Tank drain time calculator

Constant-area tank draining by gravity; no outlet submergence or viscous loss.

fluids-tank-drain.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	holeAream^2	durations
	0.0000785398	724.889
	0.0000785398	579.911

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

drain time budget724.89 s✓ passes

BASELINE INPUTS

tankArea0.2 m^2holeDiameter10 mminitialHeight0.5 mfinalHeight0.1 mcoefficient0.62 gravity9.81 m/s^2

CALCULATED

holeArea0.00007854 m^2

duration724.89 s

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Tank drain time
# Scope: Constant-area tank draining by gravity; no outlet submergence or viscous loss.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

tankArea = 0.2 m^2
holeDiameter = 10 mm
initialHeight = 0.5 m
finalHeight = 0.1 m
coefficient = 0.62
gravity = 9.81 m/s^2

holeArea := pi*holeDiameter^2/4 [m^2]
duration := 2*tankArea*(sqrt(initialHeight)-sqrt(finalHeight))/(coefficient*holeArea*sqrt(2*gravity)) [s]

check drain time budget: duration <= 1200.0 s

scenario alternative: tankArea = 0.16 m^2

Calculated from your source · not saved

Baseline · Baseline

drain time budget724.89 s ✓ passes

alternative · alternative

drain time budget579.91 s ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

hole area: holeArea = pi*holeDiameter^2/4 [m^2]
duration: duration = 2*tankArea*(sqrt(initialHeight)-sqrt(finalHeight))/(coefficient*holeArea*sqrt(2*gravity)) [s]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

tank area: 0.2 m^2
hole diameter: 10 mm
initial height: 0.5 m
final height: 0.1 m
coefficient: 0.62
gravity: 9.81 m/s^2

Calculated

hole area: 0.0000785398 m^2
duration: 724.889 s

Assumptions and limits

Constant-area tank draining by gravity; no outlet submergence or viscous loss.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Tank drain time. Inputs: tank geometry; outlet; initial head; discharge coefficient. Outputs: level versus time; drain duration. Model scope: Single-phase flow unless explicitly configured otherwise. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: tank geometry, outlet, initial head, discharge coefficient
Outputs: level versus time, drain duration
Modes: calculate, compare, sweep
Drawing: Flow network and pressure plot

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS