Depth to the Water Table from an Air-Purge Borehole Test: 04-BS-7, May 2016, Q2

Question 2: Depth to the Water Table from an Air-Purge Borehole Test (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Borehole depth L	50 m
Steady gauge reading at the pipe top	196 kPa
Water density ρ_w	1000 kg/m³

Find. (a) depth d of the water table below ground; (b) a sketch of the drawdown profile while pumping.

Fig. Q2(a) — borehole 50 m deep; water table depth d = 30.0 m below the ground surface.

Approach. At the moment air just begins to bubble from the pipe's submerged end, the air pressure inside the pipe exactly balances the hydrostatic pressure of the water column standing above that point — this "bubble point" condition converts the gauge reading directly into the height of water above the pipe's bottom.

Part (a) — relate the gauge reading to the submerged column. The pipe bottom sits at the full 50 m depth; if the water table is a depth d below the surface, the water column standing above the pipe bottom is (L−d). At bubbling onset: $$p_{gauge} = \rho_w g (L-d)$$
Solve for the submerged height, then for d. $$L-d = \frac{p_{gauge}}{\rho_w g} = \frac{196\,000}{1000(9.81)} = 19.98\ \text{m}$$ $$d = L-(L-d) = 50 - 19.98 = \boxed{30.0\ \text{m below the ground surface}}$$
Part (b) — drawdown profile. While the well is being pumped, the water table near the borehole is drawn down into a symmetric, bowl-shaped depression called a cone of depression: lowest immediately at the well wall, rising smoothly away from the well until it rejoins the flat, undisturbed water table at some radius of influence (sketched below).

Fig. Q2(b) — cone of depression: the water table dips near the pumped borehole and recovers with radial distance.

Quantity	Result
Depth to water table, d	30.0 m below ground
Pumping profile	Cone of depression, symmetric about the borehole (sketch above)

Topic: Piezometric (bubble-tube) water-table measurement and the cone of depression.

Key relations: p = ρg·h; radial drawdown described by the Thiem/Dupuit steady-state equation for an unconfined aquifer.

Why this works. Air is far less dense than water, so the air column's own weight is negligible; the steady bubbling pressure is set entirely by the water head it must overcome to escape at the pipe's submerged tip, giving a direct, non-invasive way to locate the water table.

Common pitfall. Confusing the borehole depth (50 m, the pipe length) with the submerged column height (L−d); the gauge reading fixes the SUBMERGED height directly, not the depth to the water table.

Source: White, Fluid Mechanics, Ch. 2 (manometry/piezometers); Mihelcic, Environmental Engineering (groundwater hydraulics, cone of depression).

Question 2 of 13: Depth to the Water Table from an Air-Purge Borehole Test

Question 2: Depth to the Water Table from an Air-Purge Borehole Test (5 marks)