🏢 HVAC Duct & Chilled Water Pressure Drop Calculator

Design Context & HVAC Standards

In HVAC systems, pressure drop calculations are essential for sizing fans and chilled water pumps. Excessive pressure drop increases operating costs due to high pumping power, while undersized fans/pumps fail to deliver the design flow rate.

This application utilizes the fundamental **Darcy-Weisbach** friction loss equation and the **Colebrook-White** correlation to calculate friction factors across all regimes (laminar, transitional, and turbulent). It accounts for both straight pipe friction and localized fittings (elbows, tees, valves) using minor loss K-factors.

Mathematical Formulation

The pressure drop in a piping system or duct network consists of major friction losses along the length and minor losses through fittings:

1. Major Friction Loss (Darcy-Weisbach)

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

Where:

• $f$ = Darcy friction factor [-]
• $L$ = Pipe or duct length [m]
• $D$ = Hydraulic diameter [m]
• $\rho$ = Fluid density [kg/m³]
• $V$ = Mean fluid velocity [m/s]

2. Colebrook-White Correlation (Turbulent Regime)

For turbulent flow ($Re > 4000$), the friction factor is computed iteratively using:

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

Where $\varepsilon$ is the surface roughness, and $Re = \frac{\rho V D}{\mu}$ is the Reynolds number.

3. Minor Losses in Fittings

$$\Delta P_{minor} = \sum K_i \cdot \frac{\rho V^2}{2}$$

Where $K_i$ is the minor loss resistance coefficient for elbows, tees, valves, or transitions.

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