Which equation represents the pump operating point in a system with a pump head curve and system head loss?

• A. H_p(Q) = H_f(Q)
• B. H_p(Q) = 2 H_f(Q)
• C. H_p(Q) + H_f(Q) = 60
• D. H_p(Q) - H_f(Q) = 20

Answer: (A)

The pump operating point is where the pump’s capability to add head matches the system’s requirement for head at the same flow. The pump head curve H_p(Q) shows the head the pump can generate at a given discharge Q, while the system head loss H_f(Q) shows the head the piping system needs to push that flow. When these two heads are equal for the same Q, the flow is stable and that is the operating point. That’s why H_p(Q) = H_f(Q) is the correct representation. The other forms would impose a fixed relationship that doesn’t reflect the actual balance between what the pump provides and what the system demands at the operating flow.