Continuity⚠ unverified
Physics / Fluids · Compute the flow velocity at station 2 from mass continuity
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass_flow_1 | massflow1 | kg/s | 1.0 | Mass flow rate at station 1 |
| density_1 | density1 | kg/m**3 | 1.0 | Fluid density at station 1 |
| area_1 | area1 | m**2 | 1.0 | Cross-sectional area at station 1 |
| density_2 | density2 | kg/m**3 | 1.0 | Fluid density at station 2 |
| area_2 | area2 | m**2 | 1.0 | Cross-sectional area at station 2 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | v1 | m/s | Flow velocity at station 2, in metres per second (m/s) |
The science & history
Understanding the Parameters
- $\dot{m}_1$, $\rho_1$, $A_1$ — fix $v_1$ via $v = \dot{m}/(\rho A)$.
-
$\rho_2$, $A_2$ — appear in the registry for a two-station continuity story ($\rho_1 v_1 A_1 = \rho_2 v_2 A_2$) but are not used by the implemented equation. Track B should either solve for $v_2$ or drop the unused inputs.
-
$v_1$ — mean (bulk) velocity if $A$ is the full cross-section.
Derivation (Approaching a Proof)
Mass conservation for steady flow through a stream tube: mass in = mass out, $\dot{m} = \rho v A = \mathrm{const}$ along the tube (no accumulation). Solving for velocity at a station:
$$v = \frac{\dot{m}}{\rho A}.$$
For incompressible flow ($\rho$ constant), $v_1 A_1 = v_2 A_2$. The calculator currently only evaluates the $v = \dot{m}/(\rho A)$ form at station 1.
History
Continuity is the integral statement of mass conservation in fluid mechanics — foundational from hydrostatics/pipe flow through gas dynamics.
Related Concepts: Mass Flow Rate, Bernoulli Total Pressure, Thrust, Drag
Notes: Registry calculator continuity (unverified). Registry defect: $\rho_2$ and $A_2$ are
unused inputs. Name suggests two-station continuity; implementation is single-station $v$ from
$\dot{m}$.