Knowledge card
Continuity Equation
Mathematical Modelling — Fluid Dynamics & Heat TransferContinuum mechanics; boundary-layer similarity theory
Symbol
Conservation of mass for an incompressible flow.
In words:plusequalszero.
Open full derivation chain: 1 stepsDerivation
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Open Step 1: Given / definition
Given / definition Defining ruleThe starting relation of a derivation — the definition or established equation every later step transforms; it justifies no change itself.Level 0 · more availableBrief — named quantitiesAbout levels
Why the levels load one at a time
Only level 0 travels with this article. The complete expansion is several megabytes, so deeper levels are fetched one at a time when you ask for them — and how deep it goes is not known until you get there.
To go deeper still, open any quantity in the reading as its own concept card — it carries its own derivation and its own depth ladder.
How many levels remain is not yet known — the depth is discovered one level at a time.
Equation Workspace
Set known values, calculate unknowns, inspect dependencies, and run numerical solves.
Calculator
Equation Workspace
Set known values, calculate unknowns, inspect dependencies, and run numerical solves.
Equation workspace
Set the values you know, then calculate the remaining quantities in Continuity Equation.
Domain Analysis
Unit status, dimensional trails, per-step checks, and custom unit expressions.
Domain Analysis
Unit status, dimensional trails, per-step checks, and custom unit expressions.
Step-by-step unit check (1 steps)
Step 1 given
Expand checked this step.
Try your own — the unit calculator
Ever wondered whether a formula “adds up”? This tool answers one plain question: do the units match? Pick a couple of quantities (distance, time, a speed…), join them with ×, ÷, +, or =, and press Run. It works out the resulting unit — for example distance ÷ time gives a speed, LT⁻¹ (metres per second) — and flags anything that can’t be right, like adding a length to a time.
Reads as: ∇·u
“∇·u” is analysed by expanding its full defining equation (its children and their relations), not as a bare symbol. Use Check this concept’s units above for the same result.
Mathematical Analysis
Object type, lawful operations, conditions, comparisons, and derivation-step checks.
Mathematical Analysis
Object type, lawful operations, conditions, comparisons, and derivation-step checks.
Check one step at a time (1 steps)
Step 1 — given
Dimension I
Definition
What it is — and what it is not
Dimension II
In practice
How to deal with it
No practical guidance recorded yet.