineering for dosing, metering, and high-pressure feed services such as boiler feed-water, reverse-osmosis, and chemical injection packages.

Methodology & Formulas

Convert all inputs to consistent SI units:
- \( D = D_{\text{mm}} \cdot 0.001 \) [m]
- \( L = L_{\text{mm}} \cdot 0.001 \) [m]
- \( n = N_{\text{rpm}} / 60 \) [rps]
Piston cross-sectional area: \[ A = \frac{\pi D^{2}}{4} \]
Swept (displacement) volume per stroke: \[ V_{\text{disp}} = A \cdot L \]
Ideal volumetric flow rate (one suction stroke per revolution): \[ Q_{\text{ideal}} = n \cdot V_{\text{disp}} \]
Account for volumetric efficiency: \[ Q_{\text{actual}} = Q_{\text{ideal}} \cdot \eta_{\text{v}} \]
Convert to litres per minute: \[ Q_{\text{L min}^{-1}} = Q_{\text{actual}} \cdot 1000 \cdot 60 \]

Parameter	Symbol	Unit	Typical Range
Volumetric efficiency	\( \eta_{\text{v}} \)	—	0.85 – 0.98 (single-acting water service)
Speed	\( N \)	rpm	50 – 400 (direct-drive or gear-reduced)
Stroke length	\( L \)	mm	30 – 250 (short stroke preferred for high pressure)

Theoretical capacity (Q_th) is the volume displaced per unit time assuming 100 % volumetric efficiency. Formula: Q_th = A × L × N × n / 60

A = piston area (m²) = π × (D²/4)
L = stroke length (m)
N = strokes per minute (spm)
n = number of cylinders

Result is in m³/s; multiply by 3600 for m³/h.

Typical slip for process reciprocating pumps is 2–10 %.

Low-speed, packed plunger pumps: 2–4 %
High-speed, diaphragm or packed: 5–8 %
Hot, low-viscosity liquids: up to 10 %

Always use vendor data when available; otherwise start with 5 % and field-tune.

Viscosity reduces volumetric efficiency by increasing internal leakage (slip) and valve lag.

Up to 50 cP: use standard slip
50–500 cP: add 1–3 % extra slip
>500 cP: consult manufacturer; consider speed derate

If viscosity >1000 cP, switch to positive-displacement rotary pumps.

Yes. Free gas occupies piston displacement, reducing liquid capacity.

Measure % gas volume at suction conditions
Corrected Q = Q_actual × (1 – % gas/100)
If gas >5 % v/v, install gas separator or boost suction pressure

Neglecting this step can under-deliver up to 20 % flow.

Worked Example – Reciprocating Pump Capacity

A small chemical dosing skid must meter 42 L/min of corrosion inhibitor. A single-acting plunger pump is proposed. Verify whether a 60 mm bore, 90 mm stroke unit running at 180 rpm with a volumetric efficiency of 92 % can deliver the required flow.

Knowns

Bore diameter, D = 60 mm
Stroke length, L = 90 mm
Speed, N = 180 rpm
Volumetric efficiency, η_v = 0.92

Step-by-Step Calculation

Convert diameter and stroke to metres:
D = 60 mm × 0.001 = 0.060 m
L = 90 mm × 0.001 = 0.090 m
Convert speed to revolutions per second:
N = 180 rpm × 0.01667 = 3.000 rps
Calculate swept volume per stroke:
\[ V_{\text{disp}} = \frac{\pi}{4} D^{2} L \]
\[ V_{\text{disp}} = \frac{3.142}{4}(0.060)^{2}(0.090) = 0.000254\ \text{m}^3 \]
Ideal flow rate (single-acting, single cylinder):
\[ Q_{\text{ideal}} = V_{\text{disp}} \cdot N \]
Q_ideal = 0.000763 m³/s × 3.000 s^-1 = 0.000763 m³/s
Account for volumetric efficiency:
Q_actual = Q_ideal × η_v
Q_actual = 0.000763 m³/s × 0.92 = 0.000702 m³/s
Convert to litres per minute:
Q_L/min = 0.000702 m³/s × 1000 L/m³ × 60 s/min = 42.1 L/min

Final Answer

The pump delivers 42.1 L/min, meeting the 42 L/min requirement.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle