Governing Formula
Filling a storage tank is a simple volumetric balance: the time to fill is the tank volume divided by the filling rate. Reversing the relationship gives the rate needed to meet a desired fill duration — the basis for selecting a supply pump, booster, or tanker filling regime.
t = V / Q · Q_req = V / t_target Where:
-
V= Tank volume (working capacity) [m³] -
V_L= Tank volume in litres [L] -
Q= Filling flow rate [L/min] -
t= Fill time [h : min] -
t_target= Optional target fill duration [h] -
Q_req= Filling rate required to meet target time [L/min]
Derived Equations:
V_L = V × 1000 t = V_L / Q Q = V_L / (t_target × 60) Q (m³/h) = Q (L/min) / 16.6667 How the Calculation Works
The engine first converts the tank volume to litres (1 m³ = 1000 L), then divides by the filling flow in L/min to obtain the fill time in minutes. The minutes are converted to decimal hours and to a human-readable h : min label.
t (h) = V_L / (Q × 60)
When a target time is supplied, the required filling rate is V_L / (t_target × 60) in L/min and also reported in m³/h. If no target is entered the field stays blank — the calculator only reports the actual fill time and its equivalent rate.
Worked Engineering Example
Design Scenario: 100 m³ Ground Tank Refilled at 100 L/min
- Volume in litres:
V_L = 100 × 1000 = 100,000 L - Fill time in minutes:
t = 100,000 / 100 = 1,000 min - Fill time in hours:
t = 1,000 / 60 = 16.67 h → 16 h 40 m - Equivalent rate in m³/h:
Q = 100 / 16.6667 = 6.00 m³/h - Target check — 120 m³ filled in 8 h:
Q_req = 120,000 / (8 × 60) = 250 L/min = 15.0 m³/h
Engineering Notes & Design Benchmarks
| Application | Typical Filling Rate | Notes |
|---|---|---|
| Municipal ground storage refill | 5 – 30 m³/h | Sized to restore daily draw during off-peak overnight hours |
| Rooftop / domestic pressure tank | 0.5 – 3 m³/h | Small booster duty, cycling control |
| Tanker / emergency filling | 100 – 300 L/min | Transfer pumps, rapid replenishment after fire events |
A practical benchmark for municipal ground storage is refilling the average daily draw within the overnight off-peak window (often 6–10 hours). Seasonally, inflow/maintenance constraints and pump availability should be added to the net fill schedule.
Assumptions & Limitations
- Constant filling rate — real systems fluctuate with pump curve, reservoir level, and supply pressure.
- Volume is working capacity; freeboard, dead storage below the outlet, and water lost to leaks are not included.
- No credit for simultaneous draw-off while filling; simultaneous demand shortens the net effective fill window.
- Filling flows are assumed positive and steady — meter accuracy of delivered volumes follows ISO 4064 class expectations.
Frequently Asked Questions
How long does it take to fill a 100 m³ tank at 100 L/min?
100 m³ = 100,000 litres. At 100 L/min that is 1,000 minutes = 16.67 hours = 16 h 40 m — exactly what the calculator reports for the default preset.
How do I size a pump to refill overnight?
Divide the tank working volume by the available off-peak hours. For a 120 m³ tank and an 8-hour window you need about 120,000 / 480 = 250 L/min (15 m³/h) of average filling capacity, plus margin for pump degradation and simultaneous demand.
Why would the required rate equal the filling rate?
When no target time is set, the engine mirrors the entered filling flow as the “required” value because that rate produces the computed fill time. A real target only appears once you enter a desired hours value.
Engineering Disclaimer
Engineering Note: This calculator provides fill-time estimates for preliminary planning and education. Final pump and tanker selections must verify the operating point, duty cycle, meter accuracy, and code-required fire-reserve refill rates via qualified engineering review.
Technical References
- ISO 4064 (Water meters for cold potable water and hot water) — delivered-volume metering accuracy.
- AWWA D100, Welded Carbon Steel Tanks for Water Storage — storage sizing and refill practice.
- Finnemore, E.J. & Franzini, J.B., Fluid Mechanics with Engineering Applications, McGraw-Hill.
- Perry, R.H. & Green, D.W., Perry’s Chemical Engineers’ Handbook, McGraw-Hill (pump and transfer hydraulics).