Learn: Storage continuity rate
A storage volume rises when water enters faster than it leaves. The continuity equation compares inflow and outflow rates to find the instantaneous rate of storage change.
What the formula is saying
Subtract outflow O from inflow I. A positive I − O means filling; a negative value means draining. The result is dS/dt, not the storage volume S itself.
Read the symbols in plain language
- I
- Inflow
Inflow. The selected inflow total is measured across the same boundary as the outflow.
m³/sUse m³/s as the base unit shown here. I and O both use m³/s, so the answer also uses m³/s. To obtain a volume change over a period of constant rates, multiply the answer by elapsed time in seconds; that additional time is not an input to this calculator.
- O
- Outflow
Outflow. The signed difference is the rate of filling or draining, not an absolute stored volume.
m³/sUse m³/s as the base unit shown here. I and O both use m³/s, so the answer also uses m³/s. To obtain a volume change over a period of constant rates, multiply the answer by elapsed time in seconds; that additional time is not an input to this calculator.
- dS/dt
- Result to find
Storage continuity rate. The signed difference is the rate of filling or draining, not an absolute stored volume.
m³/s
Sort out the units first
I and O both use m³/s, so the answer also uses m³/s. To obtain a volume change over a period of constant rates, multiply the answer by elapsed time in seconds; that additional time is not an input to this calculator.
Assumptions before calculating
Assume all relevant volumetric inflows and outflows are included for one clearly defined storage boundary and incompressible water. The supplied rates must refer to the same instant or consistent averaging interval.
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 dS/dt and explain the result in the stated output unit.
- I · Inflow
- 5 m³/s
- O · Outflow
- 3 m³/s
Identify flow entering the storage
The selected inflow total is measured across the same boundary as the outflow.
(5) = 5 m³/sSubtract flow leaving the storage
The signed difference is the rate of filling or draining, not an absolute stored volume.
(5)-(3) = 2 m³/s
Does this worked answer make sense?
Equal inflow and outflow give zero storage-change rate even though water may still be moving through the reservoir. Outflow larger than inflow must produce a negative result.
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.
- I · Inflow
- 2 m³/s
- O · Outflow
- 3.5 m³/s
Identify flow entering the storage
The selected inflow total is measured across the same boundary as the outflow.
(2) = 2 m³/sSubtract flow leaving the storage
The signed difference is the rate of filling or draining, not an absolute stored volume.
(2)-(3.5) = -1.5 m³/s
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.
- I · Inflow
- 4.5 m³/s
- O · Outflow
- 2 m³/s
Find: Learn: Storage continuity rate
A hint, not the answer
Subtract outflow O from inflow I. A positive I − O means filling; a negative value means draining. The result is dS/dt, not the storage volume S itself.
I and O both use m³/s, so the answer also uses m³/s. To obtain a volume change over a period of constant rates, multiply the answer by elapsed time in seconds; that additional time is not an input to this calculator.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify flow entering the storage
The selected inflow total is measured across the same boundary as the outflow.
(4.5) = 4.5 m³/sSubtract flow leaving the storage
The signed difference is the rate of filling or draining, not an absolute stored volume.
(4.5)-(2) = 2.5 m³/s
Avoid the common trap
Do not add inflow and outflow, reverse the filling sign, or call a value in m³/s a stored volume in m³. Include leakage or evaporation as outflow when they matter to the selected balance.
When this method applies — and when it does not
The relationship does not calculate water level without a stage-storage curve, or prevent physical emptying or overflow. Time-varying rates need integration and a starting storage; those cannot be inferred from this single rate difference.
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: Storage continuity rate. 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.