CALCULATORS / PUMPS, FANS AND VENTILATION

Pump and system operating point calculator

Quadratic pump-head/system-head intersection; coefficients supplied.

pumps-pump-operating-point.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	flowm^3/s	headm
	0.000316228	10
	0.000270801	8.66667

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.

positive available head20.00 m✓ passes

BASELINE INPUTS

shutoff20 mstaticHead5 mpumpCoefficient100000000 s^2/m^5systemCoefficient50000000 s^2/m^5

CALCULATED

flow0.00031623 m^3/s

head10 m

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Pump and system operating point
# Scope: Quadratic pump-head/system-head intersection; coefficients supplied.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

shutoff = 20 m
staticHead = 5 m
pumpCoefficient = 100000000 s^2/m^5
systemCoefficient = 50000000 s^2/m^5

flow := sqrt((shutoff-staticHead)/(pumpCoefficient+systemCoefficient)) [m^3/s]
head := staticHead+systemCoefficient*flow^2 [m]

check positive available head: shutoff > staticHead

scenario alternative: shutoff = 16 m

Calculated from your source · not saved

Baseline · Baseline

positive available head20.00 m ✓ passes

alternative · alternative

positive available head16.00 m ✓ 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.

flow: flow = sqrt((shutoff-staticHead)/(pumpCoefficient+systemCoefficient)) [m^3/s]
head: head = staticHead+systemCoefficient*flow^2 [m]

Original worked example

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

Given

shutoff: 20 m
static head: 5 m
pump coefficient: 100000000 s^2/m^5
system coefficient: 50000000 s^2/m^5

Calculated

flow: 0.000316228 m^3/s
head: 10 m

Assumptions and limits

Quadratic pump-head/system-head intersection; coefficients 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

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: Pump and system operating point. Inputs: pump curve; static head; resistance curve. Outputs: operating flow and head. Model scope: Measured or manufacturer curves and declared fluid conditions. 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: pump curve, static head, resistance curve
Outputs: operating flow and head
Modes: calculate, compare, sweep
Drawing: System and equipment curves

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