Open-well pumping test – identify the incorrect statement about depression head and yield While determining the yield of open wells by a pumping test, which one of the following statements is NOT correct?

Introduction / Context:
Open-well hydraulics considers the relationship between drawdown (depression head), inflow velocity through the well periphery, and safe yield. Excessive drawdown can mobilize sand and cause structural or operational problems.

Given Data / Assumptions:

• Unlined or partially lined open wells in pervious strata.
• Steady pumping during the test.
• Critical depression head corresponds to the onset of sand entry (critical approach velocity).

Concept / Approach:
As depression head increases, inflow velocity rises. Beyond a limiting value, sand begins to move, rendering the condition unsafe. Therefore, the recommended working head is a fraction (commonly about one-third) of the critical depression head to avoid sand movement and maintain sustainable yield.

Step-by-Step Solution:
(a) True: larger drawdown → higher hydraulic gradient → higher approach velocity.(b) True by definition of the critical state.(c) True: conservative working head ≈ one-third of critical is widely advised.(d) False: operating at the critical depression head risks sand entry; maximum safe yield is obtained below this limit, not at it.

Verification / Alternative check:
Design manuals stipulate safe operating heads well below the critical value to prevent turbidity and structural damage, validating (d) as the incorrect statement.

Why Other Options Are Wrong:

• (a)–(c) are consistent with standard open-well practice; (e) cannot be correct since one incorrect statement exists.

Common Pitfalls:
Over-pumping to chase short-term yield; ignoring sand content monitoring; failing to re-evaluate working head as seasonal water levels change.

Final Answer:
Maximum safe yield of an open well is expected at the critical depression head