Master Intermediate Hydraulics 2026 – Dive Into Success with This Power Test!

The operating point is found at the intersection of the pump curve and the system head curve, where the pump can just overcome the system losses. Set the two heads equal: 60 − 0.8Q = 20 + 0.5Q^2. Rearranging gives 0.5Q^2 + 0.8Q − 40 = 0, or multiplying by 2, Q^2 + 1.6Q − 80 = 0. Solving the quadratic, Q = [-1.6 ± sqrt(1.6^2 − 4(1)(−80))]/2 = [-1.6 ± sqrt(322.56)]/2. The positive root is Q ≈ (−1.6 + 17.95)/2 ≈ 8.18 m^3/s (the negative root is not physically meaningful). The corresponding head is H = 60 − 0.8×8.18 ≈ 53.46 m. So the operating point is about Q ≈ 8.18 m^3/s and H ≈ 53.46 m, matching the given option.