CivilSolve

Environmental

Tank Fill / Detention Time

The volume–flow–time triangle t = V/Q: time to fill or drain a tank, hydraulic detention (retention) time of a basin, required volume for a target time, or the flowrate implied by a fill time — with optional simultaneous outflow (net filling). Use for: 'how long to fill the tank', 'detention time of the clarifier', 'what basin volume gives 2 hours detention'. Not for: outlet flow varying with head (orifice draining).

Direct solving is free and needs no account. Have a word problem instead? Submit it as text.

Inputs

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Worked examples

These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.

Example 1

fill time: 500 m³ at 0.05 m³/s

Given

solve for
time
volume
500 m^3
flowrate
0.05 m^3/s

Assumptions

  • Constant flowrate(s) and a simple volume balance; the tank neither leaks nor overflows during the process.

Solution steps

  1. Apply the volume balance

    Volume equals flowrate times time; rearrange for the unknown.

    V = Q · t

    2.778 h

    = 2.778 h

Results

Fill / detention time t

2.778h

Where this answer was checked
source
t = V/Q — simple fill
verified by
hand-recomputed
derivation
t = 500/0.05 = 10 000 s = 2.778 h.

Example 2

US operator math: 100,000 gal at 350 gpm

Given

solve for
time
volume
100000 gal
flowrate
350 gpm

Assumptions

  • Constant flowrate(s) and a simple volume balance; the tank neither leaks nor overflows during the process.

Solution steps

  1. Apply the volume balance

    Volume equals flowrate times time; rearrange for the unknown.

    V = Q · t

    4.762 h

    = 4.762 h

Results

Fill / detention time t

4.762h

Where this answer was checked
source
t = V/Q in gallons and gpm — detention time
verified by
hand-recomputed
derivation
t = 100000/350 = 285.71 min = 4.762 h.

Example 3

size a basin for 4 h detention at 2 MGD

Given

solve for
volume
flowrate
2 mgd
time
4 h

Assumptions

  • Constant flowrate(s) and a simple volume balance; the tank neither leaks nor overflows during the process.

Solution steps

  1. Apply the volume balance

    Volume equals flowrate times time; rearrange for the unknown.

    V = Q · t

    44560 ft^3

    = 44560 ft^3

Results

Required volume V

44560ft^3

Where this answer was checked
source
V = Q·t — required volume
verified by
hand-recomputed
derivation
Q = 2 mgd = 7570.8 m³/day; V = 7570.8·(4/24) = 1261.8 m³ (= 44 563 ft³ = 333 333 gal).