§ 7.2  Module 7 — Matching and Optimising

The Operating Point, and Why It Moves

The pump does not choose the operating point. The intersection does.Module 7

7.2.1One flow satisfies both machines

A centrifugal pump curve falls with flow while a system curve rises. The station can settle only where the head the pump supplies equals the head the system demands. That crossing is the operating point. The catalogue's rated flow is not a command, and the pipe's design flow is not a prediction. Until the curves are matched, both are annotations.

Graphically, interpolate between manufacturer curve points and the calculated system points using consistent axes. Numerically, solve F(Q) = Hpump(Q) − Hsys(Q) = 0. Bisection is slow and dependable: bracket a sign change, halve the interval, retain the half containing the crossing. A fitted quadratic is useful for teaching, but procurement uses the manufacturer's tested points and the supplied impeller diameter and speed.

pump:    Hp = 42 - 900 Q²
system: Hs = 18 + 2 500 Q²
equal:  24 = 3 400 Q²
Q = sqrt(24 / 3 400) = 0.08402 m³/s = 84.02 L/s
H = 35.65 m

Closed-form check for two quadratic teaching curves.

7.2.2The point moves because the station does

Draw the wet well down and static lift rises: the system curve moves upward and the crossing moves left, toward lower flow and higher pump head. Roughen the main or partly close a valve and the curve steepens: again the crossing moves left. Raise the receiving water level and the result resembles wet-well drawdown. Trim an impeller or slow a variable-speed pump and the pump curve moves downward; the new crossing usually moves left and down. The direction is more informative than memorising a duty.

For the instrument below, change one condition at a time, then combine the credible extremes. The single dot becomes an envelope. Record flow, head, efficiency, power and NPSH requirement at every corner. A combination that is hydraulically possible may sit outside the manufacturer's allowable operating region or beyond the motor rating.

7.2.3Map the envelope before judging the pump

Use a matrix rather than one pessimistic “worst case.” Maximum head often comes from low suction level, high receiving level and aged pipe at a flow lower than peak. Maximum power may occur at a different corner because power contains both flow and head. Minimum continuous flow may govern at high suction level and a clean pipe. Two pumps running change the pump-set curve again. Keeping the rows separate prevents an impossible combination of individually conservative assumptions from masquerading as a real duty.

7.2.4Allowable region is a manufacturer limit, not a universal percentage

BEP is a useful landmark, but it is not by itself the acceptance boundary. Pump-specific preferred and allowable operating regions depend on design and service; Hydraulic Institute guidance and the manufacturer's published limits belong in the submittal. Check every envelope point against minimum continuous stable flow, runout, driver power, NPSH available versus required, vibration limits and the permitted region. Sewage passage and solids handling are separate constraints, not deductions from the curve.

When an envelope breaches a limit, do not move the dot with hope. Change the main, impeller, speed range, pump size or number of units, then redraw both curves. §7.3 takes apart the most common proposed fix: starting another identical pump.