Library / Fundamentals / FUN-05
Fundamentals
Mass flow and volume flow
Mass passing through a pipe or duct each second.
- Ref
- FUN-05
- Rev
- v1
- Field
- Fundamentals
- Result
- ṁ [kg/s]
ṁ in kg/s, ρ in kg/m³, Q in m³/s, A in m², mean velocity v̄ normal to the cross-section in m/s. Density is taken as uniform across the section.
The volume flowing past a point each second is the pipe area times the mean speed of the fluid. Multiply by density to get the mass per second.
Calculator
- Volume flow Q10 L/s
- Mass per hour36 tonne/h
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- For incompressible flow Q stays constant along a pipe, so halving the area doubles the speed.
- For gases the density changes with pressure and temperature, so mass flow is the quantity that stays constant, not volume flow.
- Area scales with diameter squared. A small diameter change has a large effect on flow.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kg/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| v̄ Mean velocity | 0.1 to 50 m/s | 0.5 | 250 | 249.5 | +10% | +10 % |
| A Flow area | 1 to 1,000 cm² | 0.2 | 200 | 199.8 | +10% | +10 % |
| ρ Density | 1 to 2,000 kg/m³ | 0.01 | 20 | 19.99 | +10% | +10 % |
Sweep of Mean velocity
| Mean velocity (m/s) | Mass flow rate (kg/s) |
|---|---|
| 0.1 | 0.5 |
| 0.2175 | 1.087 |
| 0.4729 | 2.364 |
| 1.028 | 5.141 |
| 2.236 | 11.18 |
| 4.862 | 24.31 |
| 10.57 | 52.87 |
| 22.99 | 115 |
| 50 | 250 |
Sweep one variable
Variables and how each one contributes
Mass flow rate
What the equation gives you. Everything else feeds it.
Density
Mass per unit volume of the fluid. Directly proportional: the same volume flow of a denser fluid carries more mass.
Flow area
Cross-sectional area normal to the flow. Directly proportional at fixed speed. Area grows with diameter squared, so +10% diameter gives about +21% flow.
Mean velocity
Average fluid speed over the cross-section. Directly proportional at fixed area.
Worked example with the values above
- Convert the area: 50 cm² = 0.005 m².
- Volume flow Q = Av̄ = 0.005 × 2 = 0.01 m³/s.
- Mass flow ṁ = ρQ = 1,000 × 0.01 = 10 kg/s.
Assumptions and limits
- Density uniform across the cross-section.
- Mean velocity measured normal to the section.
- Steady flow.
Common mistakes
- Using diameter instead of area.
- Mixing cm² with m² (a factor of 10 000).
- Using the pipe velocity at the centre as the mean.
Statistics and uncertainty
Independent relative errors combine as δṁ/ṁ ≈ √[(δρ/ρ)² + (δA/A)² + (δv̄/v̄)²]. The mean velocity is usually the weakest term, because real velocity profiles are not uniform and one-point readings can be 5–10% off the average.
Where it is used
- Sizing pipes and hoses for a fuel or coolant flow.
- Mass flow through an engine intake or nozzle.
- Converting a flow meter reading to mass per second.
Maths you need
- Area of a circle: A = πd²/4 for a round pipe
- Density: mass per unit volume