Gravity Tank Drain Time Calculator
Calculate changing-level gravity drain time for an open constant-area tank and small bottom orifice.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Integrate the falling-head volume balance with a constant entered discharge coefficient.
Q=Cd a√(2gh); t=2A(√h₀−√h₁)/(Cd a√(2g))
Worked example
For1m² plan area,20mm outlet, Cd=0.62 and initial1m to target0m, drain time is about38.6422003min at standard gravity. Flow decreases with head.
Assumptions and input details
Open vented tank, constant horizontal plan area, no inflow and no downstream backpressure. Require0≤target≤initial,0<Cd≤1 and outlet area≤1% of tank plan area for the small-orifice approximation. Cd is entered, not selected from an outlet shape. Pipe friction, siphons, unvented tanks, changing area, viscosity limits and final wetting/residual effects are not modeled. Equal initial/target heads give zero time.
References: MIT: draining a tank and Torricelli velocity
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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