Centrifugal & Reciprocating Pumps Notes

Last reviewed 16 Sept 2026 · 9 min read

Pumps

A pump converts mechanical energy into hydraulic (pressure) energy to lift liquid or move it through pipes.

Rotodynamic pumps — energy imparted by a rotating impeller (centrifugal, mixed-flow, axial-flow).
Positive displacement pumps — liquid trapped and forced out (reciprocating, gear, screw).

Centrifugal pump

Main parts

Impeller — rotating wheel with backward-curved vanes; types: closed (shrouds on both sides, clean water), semi-open and open (for sewage and solids).
Casing — airtight passage that converts kinetic energy to pressure:
- Volute casing — spiral of increasing area; simple, some eddy losses.
- Vortex casing — a circular chamber between impeller and volute; reduces eddy losses.
- Casing with guide blades (diffuser) — fixed diffuser vanes; highest efficiency (turbine pump).
Suction pipe with foot valve (non-return) and strainer at its lower end.
Delivery pipe with a delivery valve to regulate flow.

Priming — filling the suction pipe, casing and part of the delivery pipe with liquid before starting, to expel air. A centrifugal pump running in air develops negligible head (head ∝ density), so without priming it cannot lift water.

The pump is started with the delivery valve closed (power at shut-off is minimum for radial-flow pumps), then the valve is opened gradually.

Heads

Head	Definition
Suction head $h_{s}$	Height of pump centre above the sump water level
Delivery head $h_{d}$	Height of delivery outlet above the pump centre
Static head $H_{s}$	$h_{s} + h_{d}$
Manometric head $H_{m}$	Head actually imparted to the liquid: $H_{m} = h_{s} + h_{d} + h_{f s} + h_{f d} + \frac{V _{d}^{2}}{2 g}$ ; also = difference of pressure heads measured at outlet and inlet (+ velocity and datum corrections)
Euler (theoretical) head	$\frac{V _{w 2} u _{2}}{g}$ for radial entry ( $V_{w 1}$ = 0)

Efficiencies

Manometric efficiency: $η_{man} = \frac{g H _{m}}{V _{w 2} u _{2}}$
Mechanical efficiency: $η_{m}$ = power at impeller ÷ shaft power
Overall efficiency: $η_{o} = \frac{ρ g Q H _{m}}{shaft power} = η_{man} \times η_{m}$

Velocity triangles and work done

FormulaCentrifugal pump

Blade velocities: $u_{1} = \frac{π D _{1} N}{60}$ , $u_{2} = \frac{π D _{2} N}{60}$
Work done per second per unit weight (radial entry): $\frac{V _{w 2} u _{2}}{g}$
Outlet whirl: $V_{w 2} = u_{2} - \frac{V _{f 2}}{tan ϕ}$ ( $ϕ$ = outlet vane angle measured from the tangent)
Discharge: $Q = π D_{2} B_{2} V_{f 2}$ (outlet width $B_{2}$ )

Backward-curved vanes ( $ϕ < 90°$ ) are standard — they give a stable, non-overloading power characteristic.

Minimum starting speed

Flow begins only when the centrifugal head developed exceeds the manometric head:

\frac{u _{2}^{2} - u _{1}^{2}}{2 g} \geq H_{m} \Rightarrow N_{min} = \frac{120 η _{man} V _{w 2} D _{2}}{π ( D _{2}^{2} - D _{1}^{2} )}

(the second form uses $H_{m} = η_{man} V_{w 2} u_{2} / g$ ).

Multistage pumps

Impellers in series (on one shaft) — for high heads: total head $= n \times H_{m}$ , same discharge.
Pumps in parallel — for large discharge: total discharge $= n \times Q$ , same head.

Specific speed and similarity

FormulaPump specific speed and laws

Specific speed: $N_{s} = \frac{N Q}{H _{m}^{3/4}}$ — speed of a similar pump delivering 1 m³/s against 1 m head. Low $N_{s}$ → radial-flow (centrifugal, high head, small discharge); medium → mixed-flow; high → axial-flow (low head, large discharge).

Model laws (similar pumps): $\frac{Q}{N D ^{3}}$ , $\frac{g H}{N ^{2} D ^{2}}$ , $\frac{P}{ρ N ^{3} D ^{5}}$ constant.

Affinity laws (same pump, changed speed): $Q \propto N$ , $H \propto N^{2}$ , $P \propto N^{3}$ . (Same speed, trimmed impeller: $Q \propto D$ , $H \propto D^{2}$ , $P \propto D^{3}$ approximately.)

Characteristic curves and operating point

Main characteristics — $H_{m}$ , power and $Q$ plotted against speed.
Operating characteristics (constant design speed) — $H_{m}$ , shaft power and $η_{o}$ against $Q$ . Head is highest at zero flow (shut-off head) and falls as $Q$ rises; efficiency peaks at the design point (best efficiency point).
Constant efficiency (Muschel) curves.
System curve: $H = H_{s t a t i c} + K Q^{2}$ (friction and minor losses).
The operating point is the intersection of the pump $H$ – $Q$ curve and the system curve.

Cavitation and NPSH

When absolute pressure at the impeller eye falls to the vapour pressure, vapour bubbles form and collapse → noise, vibration, fall in head and efficiency, pitting of the impeller.

FormulaNet positive suction head

Available NPSH (pump above sump level):

N P S H_{A} = \frac{p _{a}}{ρ g} - \frac{p _{v}}{ρ g} - h_{s} - h_{f s}

Cavitation is avoided if $N P S H_{A} \geq N P S H_{R}$ (required, given by the manufacturer).

Thoma's cavitation factor for pumps: $σ = \frac{N P S H}{H _{m}}$

Theoretical maximum suction lift for water at sea level is about 10.3 m (atmospheric head), but practical suction lifts are much smaller because of vapour pressure, friction, velocity head and NPSH required.
Prevention: keep suction pipe short with large diameter and few bends, reduce suction lift (or use positive suction head/submergence), avoid running at excessive speed or far beyond the design flow.

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Centrifugal & Reciprocating Pumps