Centrifugal Pump Basics & Performance Curves

A centrifugal pump has three working parts worth naming. Fluid enters axially — along the shaft direction — at the centre of the impeller, a passage called the eye. The impeller is a disc carrying curved vanes; as it spins, the vanes sweep the fluid around and fling it radially outward by centrifugal action, accelerating it to a high tangential and radial speed. Surrounding the impeller is the volute, a spiral casing whose flow area grows steadily toward the discharge. That growing area is the point: it lets the fast fluid leaving the impeller decelerate, and by Bernoulli that deceleration is a pressure rise. The pump has turned shaft work into fluid speed (in the impeller) and then fluid speed into pressure (in the volute).

Where is the pressure lowest? Right at the eye, where the fluid is accelerating into the impeller. Remember that fact — it is the whole story of cavitation in Lesson 3. The eye is the point of minimum pressure in the entire machine, lower even than the pressure at the suction flange where the inlet pipe bolts on, because the fluid must accelerate from the flange into the impeller channels. Keep that in the back of your mind.

The energy bookkeeping is the angular-momentum relation you previewed in Module 6: a pump adds swirl (it raises r·V_t, the per-unit-mass angular momentum), and the torque is M = ṁ(r₂V_{t2} − r₁V_{t1}) with shaft power Ẇ = ωM. That is the deep theory. In day-to-day pump work you will almost never compute r·V_t by hand; instead you will read a manufacturer's measured performance curve. But it helps to know that the curve is that physics, packaged empirically.

Ask a pump engineer 'how much does this pump lift?' and the answer comes in metres, not pascals. A pump is said to deliver, say, H = 25 m of head. Head is energy per unit weight of fluid — the height to which the pump could lift that fluid against gravity — and it is related to the pressure rise by

H = Δp / (ρg),

where Δp is the pressure rise, ρ the fluid density, and g gravity. The density sits in the denominator, so it cancels: a pump that delivers 25 m of head delivers 25 m of water, 25 m of gasoline, 25 m of any liquid. That makes head a universal, fluid-independent rating of what the pump does to the flow. If pumps were rated in pressure, the same machine would have a different number for every fluid — useless for comparison.

This is the first of two facts that look like one and trip people up. Head is independent of density; pressure is not. A 25-m-head pump lifting water produces a pressure rise of ρgH = (1000)(9.81)(25) ≈ 245 kPa; lifting gasoline (ρ = 750) the same pump produces only (750)(9.81)(25) ≈ 184 kPa. Same head, different pressure — because pressure depends on density and head does not. Hold that distinction; the very next section turns it into a power calculation where density reappears with a vengeance.

Every pump comes with a measured performance curve — a plot of the head it produces against the flow it delivers. For a centrifugal pump the curve falls: head is largest at shutoff (the discharge valve closed, Q = 0) and decreases as you open the valve and let flow through. A simple model of the shape is a downward parabola,

H(Q) = H₀ − aQ²,

where H₀ is the shutoff head (the head at zero flow) and a sets how steeply the curve drops. Real curves are not perfect parabolas, but this captures the essential behaviour and is exactly the model the interactive below uses.

Where on the curve should a pump operate? Each pump has a best efficiency point (BEP): a particular flow at which its efficiency peaks. The manufacturer's curve usually overlays iso-efficiency contours, and the BEP is the design target. Running a pump far from its BEP — too far left (low flow, near shutoff) or too far right (high flow) — wastes energy and can damage the pump through recirculation or cavitation. Good pump selection means matching the operating point to the BEP, which is the entire subject of Lesson 2.

The useful power the pump actually delivers to the fluid — the rate at which it raises the fluid's energy — is the hydraulic power (sometimes called water power):

P_hyd = ρgQH.

This is the energy per unit weight (H) times the weight flow rate (ρgQ). It is the output of the pump as a fluid machine. The input is the brake (shaft) power P_shaft = ωM that the motor supplies — the angular speed times the torque. The difference between input and output is lost to friction in the bearings and seals, to internal recirculation, and to fluid friction in the impeller and volute. The ratio is the pump's efficiency:

η = P_hyd / P_shaft = ρgQH / P_shaft.

A well-designed centrifugal pump runs at η ≈ 0.70–0.85 near its BEP; small or off-design pumps can be much worse. Notice that efficiency also carries the density through P_hyd: at the same head and flow, a denser fluid means more hydraulic power out, so for the same shaft power the efficiency number changes. In practice η is read off the manufacturer's curve for the fluid being pumped.