Which of the following statements regarding the operating point and system head curve of an irrigation pumping installation are correct?
Options:
(A) The actual operating point ($Q, H$) is determined by the intersection of the pump head-capacity ($H-Q$) characteristic curve and the pipeline system head curve
(B) The system head curve is given by $H_{\text{sys}} = H_{\text{static}} + K Q^2$, where $H_{\text{static}}$ is total static lift and $K Q^2$ represents velocity and friction head losses
(C) Partially closing the pump delivery throttle valve increases system hydraulic resistance ($K$), shifting the operating point to lower discharge and higher head
(D) Shut-off head occurs when discharge $Q = 0$ against a completely closed delivery valve
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements are foundational principles of pump-pipe hydraulic matching:
- A: The operating point represents energy balance between pump energy input and system hydraulic requirements.
- B: System head combines constant static elevation difference with friction loss proportional to $Q^2$ (or $Q^{1.85}$).
- C: Throttling valve steepens the system resistance parabola, shifting the intersection point leftward.
- D: At $Q = 0$, the pump generates its maximum potential static pressure (shut-off head).