Capillary rise and surface tension calculator

Capillary rise in a circular tube, equilibrium contact angle supplied.

fluids-surface-tension.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	risemm
	29.3578
	23.4862

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.

rise budget29.36 mm✓ passes

BASELINE INPUTS

tension0.072 N/mradius0.5 mmangle0 degdensity1000 kg/m^3gravity9.81 m/s^2

CALCULATED

rise29.358 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Capillary rise and surface tension
# Scope: Capillary rise in a circular tube, equilibrium contact angle supplied.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

tension = 0.072 N/m
radius = 0.5 mm
angle = 0 deg
density = 1000 kg/m^3
gravity = 9.81 m/s^2

rise := 2*tension*cos(angle)/(density*gravity*radius) [mm]

check rise budget: rise <= 50 mm

scenario alternative: tension = 0.0576 N/m

Calculated from your source · not saved

Baseline · Baseline

rise budget29.36 mm ✓ passes

alternative · alternative

rise budget23.49 mm ✓ 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.

rise: rise = 2*tension*cos(angle)/(density*gravity*radius) [mm]

Original worked example

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

Given

tension: 0.072 N/m
radius: 0.5 mm
angle: 0 deg
density: 1000 kg/m^3
gravity: 9.81 m/s^2

Calculated

rise: 29.3578 mm

Assumptions and limits

Capillary rise in a circular tube, equilibrium contact angle supplied.

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

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Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Capillary rise and surface tension. Inputs: tube radius; wetting angle; density; surface tension. Outputs: capillary height; pressure. 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.'

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The broader study

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

Inputs: tube radius, wetting angle, density, surface tension
Outputs: capillary height, pressure
Modes: calculate, compare, sweep
Drawing: Flow network and pressure plot

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