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Exercise set

Mine Dewatering and Groundwater Control Systems Exercises

Worked mining engineering exercises for mine dewatering covering inflow balance, sump storage time, pump power, pipeline velocity, Reynolds number, hydrostatic pressure, storm storage, availability, monitoring residuals, and trigger response.

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Mining and Georesources Engineering
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Exercise set
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v1.1.0 ยท reviewed

These exercises practise first-pass calculations used in mine dewatering and groundwater control. They connect inflow balance, sump storage time, pump power, pipeline velocity, Reynolds number, hydrostatic pressure, storm storage, reliability, monitoring residuals, and trigger-response decisions.

Assume simplified nominal values unless an exercise states otherwise. Real dewatering decisions require a hydrogeological model, mine-stage geometry, rainfall data, pump curves, power reliability, sediment and water-quality review, geotechnical trigger levels, environmental permits, and emergency-response procedures.

How to Use These Exercises

For each problem:

  1. define the mine area, water source, and protected asset;
  2. separate groundwater, stormwater, process water, and storage terms;
  3. keep hydraulic units consistent between \text{m}^3/\text{s}, \text{m}^3/\text{h}, metres, pascals, and kilowatts;
  4. state whether the result controls access, stability, discharge, or emergency storage;
  5. identify which operating record would validate the result in the field.

The most common mistake is sizing pumps from average inflow while ignoring storms, sediment, power loss, blocked intakes, slope pore pressure, and treatment limits.

Use the exercises as water-control gates: add pumping capacity, reserve storage, restrict access, start backup power, clean intakes, reroute clean water, escalate geotechnical review, or hold discharge when sump level, residuals, pump availability, water quality, or permit limits no longer match the plan.

Exercise 1: Mine Water Balance During a Shift

An open pit receives groundwater inflow Q_g=180\ \text{m}^3/\text{h}, stormwater inflow Q_s=95\ \text{m}^3/\text{h}, and process water leakage Q_p=25\ \text{m}^3/\text{h}. Pumping removes 240\ \text{m}^3/\text{h}.

Find the storage change rate.

Solution

Net storage rate:

\displaystyle \frac{dS}{dt}=Q_g+Q_s+Q_p-Q_{pump}
\displaystyle \frac{dS}{dt}=180+95+25-240=60\ \text{m}^3/\text{h}

Engineering Comment

The pit is filling at 60\ \text{m}^3/\text{h}. The operating response should check sump capacity, pump availability, rainfall forecast, sediment loading, haul-road access, and whether the water source can be separated or reduced.

Exercise 2: Sump Storage Time

A sump has usable volume V=1800\ \text{m}^3. During a pump outage, expected inflow is Q=150\ \text{m}^3/\text{h}.

Estimate time to fill the usable volume.

Solution

Storage time:

\displaystyle t=\frac{V}{Q}
\displaystyle t=\frac{1800}{150}=12\ \text{h}

Engineering Comment

Twelve hours is not automatically safe. The mine needs response time for diagnosis, spare pump installation, generator startup, access restrictions, and possible evacuation if the sump protects critical electrical or travel routes.

Exercise 3: Pump Hydraulic Power

A pump delivers Q=0.090\ \text{m}^3/\text{s} against total dynamic head H=68\ \text{m}. Use \rho=1000\ \text{kg/m}^3 and g=9.81\ \text{m/s}^2.

Estimate hydraulic power.

Solution

Hydraulic power:

P_h=\rho gQH
P_h=1000(9.81)(0.090)(68)=60{,}037\ \text{W}
P_h=60.0\ \text{kW}

Engineering Comment

Electrical input power will be higher because pump, motor, drive, and cable efficiency are less than ideal. Pump selection also requires a curve check, cavitation margin, solids tolerance, and operating range.

Exercise 4: Pipeline Velocity

A mine water discharge line has internal diameter D=0.30\ \text{m} and flow Q=0.090\ \text{m}^3/\text{s}.

Find average velocity.

Solution

Area:

\displaystyle A=\frac{\pi D^2}{4}=\frac{\pi(0.30)^2}{4}=0.0707\ \text{m}^2

Velocity:

\displaystyle v=\frac{Q}{A}=\frac{0.090}{0.0707}=1.27\ \text{m/s}

Engineering Comment

Velocity should be checked against sediment transport, abrasion, pressure loss, surge risk, air pockets, pipe supports, and discharge-point erosion.

Exercise 5: Reynolds Number

Using the velocity from Exercise 4, estimate Reynolds number for water with \rho=1000\ \text{kg/m}^3 and \mu=0.001\ \text{Pa s} in a 0.30\ \text{m} pipe.

Solution

Reynolds number:

\displaystyle Re=\frac{\rho vD}{\mu}
\displaystyle Re=\frac{1000(1.27)(0.30)}{0.001}=3.81\times10^5

Engineering Comment

The flow is turbulent. This affects head-loss estimation, mixing, erosion potential, air entrainment, and how sensitive the line is to roughness, scaling, and fittings.

Exercise 6: Hydrostatic Pressure at a Pump Station

A pump station is located 38\ \text{m} below the static water level in a flooded shaft connection. Use \gamma_w=9.81\ \text{kN/m}^3.

Estimate hydrostatic gauge pressure.

Solution

Pressure:

p=\gamma_w h
p=9.81(38)=372.8\ \text{kPa}

Engineering Comment

This pressure affects doors, seals, pipe ratings, valve loads, and emergency isolation. The station design should also consider dynamic pressure, surge, debris, corrosion, and access under flood conditions.

Exercise 7: Storm Storage Deficit

An extreme storm is expected to add 12{,}500\ \text{m}^3 to a pit water system before normal pumping can recover. Available emergency storage is 9{,}800\ \text{m}^3.

Find the storage deficit.

Solution

Storage deficit:

D=12{,}500-9{,}800=2700\ \text{m}^3

Engineering Comment

The plan is short of storage under the assumed storm. Options include clean-water diversion, temporary pumping, staged shutdown, additional pond volume, storm forecast triggers, or revised mining sequence.

Exercise 8: Pumping Function Availability

A critical dewatering function requires pump, power feed, level sensor, and discharge valve to work. Estimated availabilities during the operating window are:

0.96,\ 0.98,\ 0.97,\ 0.99

Estimate simplified series availability.

Solution

Series availability:

A_{series}=0.96(0.98)(0.97)(0.99)=0.904
A_{series}=90.4\%

Engineering Comment

The function availability is lower than each component availability. A critical dewatering system may need redundancy, backup power, spare pump readiness, alarm proof testing, and common-cause failure review.

Exercise 9: Water-Balance Residual

A daily dewatering report records rainfall and inflow volume of 5100\ \text{m}^3, pumped discharge of 4550\ \text{m}^3, and measured sump storage increase of 320\ \text{m}^3.

Find the unexplained residual.

Solution

Residual:

R=Q_{in}-Q_{out}-\Delta S
R=5100-4550-320=230\ \text{m}^3

Percentage of inflow:

\displaystyle \frac{230}{5100}\times100=4.5\%

Engineering Comment

The residual may be acceptable or not depending on measurement uncertainty. Persistent residuals should trigger flow-meter calibration, unmeasured seepage review, sump survey check, and discharge-route inspection.

Exercise 10: High Sump Level Trigger

An underground sump high-level trigger is 4.2\ \text{m}. Readings during a storm are:

3.1,\ 3.6,\ 4.0,\ 4.4\ \text{m}

Identify the trigger state after the fourth reading and estimate the rise over the monitoring period.

Solution

Fourth reading:

h_4=4.4\ \text{m}

Since:

4.4>4.2

the high-level trigger has been exceeded.

Rise:

\Delta h=4.4-3.1=1.3\ \text{m}

Engineering Comment

The trigger should cause predefined action: verify pump status, inspect intakes, restrict access, check power and backup systems, notify operations and geotechnical reviewers if relevant, and confirm discharge compliance.

Review Checklist

Before accepting a mine dewatering screening calculation, check:

  • whether the water sources are separated and traceable;
  • whether pump duty includes head, solids, efficiency, and operating range;
  • whether sump storage is compared with realistic response time;
  • whether pipelines are checked for velocity, pressure, surge, abrasion, and air management;
  • whether storm storage includes clean-water diversion and emergency overflow behavior;
  • whether availability checks include common-cause failures;
  • whether water-balance residuals are reconciled with meters and surveys;
  • whether standby pumps, backup power, spares, access, telemetry, and alarm proof tests are ready before the trigger is reached;
  • whether trigger readings have named actions, escalation paths, and closeout evidence.
  • whether dewatering decisions are tied to slope pore pressure, underground access, environmental discharge, and mine-sequence constraints.

Good dewatering engineering treats water as live mine infrastructure: measured, pumped, stored, treated, monitored, and tied to geotechnical and environmental decisions.

REF

See also

  1. Mine Dewatering and Groundwater Control Systems Mining and Georesources Engineering
  2. Tailings, Mine Waste, and Closure Engineering Mining and Georesources Engineering
  3. Tailings, Mine Waste, and Closure Engineering Exercises Mining and Georesources Engineering
  4. Mine Planning, Production Scheduling, and Georesource Risk Mining and Georesources Engineering
  5. Mine Planning, Production Scheduling, and Georesource Risk Exercises Mining and Georesources Engineering
  6. Contaminated Site Remediation and Groundwater Protection Environmental Engineering
  7. Contaminated Site Remediation and Groundwater Protection Exercises Environmental Engineering
  8. Mineral Processing and Ore Handling Systems Mining and Georesources Engineering
  9. Mineral Processing and Ore Handling Systems Exercises Mining and Georesources Engineering
  10. Mine Slope Stability and Excavation Design Mining and Georesources Engineering
  11. Mine Slope Stability and Excavation Design Exercises Mining and Georesources Engineering
  12. Mine Ventilation and Underground Safety Systems Mining and Georesources Engineering
  13. Mine Ventilation and Underground Safety Systems Exercises Mining and Georesources Engineering
  14. Mine Slope and Excavation Formula Sheet Mining and Georesources Engineering
  15. Environmental Water and Wastewater Systems Environmental Engineering
  16. Environmental Water and Wastewater Systems Exercises Environmental Engineering
  17. Environmental Water Systems Formula Sheet Environmental Engineering
  18. Stormwater and Urban Flood Resilience Environmental Engineering
  19. Stormwater and Urban Flood Resilience Exercises Environmental Engineering
  20. Mechanical Fluid Flow and Piping Systems Mechanical Engineering
  21. Mechanical Fluid Flow and Piping Systems Exercises Mechanical Engineering
  22. Geotechnical Retaining Structures and Excavation Support Civil and Construction Engineering
  23. Geotechnical Retaining Structures and Excavation Support Exercises Civil and Construction Engineering
  24. Mine Dewatering Mining and Georesources Engineering process
  25. Quarry Slope Stability Mining and Georesources Engineering concept
  26. Excavation Support Civil and Construction Engineering device
  27. Hydrostatic Pressure Mechanical Engineering quantity
  28. Gauge Pressure Mechanical Engineering quantity
  29. Permeability Materials Engineering quantity
  30. Infiltration Environmental Engineering process
  31. Flow Rate Mechanical Engineering quantity
  32. Mass Balance Chemical Engineering model
  33. Density Materials Engineering quantity
  34. Continuity Equation Mechanical Engineering model
  35. Hydraulics Mechanical Engineering concept
  36. Orifice Plate Mechanical Engineering device
  37. Valve Coefficient Chemical Engineering metric
  38. Reynolds Number Mechanical Engineering quantity
  39. Laminar Flow Mechanical Engineering phenomenon
  40. Turbulence Mechanical Engineering phenomenon
  41. Viscosity Mechanical Engineering quantity
  42. Water Hammer Mechanical Engineering phenomenon
  43. Bernoulli Equation Mechanical Engineering model
  44. Cavitation Mechanical Engineering phenomenon
  45. Power Electrical Engineering quantity
  46. Efficiency Energy Engineering metric
  47. Interlock Industrial and Management Engineering device
  48. Failure Mode Industrial and Management Engineering concept
  49. Reliability Industrial and Management Engineering metric
  50. Risk Priority Number Industrial and Management Engineering metric
  51. Uncertainty Analysis Mathematical Engineering method
  52. Validation Industrial and Management Engineering method
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