Pipe Flow Calculator

The calculator combines several fundamental fluid mechanics equations:

1. Flow Rate (continuity equation):

$$Q = A \cdot v = \frac{\pi D^2}{4} \cdot v$$

2. Reynolds Number:

$$Re = \frac{\rho v D}{\mu}$$

3. Friction Factor:

For laminar flow (Re < 2,300):

$$f = \frac{64}{Re}$$

For turbulent flow (Re ≥ 2,300), the Haaland equation (explicit approximation of Colebrook-White):

$$\frac{1}{\sqrt{f}} = -1.8 \log\left[\left(\frac{\varepsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re}\right]$$

where ε is the absolute surface roughness and ε/D is the relative roughness.

4. Darcy-Weisbach head loss:

$$h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g}$$

5. Pressure drop:

$$\Delta P = f \cdot \frac{L}{D} \cdot \frac{\rho v^2}{2}$$

Common roughness values: smooth drawn tubing ε ≈ 0.0015 mm, commercial steel ε ≈ 0.045 mm, galvanized iron ε ≈ 0.15 mm, cast iron ε ≈ 0.26 mm, concrete ε ≈ 0.3–3 mm.

The Haaland equation is accurate to within about 2% of the Colebrook-White equation across the full range of Reynolds numbers and relative roughness values found in engineering practice.

The results show flow rate in both m³/s and L/min for convenience, the Reynolds number with flow regime classification, the Darcy friction factor, head loss in meters of fluid column, and pressure drop in Pascals. For pipe system design, ensure the pressure drop doesn't exceed available pump head, and keep velocities within recommended ranges to avoid erosion and excessive noise.