Pipe Size Calculator

Continuity Equation:

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

Where: $Q$ = flow rate, $A$ = cross-sectional area, $V$ = velocity, $D$ = pipe diameter

Reynolds Number:

$$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$$

Where: $\rho$ = density, $\mu$ = dynamic viscosity, $\nu$ = kinematic viscosity

• Laminar flow: $Re < 2300$
• Transitional flow: $2300 < Re < 4000$
• Turbulent flow: $Re > 4000$

Darcy-Weisbach Equation:

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

Where: $f$ = friction factor, $L$ = pipe length, $\Delta P$ = pressure drop

Friction Factor for Smooth Pipes (Blasius):

$$f = \frac{0.3164}{Re^{0.25}} \quad \text{for } Re < 10^5$$

Friction Factor for Rough Pipes (Colebrook-White):

$$\frac{1}{\sqrt{f}} = -2 \log_{10}\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}}\right)$$

Where: $\varepsilon$ = surface roughness

Turbulence Intensity:

$$I = \frac{u'}{U} = \frac{0.16}{Re^{1/8}}$$

Where: $u'$ = RMS of velocity fluctuations, $U$ = mean velocity

Head Loss:

$$h_L = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g}$$

Where: $h_L$ = head loss, $g$ = gravitational acceleration