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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.

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:

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

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

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

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

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

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

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.

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:

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

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

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

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

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

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