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System curve and operating point

The piping system needs a head that rises with flow rate, because friction losses grow roughly with the square of the velocity. The pump curve falls with flow rate. Where the two curves cross is the operating point.

Hsys=Hs+k Q2H_{sys} = H_s + k\,Q^2system curve
Hpump(Q)=Hsys(Q)H_{pump}(Q) = H_{sys}(Q)operating point

Symbols

HsH_sstatic headm
kkloss coefficients²/m⁵
QQflow ratem³/s

Example

Pump H=30−5000Q2H = 30 - 5000Q^2 and system H=10+15 000Q2H = 10 + 15\,000Q^2:

20 000Q2=20⇒Q≈0.03220\,000Q^2 = 20 \Rightarrow Q \approx 0.032 m³/s.

Changing a valve opening changes the system curve, not the pump curve.
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Part of Fluid Mechanics: Pumps and pipe systems.