Reynolds Number for water Calculator
Design Philosophy
(Source: CPHEEO Manual on Water Supply and Treatment, 2013; supplemented by Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th Ed.)
The Reynolds Number (Re) is a dimensionless parameter that characterizes the nature of fluid flow in a conduit. It represents the ratio of inertial forces to viscous forces acting on the fluid. The CPHEEO Manual recommends the Reynolds Number as a primary criterion for classifying the flow regime in water supply and sewerage pipelines and channels. The generalized Reynolds Number formula is:
where,
ρ : Density of the fluid (kg/m³) — a function of temperature
v : Mean velocity of flow (m/s)
Dh : Hydraulic diameter of the conduit (m)
μ : Dynamic viscosity of the fluid (Pa·s) — a function of temperature
Flow Regime Classification (as per CPHEEO Manual)
• Re < 2000 → Laminar flow: smooth, layer-by-layer flow; dominant in slow or viscous flows
• 2000 ≤ Re ≤ 4000 → Transitional flow: unstable, mixed characteristics
• Re > 4000 → Turbulent flow: chaotic; the normal regime in water supply pipelines
Hydraulic Diameter (Dh)
For non-circular conduits — rectangular ducts, trapezoidal channels, partially filled circular pipes — the hydraulic diameter is used as the equivalent characteristic length in the Reynolds Number calculation. It is defined as:
where A is the cross-sectional area of flow (m²) and P is the wetted perimeter (m). For a circular pipe flowing full, Dh equals the pipe internal diameter.
Temperature Dependence of Fluid Properties
The density (ρ) and dynamic viscosity (μ) of water vary significantly with temperature. Values used in this calculator are interpolated from standard reference tables for pure water. At 20°C, ρ ≈ 998 kg/m³ and μ ≈ 1.002 × 10⁻³ Pa·s. Designers should verify and adjust these values for the actual water temperature prevailing at the project site, particularly for groundwater sources at different depths.
Conduit Shape Support
The calculator supports the following cross-sectional shapes, each with its respective formula for area and wetted perimeter: Circular pipe, square duct, rectangular duct, Circular open channel (partial flow), and Trapezoidal channel.
Calculator
(Note – all Yellow are user defined value, all white are fixed values, all green are calculated value, all orange is calculated not to be shown)
Instructions
Enter values highlighted in the Yellow
Green highlights are the results
In case of any invalid result of non-functioning of the calculator, please write to us at design@swaenviro.com. We will try and help you with your sizing and calculation
INPUT
| Parameter | Values | Unit | |
|---|---|---|---|
| Shape of conduit | |||
| Dimensions | Bottom Width (m) | ||
| Top Width (m) | |||
| Depth (m) | |||
| Hydraulic Diameter | Dh | 0.995307592937346 | m |
| Temperature | T | °C | |
| Viscosity of fluid | μ | 1.01E-03 | Pa-s |
| Density of fluid | ρ | 999.6 | kg/m3 |
| Flowrate | Q | cum/hr | |
| Area | A | 1.032 | m2 |
| Velocity | v | 0.001 | m/s |
| Reynold’s number | 665.875 | ||
| Laminar |