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Pump Operating Point

Also known as duty point · pump duty point · intersection of pump and system curve · where the pump runs · natural operating point · pump curve system curve crossing

Qop=H0−Hstk+cQ_{op} = \sqrt{\frac{H_{0} - H_{st}}{k + c}}
s²/m⁵
s²/m⁵

Worked example: 50 m shutoff, c = 1000, on 20 m static with k = 2000 → 360 m³/h — press Try an example to run it live, then adjust anything.

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See also
Pump System Curve — The system side of the crossing, and where the resistance coefficient k comes from.Pump Affinity Law — Head vs Speed — Slowing the pump lowers H₀ and moves the crossing down the system curve — this is what a variable-speed drive is doing.Pump Water Horsepower — Turns the flow and head at the operating point into the useful power the pump is delivering there.Net Positive Suction Head Available (NPSHa) — The operating point sets the flow, and NPSH required rises steeply with flow — check cavitation at the point the pump actually runs, not at the design point.Pump Efficiency from Hydraulic and Shaft Power — Efficiency is a function of flow, so it is the operating point that decides how much of the shaft power does work.

Learning zone

A pump does not have a flow rating. This is the single most useful thing to know about pumps, and it is routinely obscured by catalogues that print one flow beside a model number. What a pump has is a CURVE: head against flow, falling from a shutoff head at zero flow to a runout flow at zero head. The pipework has a curve too. The machine runs where the two cross, at one flow, and it cannot run anywhere else.

Model the pump curve as H=H0−cQ2H = H_0 - cQ^2 and the system as H=Hst+kQ2H = H_{st} + kQ^2, set them equal, and the crossing falls out in one line: Qop=(H0−Hst)/(k+c)Q_{op} = \sqrt{(H_0 - H_{st})/(k + c)}. Take a pump with a 50 m shutoff head and c = 1000, on a system lifting 20 m with k = 2000. The operating flow is 30/3000=0.1\sqrt{30/3000} = 0.1 m³/s, or 360 m³/h, and both curves agree there: the system wants 20 + 2000(0.01) = 40 m and the pump makes 50 − 1000(0.01) = 40 m.

Once the picture is in your head, everything anyone does to a pumped system becomes a move of one curve or the other. Throttling a discharge valve raises k, steepens the system parabola, and slides the point up and to the LEFT — less flow at more head, with the extra head thrown away across the valve as heat. Opening a valve lowers k and slides it down and to the right. Slowing the pump lowers H0H_0 and drops the whole pump curve, which is what a variable-speed drive does and why it saves what throttling wastes. Trimming the impeller does much the same, permanently and cheaply. Fouling raises k slowly and walks the point left over a season.

Where on the curve the point lands matters as much as the flow it gives. Far out toward runout is where NPSH required is highest, where efficiency has usually fallen away again, and where a pump can cavitate despite plenty of static suction head. Well back toward shutoff brings recirculation, radial thrust on the shaft and the pump heating the liquid it is churning; many pumps carry a minimum continuous flow for exactly that reason. The target is the best-efficiency point, and "somewhere on the curve" is not a specification.

Two honest limitations. H=H0−cQ2H = H_0 - cQ^2 is a two-parameter fit, not a law: it describes most centrifugal curves well across their working range and departs from some — particularly steep or drooping ones — near shutoff. Get c from a point in the middle of the working range, c=(H0−H1)/Q12c = (H_0 - H_1)/Q_1^2, and trust the fit only over that range. And the answer is a flow, not a selection: read the efficiency, the NPSH required and the shaft power at THIS flow off the manufacturer's own curve sheet before ordering anything. It is also worth expecting the real machine to run left of the calculated point, because a design k built from a fitting schedule is nearly always optimistic against the system that gets installed.

Pump Operating Point
Qop=H0−Hstk+cQ_{op} = \sqrt{\frac{H_{0} - H_{st}}{k + c}}
Where
  • QopQ_{op}= Operating flow (m³/h)
  • H0H_{0}= Pump shutoff head (m)
  • HstH_{st}= System static head (m)
  • kk= System resistance coefficient (s²/m⁵)
  • cc= Pump curve droop coefficient (s²/m⁵)
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