Start viscosity unit conversion by identifying the quantity: dynamic viscosity or kinematic viscosity. Convert within that family first. Enable a relationship between the two only when an independently supplied density describes the same sample and state.
This educational packet prepares two unit modes, an original supplied-density example, and an acceptance ledger. The density is fictional arithmetic input, not a lookup for water, oil, or any other material. The companion converts the supplied numbers; it does not supply an experiment or equipment recommendation.
Choose the quantity before the unit
| Quantity | Supported units in this packet | Base unit |
|---|---|---|
| Dynamic viscosity, μ | cP, P, Pa·s | Pa·s |
| Kinematic viscosity, ν | cSt, St, m²/s | m²/s |
NIST lists the dynamic and kinematic conversion factors separately. The relevant factors are cP to Pa·s at 0.001, P to Pa·s at 0.1, cSt to m²/s at 0.000001, and St to m²/s at 0.0001. NIST's viscosity conversion factors.
Use a base-unit factor only within its family:
Base value = supplied value × source-unit factor.
Target value = base value ÷ target-unit factor.
The factor for either base unit is 1. A target unit from the other family is not another entry in the same factor menu. It is a request for a quantity relationship and needs another input.
Work the two 12-unit cases separately
For dynamic viscosity:
12 cP × 0.001 Pa·s/cP = 0.012 Pa·s.
As an additional same-family check, 0.012 Pa·s ÷ 0.1 Pa·s/P = 0.12 P. All three values represent the same supplied dynamic viscosity.
For kinematic viscosity:
12 cSt × 0.000001 m²/s per cSt = 0.000012 m²/s.
The corresponding stokes value is 0.000012 ÷ 0.0001 = 0.12 St. These are representations of the supplied kinematic viscosity.
Neither calculation establishes that 12 cP equals 12 cSt. The starting number is the same, but the quantity and base units differ.
Keep the source label, sample/state information, and value with the result. Changing units does not change the recorded temperature, infer material identity, or adjust the underlying value to another physical condition.
Require a matching density for the relationship
NASA defines kinematic viscosity as dynamic viscosity divided by density:
ν = μ / ρ.
The reverse relationship is μ = ν × ρ. This is the quantity relationship used here, not a material-property model. NASA's dynamic/kinematic relationship.
Prepare this original matching record:
| D1 field | Authored value |
|---|---|
| Sample/state tag | D1, fictional matching state |
| Dynamic viscosity | 0.012 Pa·s, equivalent to 12 cP |
| Supplied density | 800 kg/m³ |
| Density sample/state tag | D1 |
| Actual measurement/property source |
The density of 800 kg/m³ is supplied for arithmetic. Do not identify it as water, an oil grade, or a measured material property. The shared D1 tag explicitly defines a matching fictional record; it is not proof that two real measurements match.
Calculate:
0.012 Pa·s ÷ 800 kg/m³ = 0.000015 m²/s.
Then convert within the kinematic family:
0.000015 m²/s ÷ 0.000001 m²/s per cSt = 15 cSt.
The density makes the difference: this D1 relationship yields 15 cSt from 12 cP, not 12 cSt.
Show why the units cancel
Using Pa·s = kg/(m·s), the dimensional trace is:
[kg/(m·s)] ÷ [kg/m³] = [kg/(m·s)] × [m³/kg] = m²/s.
The reverse trace returns dynamic viscosity:
[m²/s] × [kg/m³] = kg/(m·s) = Pa·s.
For D1, the numerical reverse check is:
0.000015 m²/s × 800 kg/m³ = 0.012 Pa·s = 12 cP.
Keep raw calculation values distinct from a rounded display. If a display presents 0.000015 as 1.5 × 10⁻⁵, it should still retain the quantity and units. Do not round a small positive value to a displayed zero and imply that the original input was zero.
The packet does not supply measurement uncertainty or significant-figure evidence. Its tidy numbers are authored arithmetic cases, not a precision statement about a fluid.
Hold invalid and mismatched inputs
A request from cP to cSt with no density remains pending. Do not assume a water density or insert 1 to make the calculation run.
For the companion, viscosity inputs must be positive finite numbers. Density used in a relation must also be positive and finite, in the specified kg/m³ unit. Blank, zero, negative, nonfinite, or unsupported-unit inputs do not produce an accepted result.
A positive density with a different sample/state tag also fails the matching requirement. Preserve source and temperature/state labels beside both values. Missing labels or an unconfirmed match should remain unresolved for the relationship.
These are authored validation rules for a bounded educational helper. They do not establish valid material properties or general rheological behavior.
Review the prepared helper
Put the selected family, source value, base calculation, and target result together. For the relationship mode, show D1, the separately supplied density, and the dimensional cancellation alongside 15 cSt.
That placement gives a reviewer a specific task: distinguish a same-family conversion from a density-dependent relation. Keep native input/source/state records authoritative. HTML saving and rendering does not establish that calculation controls run correctly or that answers persist.
The companion requires explicit relation enablement rather than silently switching families. Editing an input, unit, density, sample/state match, or mode would clear the old accepted output. A valid Calculate action would produce a fresh trace; invalid data would keep the result area pending.
Reset would restore Dynamic mode with 12 cP targeting Pa·s, disable the relationship, leave density and match fields blank, and clear current output and validation messages. The separate D1 worked record would remain available for review. Historical native records would remain separate. All scripts, keyboard/focus behavior, actual article-width and narrow-screen presentation, host behavior, and test observations remain pending.
Keep the acceptance cases distinct
| Case | Input | Expected outcome | Actual observation |
|---|---|---|---|
| U1 | Dynamic: 12 cP → Pa·s | 0.012 Pa·s | |
| U2 | Kinematic: 12 cSt → m²/s | 0.000012 m²/s | |
| R1 | 12 cP → cSt, density absent | Held; no result | |
| R2 | D1: 0.012 Pa·s and matching 800 kg/m³ | 0.000015 m²/s = 15 cSt | |
| R3 | D1 reverse: 15 cSt and matching 800 kg/m³ | 0.012 Pa·s = 12 cP | |
| R4 | Density 0, negative, blank or nonfinite | Invalid; clear stale result | |
| R5 | Density tag differs from viscosity tag | Match unresolved; no relation result |
The actual column is empty because no helper has been implemented or run. Keep U1/U2 as independent conversions, not an accidental cross-family equality.
Copy this prompt for the conversion packet
Create one complete, self-contained US-English HTML companion for “Viscosity • quantity first”. Return the full HTML document, with inline CSS and any JavaScript needed for the local interactions. Use the original scenario, named records, numbers and expected cases below.
Design the page for this task: use clearly labeled input or source records, a readable result or worked example, and an adjacent explanation of the evidence. Use a restrained visual hierarchy, left-aligned text, readable tables or stacked records, and a responsive layout at 720px and 360px. Provide meaningful labeled controls for Dynamic μ; Kinematic ν; Load fictional D1; Calculate; Reset. Use keyboard-accessible native controls and visible focus. Keep the complete content readable without an external dependency.
The following brief supplies the substantive content and constraints. Native-format requests describe the material to represent or copy manually; this HTML must not pretend to create DOCX, XLSX, PDF, PPTX, H5P or another native file, run Python/Flask/Django/Snowflake/Power BI, connect a live service, send messages, or perform an authorized real-world action. Where the task requires a native source, actual observation or separate approval, retain that requirement and leave unsupplied evidence blank.
Prepare an original English educational viscosity-conversion packet. Do not claim native conversion or unobserved runtime checks, copy an applet/property table,
perform experiments, recommend materials/equipment, capture, or publish.
Separate quantity families:
Dynamic units cP, P, Pa·s; factors to Pa·s:
cP = 0.001, P = 0.1, Pa·s = 1. Kinematic units cSt, St, m²/s; factors to m²/s:
cSt = 0.000001, St = 0.0001, m²/s = 1. Within-family conversion: multiply by source factor, divide by target.
Authored expected cases:
12 cP = 0.012 Pa·s = 0.12 P.
12 cSt = 0.000012 m²/s = 0.12 St. Do not equate cP with cSt.
Enable the quantity relationship only explicitly:
ν = μ / ρ and μ = ν × ρ. Density must be independently supplied, positive, finite, in kg/m³,
and confirmed to match the viscosity sample/state. Missing density or unknown/mismatched sample/state holds the relation. No water default, material lookup, copied property, or inferred density.
Fictional D1 record:
μ = 0.012 Pa·s, equivalent to 12 cP.
ρ = 800 kg/m³, same explicitly authored D1 sample/state.
ν = 0.012 / 800 = 0.000015 m²/s = 15 cSt. Reverse: 0.000015 × 800 = 0.012 Pa·s = 12 cP. Density 800 is fictional arithmetic input, not a measured material fact. Actual property/measurement source stays blank.
Show dimensional cancellation:
(kg/(m·s)) / (kg/m³) = m²/s.
(m²/s) × (kg/m³) = kg/(m·s) = Pa·s. Preserve raw values and separately labeled display rounding. No measurement precision or significant figures are established.
Local helper contract:
Positive finite viscosity; supported units only. Positive finite density only when relationship enabled. Blank, zero, negative, nonfinite or unsupported inputs held. Source/temperature/state labels remain with values. Unit conversion does not adjust temperature or infer rheology. Input/unit/mode/density/match edits clear accepted output. Calculate requires valid current inputs. Invalid data clears stale result. Reset restores Dynamic mode, 12 cP targeting Pa·s, relationship disabled,
density/match fields blank and current output/messages cleared. The separate D1 worked record and native history remain available.
Deliver the native factor/quantity ledger, D1 worked record, dimensional
trace and expected-case matrix with blank actual observations. Plan calculation, invalid-input, stale-output, keyboard/focus, native
source/state, article-width/narrow and host checks; tests remain pending.
Native source/value/state
records remain authoritative. Do not promise calculation execution,
saved answers, property validation, API lookup or equipment performance. End with an appropriate CTA for the prepared comparison copy.
COMPLETE AUTHORED SCENARIO AND EXPECTED CASES
The following is the supplied reading/teaching/calculation record to represent in the companion. Preserve its particular content, examples, source references and unknowns. Wording about a future native implementation refers to that native task, not permission to omit this HTML companion.
# Viscosity Unit Conversion: Keep cP and cSt in Separate Families
You have a viscosity value of 12 and need another unit. One source says cP; another asks for cSt. A converter that treats both as alternate labels for the same quantity can give a neat number without the density needed to relate them.
Start viscosity unit conversion by identifying the quantity: **dynamic viscosity** or **kinematic viscosity**. Convert within that family first. Enable a relationship between the two only when an independently supplied density describes the same sample and state.
This educational packet prepares two unit modes, an original supplied-density example, and an acceptance ledger. The density is fictional arithmetic input, not a lookup for water, oil, or any other material. The companion converts the supplied numbers; it does not supply an experiment or equipment recommendation.
## Choose the quantity before the unit
| Quantity | Supported units in this packet | Base unit |
| --- | --- | --- |
| Dynamic viscosity, μ | cP, P, Pa·s | Pa·s |
| Kinematic viscosity, ν | cSt, St, m²/s | m²/s |
NIST lists the dynamic and kinematic conversion factors separately. The relevant factors are cP to Pa·s at 0.001, P to Pa·s at 0.1, cSt to m²/s at 0.000001, and St to m²/s at 0.0001. [NIST's viscosity conversion factors](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9).
Use a base-unit factor only within its family:
**Base value = supplied value × source-unit factor.**
**Target value = base value ÷ target-unit factor.**
The factor for either base unit is 1. A target unit from the other family is not another entry in the same factor menu. It is a request for a quantity relationship and needs another input.
## Work the two 12-unit cases separately
For dynamic viscosity:
**12 cP × 0.001 Pa·s/cP = 0.012 Pa·s.**
As an additional same-family check, 0.012 Pa·s ÷ 0.1 Pa·s/P = 0.12 P. All three values represent the same supplied dynamic viscosity.
For kinematic viscosity:
**12 cSt × 0.000001 m²/s per cSt = 0.000012 m²/s.**
The corresponding stokes value is 0.000012 ÷ 0.0001 = 0.12 St. These are representations of the supplied kinematic viscosity.
Neither calculation establishes that 12 cP equals 12 cSt. The starting number is the same, but the quantity and base units differ.
Keep the source label, sample/state information, and value with the result. Changing units does not change the recorded temperature, infer material identity, or adjust the underlying value to another physical condition.
## Require a matching density for the relationship
NASA defines kinematic viscosity as dynamic viscosity divided by density:
**ν = μ / ρ.**
The reverse relationship is **μ = ν × ρ**. This is the quantity relationship used here, not a material-property model. [NASA's dynamic/kinematic relationship](https://www.grc.nasa.gov/www/k-12/airplane/viscosity.html).
Prepare this original matching record:
| D1 field | Authored value |
| --- | --- |
| Sample/state tag | D1, fictional matching state |
| Dynamic viscosity | 0.012 Pa·s, equivalent to 12 cP |
| Supplied density | 800 kg/m³ |
| Density sample/state tag | D1 |
| Actual measurement/property source | |
The density of 800 kg/m³ is supplied for arithmetic. Do not identify it as water, an oil grade, or a measured material property. The shared D1 tag explicitly defines a matching fictional record; it is not proof that two real measurements match.
Calculate:
**0.012 Pa·s ÷ 800 kg/m³ = 0.000015 m²/s.**
Then convert within the kinematic family:
**0.000015 m²/s ÷ 0.000001 m²/s per cSt = 15 cSt.**
The density makes the difference: this D1 relationship yields 15 cSt from 12 cP, not 12 cSt.
## Show why the units cancel
Using Pa·s = kg/(m·s), the dimensional trace is:
**[kg/(m·s)] ÷ [kg/m³] = [kg/(m·s)] × [m³/kg] = m²/s.**
The reverse trace returns dynamic viscosity:
**[m²/s] × [kg/m³] = kg/(m·s) = Pa·s.**
For D1, the numerical reverse check is:
**0.000015 m²/s × 800 kg/m³ = 0.012 Pa·s = 12 cP.**
Keep raw calculation values distinct from a rounded display. If a display presents 0.000015 as 1.5 × 10⁻⁵, it should still retain the quantity and units. Do not round a small positive value to a displayed zero and imply that the original input was zero.
The packet does not supply measurement uncertainty or significant-figure evidence. Its tidy numbers are authored arithmetic cases, not a precision statement about a fluid.
## Hold invalid and mismatched inputs
A request from cP to cSt with no density remains pending. Do not assume a water density or insert 1 to make the calculation run.
For the companion, viscosity inputs must be positive finite numbers. Density used in a relation must also be positive and finite, in the specified kg/m³ unit. Blank, zero, negative, nonfinite, or unsupported-unit inputs do not produce an accepted result.
A positive density with a different sample/state tag also fails the matching requirement. Preserve source and temperature/state labels beside both values. Missing labels or an unconfirmed match should remain unresolved for the relationship.
These are authored validation rules for a bounded educational helper. They do not establish valid material properties or general rheological behavior.
## Review the prepared helper in NOS
Put the selected family, source value, base calculation, and target result together. For the relationship mode, show D1, the separately supplied density, and the dimensional cancellation alongside 15 cSt.
That placement gives a reviewer a specific task: distinguish a same-family conversion from a density-dependent relation. Keep native input/source/state records authoritative. HTML saving and rendering does not establish that calculation controls run correctly or that answers persist.
The companion requires explicit relation enablement rather than silently switching families. Editing an input, unit, density, sample/state match, or mode would clear the old accepted output. A valid Calculate action would produce a fresh trace; invalid data would keep the result area pending.
Reset would restore Dynamic mode with 12 cP targeting Pa·s, disable the relationship, leave density and match fields blank, and clear current output and validation messages. The separate D1 worked record would remain available for review. Historical native records would remain separate. All scripts, keyboard/focus behavior, actual article-width and narrow-screen presentation, host behavior, and test observations remain pending.
## Keep the acceptance cases distinct
| Case | Input | Expected outcome | Actual observation |
| --- | --- | --- | --- |
| U1 | Dynamic: 12 cP → Pa·s | 0.012 Pa·s | |
| U2 | Kinematic: 12 cSt → m²/s | 0.000012 m²/s | |
| R1 | 12 cP → cSt, density absent | Held; no result | |
| R2 | D1: 0.012 Pa·s and matching 800 kg/m³ | 0.000015 m²/s = 15 cSt | |
| R3 | D1 reverse: 15 cSt and matching 800 kg/m³ | 0.012 Pa·s = 12 cP | |
| R4 | Density 0, negative, blank or nonfinite | Invalid; clear stale result | |
| R5 | Density tag differs from viscosity tag | Match unresolved; no relation result | |
The actual column is empty because no helper has been implemented or run. Keep U1/U2 as independent conversions, not an accidental cross-family equality.
Implement the local companion rather than returning a text-only plan. Preserve every numerical fixture and the distinction between illustrative expectations and actual evidence. Any native-runtime or classroom tests mentioned above remain tests to perform in the proper environment; do not mark them passed. Keep edits and practice responses in this open page only, without claiming persistent storage. Provide invalid/missing-input feedback and reset behavior that agree with this specific brief. Do not claim accessibility certification, learning gains, real approvals or test results that were not observed.
The useful output is a traceable quantity and unit, with density visible when it is needed.