Pump and system curves

Description

The calculation of the operating point of a pump is essential to determine the ideal flow rate and head for a pumping system. This point is found at the intersection of the pump's characteristic curve and the system curve.

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Pump Characteristic Curve

The pump's characteristic curve is typically provided by the manufacturer and represents the relationship between flow rate ($Q$) and head ($H$). This curve can be fitted by a quadratic polynomial of the form:

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$$ H_b(Q) = aQ^2 + bQ + c $$

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where $a$, $b$, and $c$ are coefficients determined from the manufacturer's data.

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System Curve

The system curve represents the relationship between flow rate and the head required to overcome system losses. This curve can be expressed as:

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$$ H_s(Q) = dQ^2 + eQ + f $$

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where $d$, $e$, and $f$ are coefficients describing the system's characteristics, including friction losses and elevation changes.

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Intersection of the Curves

The operating point is found at the intersection of the two curves, where $H_b(Q) = H_s(Q)$.