Governing Formula
Mass flow is volumetric flow multiplied by fluid density. Because dosing, sludge, brine, and chemical loading are specified and measured as masses, converting between the volume delivered and the mass transported requires the density of the actual fluid — not the 1000 kg/m³ fresh-water value.
ṁ = ρ × Q Where:
-
Q= Volumetric flow (canonical basis m³/h) [m³/h, L/min, GPD] -
ρ= Fluid density [kg/m³] -
ṁ= Mass flow rate [kg/h] -
ṁ_d= Daily mass flow [t/day] -
ṁ_lb= Mass flow in imperial units [lb/h]
Derived Equations:
ṁ = ρ × Q Q = ṁ / ρ ṁ_d = ṁ × 24 / 1000 ṁ_lb = ṁ × 2.2046226218 How the Calculation Works
The engine first normalises any entered volumetric unit into a canonical m³/h (L/min divides by 16.6667 — equivalently 60/1000 — and GPD divides by 264.172 × 24), then multiplies by the density to obtain kg/h:
ṁ (kg/h) = Q (m³/h) × ρ (kg/m³)
Daily tonnes multiply the hourly mass by 24 hours and divide by 1000; imperial pounds per hour use the exact 2.2046226218 lb/kg factor. In Mass → Volumetric mode the input is treated as kg/h and divided by density to recover the equivalent m³/h flow.
Worked Engineering Example
Design Scenario: 100 m³/h Potable Water Transfer (ρ = 1000 kg/m³)
- Canonical volumetric flow:
Q = 100 m³/h (already canonical) - Mass flow:
ṁ = 100 × 1000 = 100,000 kg/h - Daily mass:
ṁ_d = 100,000 × 24 / 1000 = 2,400 t/day - Imperial basis:
ṁ_lb = 100,000 × 2.2046226218 = 220,462 lb/h - Brine check (200 L/min, ρ = 1050):
Q = 200 / 16.6667 = 12.0 m³/h → ṁ = 12.0 × 1050 = 12,600 kg/h - GPD basis (500,000 GPD, ρ = 1000):
Q = 500,000 / (264.172 × 24) = 78.86 m³/h → ṁ ≈ 78,863 kg/h
Engineering Notes & Design Benchmarks
| Fluid | Density (kg/m³) | Typical Use |
|---|---|---|
| Fresh water (4 °C) | 1,000 | Canonical basis for potable systems |
| Seawater | ≈ 1,025 | Desalination feed and brine |
| Brine / 3.5% saline | ≈ 1,050 | RO concentrate, chemical brine |
| Dewatered sludge / slurries | 1,050 – 1,300 | Wastewater solids haulage |
Always use the site-measured density for mass-based dosing or civil-haulage calculations; assuming 1000 kg/m³ for brine, seawater, or sludge understates the transported mass by the density ratio and leads to underestimated loads.
Assumptions & Limitations
- Density is a fixed input; temperature and dissolved solids change density for real fluids.
- GPD is US liquid gallon per day (1 US gal = 231 in³ exactly).
- Conversions are exact and unit-anchored; only the user-supplied density carries engineering uncertainty.
- Reverse mode assumes the mass flow is already expressed in kg/h regardless of the selected unit label.
Frequently Asked Questions
Why use density at all — isn’t 1 m³ of water 1000 kg?
Only for fresh water at ≈ 4 °C. Brine at 1050 kg/m³ gives 1050 kg per m³, and dewatered sludge can reach 1300 kg/m³. For mass-based payments, dosing, and haulage the density must match the actual fluid.
What is 100 m³/h of water in kg/h?
Exactly 100,000 kg/h at ρ = 1000 kg/m³, which is 2,400 t/day or about 220,462 lb/h — the default values you see when the calculator loads.
How is GPD converted?
US gallons per day divides by 264.172 gallons per m³ and by 24 hours to reach m³/h (500,000 GPD ≈ 78.86 m³/h). At ρ = 1000 kg/m³ that is about 78,863 kg/h.
Engineering Disclaimer
Engineering Note: This converter applies exact unit factors and user-supplied density for design documentation. Always verify the operating fluid density with measurement or supplier data before releasing mass-based calculations.
Technical References
- Perry, R.H. & Green, D.W., Perry’s Chemical Engineers’ Handbook, 8th ed., McGraw-Hill.
- Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe (TP 410), density and flow measurement.
- ISO 80000-4 (Mechanics) & ISO 80000-9 (Physical chemistry) — quantity and unit conventions.
- NIST, Guide for the Use of the International System of Units (SP 811), 2008.