mass continuity formulas and interpretation
Mass continuity conserves mass flow even when fluid density changes between sections.
The calculator preserves compressible and incompressible modes plus geometry assistance.
How to use the mass continuity calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
For steady one-dimensional flow, density times area times average velocity is constant.
ρ₁A₁v₁ = ρ₂A₂v₂- ρ₁,ρ₂ — Densities
- Section fluid densities (kg/m³)
- A₁,A₂ — Areas
- Flow cross-sections (m²)
- v₁,v₂ — Velocities
- Average velocities (m/s)
- ṁ — Mass flow
- Conserved mass per time (kg/s)
Changing-density example
Inlet density is 2 kg/m³, area 0.1 m², and speed 5 m/s; outlet density and area are 1 kg/m³ and 0.05 m².
- Inlet mass flow
- 1 kg/s
- Outlet density-area
- 0.05 kg/m
- v₂ = 2 × 0.1 × 5 /(1 × 0.05)
- v₂ = 20 m/s
Result: Outlet velocity is 20 m/s.
Lower density and area require higher velocity to conserve mass.
Understanding your results
Interpreting the result
The equation assumes steady flow with no mass added, removed, or accumulated between sections.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.