Formula sheet

Mine Dewatering and Groundwater Control Systems Formula Sheet

Mine dewatering formulas for water balance, sump storage, storm recovery, Darcy inflow, pore pressure, pump duty, standby, water quality, reliability, and validation.

Branch: Mining and Georesources Engineering
Content: Formula sheet
Updated: Jun 24, 2026
Revision: v1.0.0 · reviewed

This formula sheet collects first-pass calculations used in mine dewatering and groundwater control. Use it to screen pit and underground water balances, sump storage, storm recovery, groundwater inflow, pore-pressure reduction, pump duty, pipeline velocity, standby capacity, water-quality load, availability, monitoring residuals, and validation evidence.

The equations are engineering screening tools. They do not replace hydrogeological modelling, surveyed mine geometry, pump curves, transient hydraulic analysis, geotechnical review, rainfall frequency analysis, water-treatment design, environmental permits, electrical studies, emergency-response planning, or competent professional judgement.

Before calculating, state the boundary: open pit, underground level, sump, wellfield, drainage gallery, tailings interface, discharge line, treatment plant, or receiving water. A dewatering number is meaningful only when the protected asset, water source, operating state, time basis, uncertainty, and validation evidence are explicit.

Symbols and Basis

Symbol	Meaning	Common unit
$S$	stored water volume	$\text{m}^3$
$Q$	volumetric flow rate	$\text{m}^3/\text{s}$ or $\text{m}^3/\text{h}$
$Q_g$	groundwater inflow	$\text{m}^3/\text{h}$
$Q_s$	stormwater or surface runoff inflow	$\text{m}^3/\text{h}$
$Q_p$	process, washdown or seepage contribution	$\text{m}^3/\text{h}$
$Q_{pump}$	pumping discharge flow	$\text{m}^3/\text{h}$
$V$	usable storage volume	$\text{m}^3$
$A$	area normal to flow, catchment area, or aquifer area by context	$\text{m}^2$
$K$	hydraulic conductivity or permeability coefficient in Darcy screen	$\text{m/s}$
$i$	hydraulic gradient	dimensionless
$S_y$	specific yield for unconfined drawdown screen	dimensionless
$\Delta h$	head or water-level change	$\text{m}$
$u$	pore pressure	$\text{kPa}$
$\gamma_w$	unit weight of water	$\text{kN/m}^3$
$H$	total dynamic head	$\text{m}$
$\rho$	water density	$\text{kg/m}^3$
$g$	gravitational acceleration	$\text{m/s}^2$
$\eta$	overall pump, motor and drive efficiency	dimensionless
$D$	pipe internal diameter	$\text{m}$
$v$	average pipe velocity	$\text{m/s}$
$\mu$	dynamic viscosity	$\text{Pa s}$
$C$	concentration	$\text{mg/L}$
$L_m$	mass load	$\text{kg/h}$

Keep time units consistent. A common dewatering error is mixing $\text{m}^3/\text{h}$ inflows with $\text{m}^3/\text{s}$ pump equations without conversion.

Mine Water Balance

A practical storage balance is:

\displaystyle \frac{dS}{dt}=Q_g+Q_s+Q_p+Q_{other}-Q_{pump}-Q_{reuse}-Q_{discharge}

For many first-pass operating checks:

\displaystyle \frac{dS}{dt}=Q_{in}-Q_{out}

where positive $dS/dt$ means the sump, pit, heading, pond, or storage basin is filling.

Mini-Check

Groundwater inflow is:

Q_g=320\ \text{m}^3/\text{h}

process and seepage water is:

Q_p=45\ \text{m}^3/\text{h}

storm runoff is:

Q_s=580\ \text{m}^3/\text{h}

and duty pumping is:

Q_{pump}=720\ \text{m}^3/\text{h}

Net filling rate during the storm is:

\displaystyle \frac{dS}{dt}=320+45+580-720=225\ \text{m}^3/\text{h}

Engineering Comment

The pit is filling during the storm even though the pumps are running. That does not mean the system fails if storage and recovery capacity are adequate. It does mean the storm case must be checked separately from the normal groundwater case.

Sump Storage Time

If net inflow is positive:

\displaystyle t_{fill}=\frac{V_{free}}{Q_{in}-Q_{out}}

If pumps are off and there is no other outflow:

\displaystyle t_{fill}=\frac{V_{free}}{Q_{in}}

Mini-Check

Usable free storage below the action level is:

V_{free}=4200\ \text{m}^3

Storm filling rate is:

225\ \text{m}^3/\text{h}

Then:

\displaystyle t_{fill}=\frac{4200}{225}=18.7\ \text{h}

Engineering Comment

An 18.7 hour storage time is not automatically safe. Compare it with storm duration, inspection access, generator start time, spare pump installation time, safe evacuation time, and treatment or discharge constraints.

Storm Volume and Recovery Time

Storm storage consumed during a storm of duration $t_s$ is:

V_s=(Q_{in}-Q_{out})t_s

Post-storm recovery time for that volume is:

\displaystyle t_{rec}=\frac{V_s}{Q_{pump}-Q_{normal}}

where $Q_{pump}>Q_{normal}$ after the storm.

Mini-Check

The storm lasts:

t_s=8\ \text{h}

Storm storage consumed:

V_s=225(8)=1800\ \text{m}^3

Normal inflow after the storm is:

Q_{normal}=320+45=365\ \text{m}^3/\text{h}

Drawdown capacity after the storm:

Q_{drawdown}=720-365=355\ \text{m}^3/\text{h}

Recovery time:

\displaystyle t_{rec}=\frac{1800}{355}=5.1\ \text{h}

Engineering Comment

The system can recover the storm volume in about 5.1 hours after rainfall stops, provided the pumps, power, pipeline, sump intake, sediment controls, and discharge route remain available. Recovery time should be shorter than the interval between credible storm events or operational access constraints.

Drawdown Volume

For a simple unconfined aquifer drawdown screen:

V_{drain}=S_yA\Delta h

where $S_y$ is specific yield, $A$ is the influenced area, and $\Delta h$ is desired water-level reduction.

Drawdown time using excess pumping capacity:

\displaystyle t_{drawdown}=\frac{V_{drain}}{Q_{excess}}

Mini-Check

Assume:

S_y=0.08

A=120000\ \text{m}^2

\Delta h=1.5\ \text{m}

Then:

V_{drain}=0.08(120000)(1.5)=14400\ \text{m}^3

If excess pumping capacity is:

Q_{excess}=300\ \text{m}^3/\text{h}

drawdown time is:

\displaystyle t_{drawdown}=\frac{14400}{300}=48\ \text{h}

Engineering Comment

The result is a screening estimate. Real drawdown depends on aquifer boundaries, well efficiency, delayed drainage, fracture networks, recharge, anisotropy, and interference between wells. Use field pumping tests and piezometer response to validate the model.

Darcy Inflow Screen

A simple groundwater flow screen is:

Q=KiA

where $K$ is hydraulic conductivity, $i$ is hydraulic gradient, and $A$ is the effective flow area.

Mini-Check

Use:

K=4.0\times10^{-5}\ \text{m/s}

i=0.030

A=1800\ \text{m}^2

Then:

Q=(4.0\times10^{-5})(0.030)(1800)=0.00216\ \text{m}^3/\text{s}

Convert to $\text{m}^3/\text{h}$ :

Q=0.00216(3600)=7.78\ \text{m}^3/\text{h}

Engineering Comment

This equation is useful for order-of-magnitude checks. It can be misleading in fractured rock, faulted ground, karst, old workings, perched water, or strongly anisotropic materials. Field inflow history and monitoring usually matter more than a single average $K$ value.

Pore Pressure Reduction

Hydrostatic pore pressure is:

u=\gamma_w h_w

A water-level reduction changes pore pressure by:

\Delta u=\gamma_w\Delta h

when the simplified hydrostatic assumption applies.

Mini-Check

Use:

\gamma_w=9.81\ \text{kN/m}^3

and drawdown:

\Delta h=4.0\ \text{m}

Then:

\Delta u=9.81(4.0)=39.2\ \text{kPa}

Engineering Comment

A 39.2 kPa pore-pressure reduction can materially affect effective stress and slope stability. The value must be connected to the actual failure surface or monitored zone. Lowering water in a sump does not guarantee pore-pressure reduction inside a low-permeability slope or behind a structural discontinuity.

Pump Total Dynamic Head

For a dewatering discharge system:

H=H_{static}+H_f+H_m+H_{discharge}

where $H_{static}$ is elevation difference, $H_f$ is pipe friction head, $H_m$ is minor losses and allowances, and $H_{discharge}$ is any required terminal pressure head.

Mini-Check

Use:

H_{static}=70\ \text{m}

H_f=18\ \text{m}

H_m=12\ \text{m}

H_{discharge}=0\ \text{m}

Then:

H=70+18+12+0=100\ \text{m}

Engineering Comment

This head is an installed-system requirement, not a pump selection by itself. Select pumps from curves at the expected flow, check efficiency range, solids tolerance, suction conditions, parallel operation, motor power, power quality, and transient pressure.

Pump Power

Hydraulic power is:

P_h=\rho gQH

Electrical input power using overall efficiency is:

\displaystyle P_{in}=\frac{\rho gQH}{\eta}

Mini-Check

Use:

\rho=1000\ \text{kg/m}^3

g=9.81\ \text{m/s}^2

Q=0.200\ \text{m}^3/\text{s}

H=100\ \text{m}

\eta=0.72

Input power:

\displaystyle P_{in}=\frac{1000(9.81)(0.200)(100)}{0.72}=272500\ \text{W}

P_{in}=272.5\ \text{kW}

Engineering Comment

Motor rating should include service factor, starting method, cable losses, variable-speed drive losses, altitude or temperature derating, and standby generator capacity. The hydraulic power calculation is only one part of electrical readiness.

Pipeline Velocity and Reynolds Number

Pipe area:

\displaystyle A_p=\frac{\pi D^2}{4}

Velocity:

\displaystyle v=\frac{Q}{A_p}

Reynolds number:

\displaystyle Re=\frac{\rho vD}{\mu}

Mini-Check

Use:

D=0.40\ \text{m}

Q=0.200\ \text{m}^3/\text{s}

Pipe area:

\displaystyle A_p=\frac{\pi(0.40)^2}{4}=0.1257\ \text{m}^2

Velocity:

\displaystyle v=\frac{0.200}{0.1257}=1.59\ \text{m/s}

With:

\rho=1000\ \text{kg/m}^3,\quad \mu=0.001\ \text{Pa s}

Reynolds number:

\displaystyle Re=\frac{1000(1.59)(0.40)}{0.001}=636000

Engineering Comment

The flow is turbulent. The velocity is plausible for a mine water discharge line, but sediment transport, abrasion, air entrainment, freezing, surge, pipe rating, and treatment constraints still need review.

Standby Pumping Margin

Available pumping capacity under a specified outage state is:

Q_{avail}=n_{avail}Q_{pump}

Capacity margin:

\displaystyle M_Q=\frac{Q_{avail}-Q_{basis}}{Q_{basis}}100\%

Mini-Check

Three pumps are installed, each rated:

Q_{pump}=360\ \text{m}^3/\text{h}

With one unavailable, two remain:

Q_{avail}=2(360)=720\ \text{m}^3/\text{h}

Normal inflow basis:

Q_{basis}=365\ \text{m}^3/\text{h}

Margin:

\displaystyle M_Q=\frac{720-365}{365}100\%=97.3\%

For the storm basis:

Q_{basis}=945\ \text{m}^3/\text{h}

all three pumps give:

Q_{avail}=1080\ \text{m}^3/\text{h}

storm margin:

\displaystyle M_Q=\frac{1080-945}{945}100\%=14.3\%

Engineering Comment

The station has strong one-pump-out margin for normal inflow but much thinner margin for storm inflow. The operating plan should define when the standby pump starts, whether backup power can support all pumps, and what happens if a pump is out of service before a forecast storm.

Water-Quality Mass Load

For concentration $C$ in $\text{mg/L}$ and flow $Q$ in $\text{m}^3/\text{h}$ :

\displaystyle L_m=\frac{CQ}{1000}

where $L_m$ is in $\text{kg/h}$ because $1\ \text{mg/L}=1\ \text{g/m}^3$ .

Removal fraction:

\displaystyle R=\frac{C_{in}-C_{out}}{C_{in}}

Mini-Check

Mine water total suspended solids before treatment:

C_{in}=650\ \text{mg/L}

Flow:

Q=720\ \text{m}^3/\text{h}

Mass load:

\displaystyle L_m=\frac{650(720)}{1000}=468\ \text{kg/h}

Discharge target:

C_{out}=50\ \text{mg/L}

Target discharge load:

\displaystyle L_{out}=\frac{50(720)}{1000}=36\ \text{kg/h}

Removal fraction:

\displaystyle R=\frac{650-50}{650}=0.923

or:

92.3\%

Engineering Comment

Flow and concentration must be interpreted together. A moderate concentration at high flow can exceed treatment, settling, sludge-handling, or discharge capacity. Dewatering release should check both hydraulic rate and contaminant or solids load.

Pump Availability Screen

For one repairable pump:

\displaystyle A=\frac{MTBF}{MTBF+MTTR}

For three identical independent pumps where at least two are needed:

A_{\geq2}=A^3+3A^2(1-A)

Mini-Check

Assume one pump has:

MTBF=1500\ \text{h}

and:

MTTR=10\ \text{h}

Single-pump availability:

\displaystyle A=\frac{1500}{1500+10}=0.9934

Availability of at least two out of three pumps:

A_{\geq2}=0.9934^3+3(0.9934)^2(1-0.9934)=0.9999

Engineering Comment

The calculation assumes independent failures, which is often optimistic. Shared power, flooded electrical rooms, common intake blockage, sediment, maintenance access, control logic, spare parts, and operator response can create common-cause failures. Treat this as a screening result, not a proof of emergency readiness.

Monitoring Residual

A monitoring residual compares measured and expected flow:

\displaystyle R_Q=\frac{Q_{meas}-Q_{model}}{Q_{model}}100\%

Mini-Check

The model predicts:

Q_{model}=720\ \text{m}^3/\text{h}

The flow meter reports:

Q_{meas}=690\ \text{m}^3/\text{h}

Residual:

\displaystyle R_Q=\frac{690-720}{720}100\%=-4.17\%

Engineering Comment

A negative residual means measured flow is below the model. That may be acceptable within uncertainty, or it may indicate pump wear, partial blockage, air entrainment, valve misposition, flow-meter error, changed water level, or an incorrect system curve. Residuals should trigger investigation when they persist or coincide with rising sump level.

Validation Gates

Use formula results as gates for field evidence.

Formula result	Required validation evidence
Water balance	measured inflow, pump flow, rainfall, storage level and source separation
Sump storage time	surveyed usable volume, level sensor calibration, sediment survey and emergency access limit
Storm recovery time	pump run records, rainfall hyetograph, discharge route capacity and treatment readiness
Drawdown volume	piezometer response, pumping test, specific yield basis and geotechnical trigger
Darcy inflow	field inflow history, packer or pump test, fracture mapping and boundary conditions
Pore pressure reduction	piezometers tied to the relevant slope, floor or excavation failure mechanism
Pump head and power	pump curve, installed pressure readings, motor current, generator capacity and valve state
Pipeline velocity	flow meter, line diameter, sediment behavior, pressure class and surge review
Water-quality load	paired flow and concentration measurements, treatment capacity and discharge records
Availability	maintenance history, standby test, backup power test and common-cause review

Common Mistakes

Common mistakes include:

sizing pumps from average inflow while ignoring storm inflow and recovery time;
treating sump volume as available after sediment accumulation has reduced it;
assuming one-pump-out capacity is enough for storm operation;
checking pump power without checking the pump curve and system head;
ignoring water hammer, valve closure, check-valve slam and power trip transients;
using a Darcy inflow number in fractured rock without field calibration;
assuming visible dry working areas mean pore pressure has fallen in the slope;
reporting water concentration without multiplying by flow to get mass load;
validating dewatering only by pump runtime rather than water level, flow, pressure, power and water quality;
bypassing high-level alarms so often that the alarm no longer controls risk.

Engineering Takeaway

Mine dewatering formulas become useful only when they are tied to operational decisions. A water balance says whether the mine is filling. Sump storage says how long the team has to respond. Pump head and power say whether hardware can move the water. Pore pressure says whether groundwater control protects the ground. Water-quality load says whether discharge is acceptable. The engineering task is to connect all of them into a validated operating envelope.

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