The Darcy-Weisbach equation is a popular formula for estimating the head loss (or pressure drop) along a pipe or duct due to friction. The equation can be used in laminar flow conditions. Below is the equation and its parameters in Imperial (or English) units:

Where:

Explanation:

**Friction Factor (****f)**:It represents the resistance offered by the inner surface of the duct or pipe to the fluid flow. It depends on the material and roughness of the duct/pipe and the properties of the fluid.

For example, smooth metal ducts usually have a lower friction factor compared to rough ducts.

**Duct Length (***L***) and Diameter (***D***)**:is the length of the duct or pipe, and*L*is its hydraulic diameter. The ratio*D***(***D/L***)**represents how the length and diameter of the duct affect the head loss.

**Fluid Velocity (***v***)**:This is the speed at which the fluid is moving through the duct or pipe. Higher velocities generally result in higher frictional losses. In the ducted system for HVAC, the fluid is air.

**Water Density (p_water), Gravitational Acceleration (***g***)**:Used to calculate the specific weight of water to express head loss as water column.

**Unit Conversion:**

Units must be consistent to use the Darcy-Weisbach equation in the Imperial system. Pressure drop (ΔP) is often represented in inches of water column (in w.c.). To convert from feet to inches, multiply by 12 (as shown in the first equation above). Also, ensure that the velocity is in feet per second (fps) and the length and diameter are in feet.

If we want to use CFM (cubic feet per minute) instead of velocity (feet per minute or FPM), we can substitute the velocity using the formula for airflow:

Where:

The cross-sectional area of a circular duct can be calculated as:

So,

Now, substitute ** v_fps** in the Darcy-Weisbach equation:

Now, replace **Q **with its value in CFS (CFM/60) for calculation purposes.

This will give you the Darcy-Weisbach equation using CFM for airflow. Ensure that units are consistent when using this formula.

View the interactive parametric curve on Desmos __here__.

Note: this equation applies generally also to other fluids (like water). Good break down of ways to view and apply the equation is here. It would be great if somone created a desmos calculator that represented multiple trunks of duct (perhaps 3 or 4) that could be summed into a single system curve. This might help estimate ESP for fan selections at the early design phase of a project.