Learn: Simple water balance
A water balance accounts for everything crossing a selected boundary during a selected period. Storage change is total water entering minus total water leaving during that same period.
What the formula is saying
Add precipitation volume P and other inflow volume Qi. Add outflow volume Qo and evapotranspiration volume ET. Subtract the second total from the first; a negative answer means storage has decreased.
Read the symbols in plain language
- P
- Precipitation volume
Precipitation volume. Both precipitation and other inflow have already been expressed as matching volumes.
m³Cubic metres measure volume, or a first moment of area where explicitly identified.
- Qin
- Other inflow
Other inflow. Both precipitation and other inflow have already been expressed as matching volumes.
m³Cubic metres measure volume, or a first moment of area where explicitly identified.
- Qout
- Outflow
Outflow. Keep evapotranspiration separate only if it has not already been included in outflow.
m³Cubic metres measure volume, or a first moment of area where explicitly identified.
- ET
- Evapotranspiration
Evapotranspiration. Keep evapotranspiration separate only if it has not already been included in outflow.
m³Cubic metres measure volume, or a first moment of area where explicitly identified.
- ΔS
- Result to find
Simple water balance. Incoming minus outgoing volume gives the gain or depletion of stored water.
m³
Sort out the units first
Every term is a volume in m³ for the same period and area. Rainfall measured as a depth must first be converted to volume using the appropriate area. Qi and Qo here are volumes despite the familiar Q-style symbols, not m³/s.
Assumptions before calculating
Assume the control volume and time period are defined and all material water exchanges are either included in the named terms or negligibly small. Use nonnegative magnitudes for these four input and output categories.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find ΔS and explain the result in the stated output unit.
- P · Precipitation volume
- 1000 m³
- Qin · Other inflow
- 200 m³
- Qout · Outflow
- 700 m³
- ET · Evapotranspiration
- 250 m³
Add water entering during the period
Both precipitation and other inflow have already been expressed as matching volumes.
(1000) + (200) = 1200 m³Add water leaving during the period
Keep evapotranspiration separate only if it has not already been included in outflow.
(700) + (250) = 950 m³Find the signed storage change
Incoming minus outgoing volume gives the gain or depletion of stored water.
(1200)-(950) = 250 m³
Does this worked answer make sense?
If total input equals total output, storage change is zero. A negative change must be interpreted against available starting storage before claiming that the balance is physically possible.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- P · Precipitation volume
- 800 m³
- Qin · Other inflow
- 100 m³
- Qout · Outflow
- 700 m³
- ET · Evapotranspiration
- 300 m³
Add water entering during the period
Both precipitation and other inflow have already been expressed as matching volumes.
(800) + (100) = 900 m³Add water leaving during the period
Keep evapotranspiration separate only if it has not already been included in outflow.
(700) + (300) = 1000 m³Find the signed storage change
Incoming minus outgoing volume gives the gain or depletion of stored water.
(900)-(1000) = -100 m³
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- P · Precipitation volume
- 1200 m³
- Qin · Other inflow
- 150 m³
- Qout · Outflow
- 900 m³
- ET · Evapotranspiration
- 200 m³
Find: Learn: Simple water balance
A hint, not the answer
Add precipitation volume P and other inflow volume Qi. Add outflow volume Qo and evapotranspiration volume ET. Subtract the second total from the first; a negative answer means storage has decreased.
Every term is a volume in m³ for the same period and area. Rainfall measured as a depth must first be converted to volume using the appropriate area. Qi and Qo here are volumes despite the familiar Q-style symbols, not m³/s.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Add water entering during the period
Both precipitation and other inflow have already been expressed as matching volumes.
(1200) + (150) = 1350 m³Add water leaving during the period
Keep evapotranspiration separate only if it has not already been included in outflow.
(900) + (200) = 1100 m³Find the signed storage change
Incoming minus outgoing volume gives the gain or depletion of stored water.
(1350)-(1100) = 250 m³
Avoid the common trap
Do not subtract ET twice if it is already included in Qo. Do not mix daily inflow with annual precipitation or add rainfall in mm directly to water volume in m³.
When this method applies — and when it does not
The result is a change, not the final storage or proof that measurements close accurately. Groundwater exchanges, seepage and withdrawals must be included consistently when relevant. Final storage would additionally require initial storage.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Simple water balance. Water-cycle stores and transfers. Define a control volume and use matching time intervals before forming its storage balance.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.