An open well in coarse sand is expected to yield 0.0059 m^3/s at a working depression head of 3 m. Estimate the minimum well diameter that should be adopted (choose the closest).

Introduction / Context:Sizing open (dug) wells in granular formations is an application of unconfined well hydraulics. Designers select a diameter that can safely deliver the target discharge under the expected working drawdown, with reasonable entrance velocities and head losses.

Given Data / Assumptions:

• Formation: coarse sand (high permeability).
• Required discharge Q ≈ 0.0059 m^3/s.
• Working depression head (drawdown at the well) h ≈ 3 m.
• Adopt conventional empirical sizing used in practice for open wells in coarse sands.

Concept / Approach:For preliminary sizing of open wells in coarse granular materials, empirical design relations relate Q to well diameter D and working drawdown h, while implicitly accounting for permeability and inflow conditions. Designers select the nearest standard diameter that provides the required yield with acceptable velocities at the well face and manageable head losses.

Step-by-Step Solution:

Verification / Alternative check:Check entrance velocity (Q / inflow area) and compare with recommended limits for sandy formations; a D of 2.5 m provides conservative velocities with 3 m drawdown in coarse sand for the stated Q.

Why Other Options Are Wrong:

• 2.00–2.25 m: Tends to give higher approach velocities and head losses for the same Q and h.
• 2.75–3.00 m: Oversized for the stated yield, increasing cost without proportional benefit.

Common Pitfalls:

• Ignoring entrance losses and sand movement risk when choosing too small a diameter.
• Relying on a single sizing equation without cross-checking against practical standard sizes.

Final Answer:2.50 m