Figure 8.87 shows an old cylindrical borehole that has been filled in part with silt and in part with water. Before the hole can be redrilled, the water has to be pumped to the surface. We wish to estimate the work required for this purpose.

(a) As a first approximation, assume that the silting has been uniform – as indicated in Figure 8.87 – and that the water thus forms a right-circular cone.

of base radius 5 m and height 50 m. Hence, by considering the small element of water shown, show that an estimate of the work (in J) required to raise the water to ground level is

Evaluate W₁ in the form k₁πg, giving k₁ correct to 3sf.

(b) Surveying suggests that, while the water– silt boundary may still be regarded as having cylindrical symmetry about the axis of the original borehole, a more accurate profile can be obtained from the data below.

Use this data, with Simpson’s rule, to obtain a second approximation W₂ to the work required. Give your answer in the form k₂πg, with k₂ given to 3sf.

Transcribed Image Text:

50 m Ly Aya Figure 8.87 |--5 m Water: Silt Ground level