Centrifugal pumps: characteristics, NPSH and cavitation

Why it matters

Centrifugal pumps move most of the liquid in any chemical plant. Choosing one means matching its head–capacity curve to the piping system, checking power and efficiency, and — most often overlooked — making sure enough suction head is available to avoid cavitation. A pump that cavitates loses head, vibrates and erodes its impeller within weeks.

Key ideas

How it works. Liquid enters the eye of a rotating impeller, is flung outward by the vanes, and leaves with high tangential velocity. The volute or diffuser converts much of this kinetic energy into pressure. The ideal head comes from the angular-momentum balance (Euler's turbomachine equation): H_th = (u₂V_w2 − u₁V_w1)/g, with u the blade speed and V_w the whirl (tangential) component of the absolute velocity. With radial (shock-free) entry, V_w1 = 0. Backward-curved vanes, used in almost all process pumps, give a head that falls with flow and a stable, non-overloading power curve.

Characteristic curves (at constant speed).

• Head–capacity (H–Q): highest at shut-off and falling with flow. Actual head is below the Euler value because of slip, friction and shock losses.
• Power–capacity: brake power P = ρgQH/η rises with flow for backward-curved vanes; lowest at shut-off, so centrifugal pumps are started with the discharge valve closed (unlike positive displacement pumps).
• Efficiency: peaks at the best efficiency point (BEP). Operate near the BEP (typically 80–110 % of BEP flow).
• NPSH required: rises with flow.

Operating point. The system curve H_sys = Δz + Δp/ρg + kQ² (static head plus friction head, which grows with Q²). The pump operates where its H–Q curve crosses the system curve. Flow is controlled by throttling a discharge valve (steepens the system curve, wastes energy) or by changing speed with a variable-frequency drive (more efficient).

Affinity (similarity) laws for a given pump (or geometrically similar pumps with diameter D) at similar operating points: Q ∝ N·D³, H ∝ N²·D², P ∝ N³·D⁵. For impeller trimming of the same pump, approximately Q ∝ D, H ∝ D², P ∝ D³.

Pumps in series and parallel. In series, heads add at the same flow (for high head). In parallel, flows add at the same head (for high flow). The actual gain depends on the system curve.

Cavitation and NPSH. Where local pressure at the impeller eye falls below the liquid's vapour pressure, vapour bubbles form and then collapse violently in higher-pressure regions, pitting the impeller, causing noise, vibration and a drop in head.

• NPSH available (system property): the total head at the pump suction above the vapour-pressure head. Referred to the suction-tank surface: NPSH_A = (p_s,tank − p_v)/ρg + z_s − h_f,s, with z_s the liquid level above the pump centreline (negative for a suction lift) and h_f,s the suction-line friction loss.
• NPSH required (pump property, from the manufacturer's test, usually at a 3 % head drop): rises with flow and speed.
• Requirement: NPSH_A > NPSH_R with a margin (commonly 0.5–1 m or a ratio of 1.1–1.3, per code or company practice).
• To increase NPSH_A: raise the liquid level or lower the pump, enlarge and shorten the suction line, cool the liquid (lower p_v), pressurise the suction vessel. To reduce NPSH_R: lower speed, larger impeller eye, inducer, double-suction impeller.
• For a liquid at its boiling point in a closed vessel (p = p_v), NPSH_A is only the static head minus friction — why reboiler and condensate pumps sit well below their vessels.

Priming. Centrifugal pumps cannot pump air; the casing must be full of liquid before starting.

Formulas

• H_th = (u₂·V_w2 − u₁·V_w1)/g — Euler head (m); u = πDN/60 (m/s), N (rpm).
• P = ρ·g·Q·H/η — shaft power (W); Q (m³/s), H (m), η overall efficiency.
• H_sys = Δz + Δp/(ρg) + k·Q² — system curve (m).
• Q₂/Q₁ = N₂/N₁, H₂/H₁ = (N₂/N₁)², P₂/P₁ = (N₂/N₁)³ — affinity laws, same pump.
• NPSH_A = (p_tank − p_v)/(ρg) + z_s − h_f,s — from the suction vessel (m); p_tank, p_v absolute (Pa).
• NPSH_A = p_suction/(ρg) + V_s²/(2g) − p_v/(ρg) — the same quantity from absolute pressure and velocity measured at the suction flange (heads referred to the pump centreline).
• N_s = N·√Q/H^0.75 — specific speed (units depend on convention); classifies impeller type.

Worked examples

Example 1 (standard). A pump lifts water at 30 °C (ρ = 996 kg/m³, p_v = 4.25 kPa) from an open sump whose level is 3 m below the pump centreline. Suction-line friction is 1.2 m and p_atm = 101.325 kPa. NPSH_R = 4 m. Is the pump safe?

1. NPSH_A = (p_atm − p_v)/(ρg) + z_s − h_f,s.
2. (101 325 − 4246)/(996 × 9.81) = 9.94 m.
3. NPSH_A = 9.94 − 3 − 1.2 = 5.74 m.
4. Margin = 5.74 − 4 = 1.74 m. NPSH_A ≈ 5.7 m > 4 m required: safe, with about 1.7 m margin. At 80 °C (p_v ≈ 47 kPa) the same layout would leave little margin.

Example 2 (GATE level). A pump curve is H = 40 − 2000Q² and the system curve is H = 10 + 8000Q² (H in m, Q in m³/s). The pump runs at 1450 rpm with η = 0.72 at the operating point. Find the operating flow, head and power, and the flow and head if the speed is raised to 1750 rpm along a similarity parabola.

1. Equate: 40 − 2000Q² = 10 + 8000Q² → 10 000Q² = 30 → Q = 0.0548 m³/s.
2. H = 40 − 2000 × 0.003 = 34.0 m.
3. P = ρgQH/η = 1000 × 9.81 × 0.0548 × 34.0 / 0.72 = 25.4 kW.
4. Affinity at similar points: Q₂ = 0.0548 × (1750/1450) = 0.0661 m³/s; H₂ = 34.0 × (1750/1450)² = 49.5 m. Q ≈ 0.0548 m³/s, H = 34 m, P ≈ 25.4 kW. Note: the new actual operating point must be found by intersecting the new pump curve with the system curve; the affinity laws alone give the similar point, which lies on the system curve only if the system has no static head.

Common mistakes

• Using gauge pressure or forgetting vapour pressure in NPSH_A.
• Adding a velocity head to an NPSH_A calculated from the tank surface (it is already accounted for).
• Applying affinity laws between two points that are not dynamically similar (systems with static head).
• Assuming a centrifugal pump can be started against a closed valve without limit — it overheats if left running at shut-off.
• Mixing up NPSH_A (system) with NPSH_R (pump).

For GATE CH

Expect NPSH_A numericals (open and closed suction tanks, hot liquids), operating point from given pump and system curves, power and efficiency calculations, affinity-law scaling, pumps in series and parallel, and conceptual questions on cavitation and characteristic curve shapes. Practise writing NPSH_A from first principles with absolute pressures.

Quick check

1. If speed doubles, what happens to the head and power of a centrifugal pump?
2. Why is a centrifugal pump started with the discharge valve closed?
3. A liquid is pumped from a closed drum at its vapour pressure, 5 m above the pump, with 1 m suction loss. Find NPSH_A.
4. Which NPSH is provided by the manufacturer?

Answers: 1. Head ×4, power ×8. 2. Power is lowest at shut-off. 3. 5 − 1 = 4 m. 4. NPSH required.