Exercise 9 Solution
Part 1
Aquifer types that may have extremely large pores and high hydraulic conductivity, where water can flow at both laminar and turbulent flow conditions include:
- volcanic aquifers with large lava tubes;
- clean well-sorted large gravel point bar deposits (4 cm diameter or greater); and,
- fractured rock with large fracture aperture openings.
Part 2
Average velocity for radial distances of 0.25, 0.5, 1, 5, and 10 m.
| Aquifer type | Pumping Rate (m3/d) | Thickness (m) | Radial Distance in Meters | |||||||||
| 0.25 | 0.5 | 1 | 5 | 10 | 0.25 | 0.5 | 1 | 5 | 10 | |||
| Area m2 | Velocity m/d | |||||||||||
| Alluvial, K=10 m/d, and average pore diameter 0.005 m | 300 | 10 | 16 | 31 | 63 | 314 | 628 | 19.1 | 9.55 | 4.77 | 0.95 | 0.48 |
| same | 300 | 50 | 79 | 157 | 314 | 1571 | 3142 | 3.82 | 1.91 | 0.95 | 0.19 | 0.1 |
| same | 300 | 100 | 157 | 314 | 628 | 3142 | 6283 | 1.91 | 0.95 | 0.48 | 0.1 | 0.05 |
| Point Bar gravel, K=100 m/d and average pore diameter 0.02 m | 1000 | 10 | 16 | 31 | 63 | 314 | 628 | 63.66 | 31.83 | 15.92 | 3.18 | 1.59 |
| same | 1000 | 50 | 79 | 157 | 314 | 1571 | 3142 | 12.73 | 6.37 | 3.18 | 0.64 | 0.32 |
| same | 1000 | 100 | 157 | 314 | 628 | 3142 | 6283 | 6.37 | 3.18 | 1.59 | 0.32 | 0.16 |
| Sandstone, K=1 m/d and average pore diameter 0.001 m | 100 | 10 | 16 | 31 | 63 | 314 | 628 | 6.37 | 3.18 | 1.59 | 0.32 | 0.16 |
| same | 100 | 50 | 79 | 157 | 314 | 1571 | 3142 | 1.27 | 0.64 | 0.32 | 0.06 | 0.03 |
| same | 100 | 100 | 157 | 314 | 628 | 3142 | 6283 | 0.64 | 0.32 | 0.16 | 0.03 | 0.02 |
Based on the equation alone, the average velocity is inversely and linearly correlated to both radial distance and thickness as both are used to calculate the cross-sectional surface area perpendicular to flow to the pumping well in a homogeneous aquifer of constant thickness. The cross-sectional area is provided in the answer at each radial distance along with the average velocity. As the thickness increases the area increases and so velocity decreases. Note, hydraulic conductivity is not used in any of the equations. However, the pumping rate selected is based on knowing typical pumping rates that are possible for these types of confined aquifers, such that there is not too much drawdown at the pumping well.
Return to where text linked to Exercise 9