Fluid Flow Calculator — Reynolds Number, Velocity & Pipe Diameter

What This Calculator Does

We assume steady, incompressible, fully developed internal flow in a circular pipe. Provide any two of \(Q\) (m³/s), \(D\) (m), and \(v\) (m/s) and we solve the missing one via \( v = \dfrac{4Q}{\pi D^2} \), \( D = \sqrt{\dfrac{4Q}{\pi v}} \), or \( Q = v \cdot \dfrac{\pi D^2}{4} \). Then Reynolds number is \( \mathrm{Re} = \dfrac{vD}{\nu} = \dfrac{\rho v D}{\mu} \). We classify \( \mathrm{Re} < 2300 \) as laminar, \( 2300 \le \mathrm{Re} < 4000 \) as transitional, and \( \mathrm{Re} \ge 4000 \) as turbulent.

Fluid Flow in Pipes — Quick Primer

Understanding how fluids behave inside pipes is central to civil, mechanical, chemical, and process engineering. The Reynolds number (Re) is a dimensionless ratio that compares inertial forces to viscous forces in a flowing fluid. Its value predicts whether the flow will be smooth and orderly (laminar) or chaotic and mixing-dominated (turbulent). Transitional cases occur between those extremes. This classification is not merely academic — it directly influences how engineers size pumps, select flow meters, design heat exchangers, and estimate pressure losses in pipelines and ductwork.

In laminar flow (Re < 2300), fluid particles progress in parallel layers with a stable, parabolic velocity profile. Energy losses are more predictable and friction factor correlations are simple. In turbulent flow (Re > 4000), eddies and mixing dominate; momentum and heat transfer are enhanced, but pressure losses increase. The transitional regime (roughly Re = 2300–4000) is unstable and difficult to model; designs usually aim to operate well below or above this band.

Key Equations

\( \mathrm{Re} = \dfrac{vD}{\nu} = \dfrac{\rho v D}{\mu} \),   \( v = \dfrac{4Q}{\pi D^2} \),   \( D = \sqrt{\dfrac{4Q}{\pi v}} \),   \( Q = v \dfrac{\pi D^2}{4} \).

These relationships let you solve for any missing variable when the others are known. For example, with a flow rate and pipe diameter you can compute velocity, then Reynolds number, and finally determine the flow regime. Because \( \nu = \mu / \rho \), you may supply either ρ and μ or directly the kinematic viscosity ν. This calculator prioritizes ν when present for clarity.

Units & Assumptions

• SI units: \(Q\) in m³/s, \(D\) in m, \(v\) in m/s, \(ρ\) in kg/m³, \(μ\) in Pa·s, \(ν\) in m²/s.
• Assumptions: circular pipe, steady and incompressible flow, Newtonian fluid.
• Focus: Reynolds number and regime only. Minor losses, fittings, roughness, and entrance effects are not included.
• Non-circular ducts: use the hydraulic diameter \(D_h = 4A/P_{\text{wetted}}\) as an equivalent diameter.

Why It Matters

Getting Reynolds number right is essential for selecting friction factor correlations (e.g., Darcy–Weisbach), sizing pumps and fans, and predicting thermal performance in heat exchangers. In HVAC, water distribution, oil & gas pipelines, food processing, and biomedical flows, the regime strongly influences energy requirements. By experimenting with diameters, flow rates, or fluid properties in this tool, you can see how small design choices push a system into laminar, transitional, or turbulent behavior.

Disclaimer: Educational calculator only — not a substitute for detailed engineering design or code compliance.