When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.

Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to viscous forces in the fluid. In laminar flow (Re < 2000), the fluid flows in parallel layers, or streamlines, with minimal cross-stream mixing. Here, the pressure drop mostly depends on the fluid's viscosity and is generally lower. In contrast, turbulent flow (Re > 4000) is characterized by chaotic eddies and swirling motions. In this regime, the pressure drop is influenced not only by viscosity but also by the roughness of the pipe wall, as these irregularities disrupt the flow further, increasing energy losses.

The pressure drop in a pipe depends on several factors: fluid properties, flow velocity, pipe characteristics, and dimensionless numbers.

The Darcy-Weisbach equation is the standard approach for quantifying the pressure drop due to frictional losses in pipe flow:

Where:

1. ΔP is the pressure drop,
2. f is the friction factor,
3. L is the length of the pipe,
4. D is the pipe diameter,
5. ρ is the fluid density,
6. v is the flow velocity.

The friction factor f is crucial for calculating pressure drops, especially in turbulent flow. It depends on the Reynolds number and the relative roughness of the pipe. Engineers often refer to the Moody chart, which provides empirical values of friction factors across flow regimes and roughness levels.

The Colebrook equation

Where:

1. f is the friction factor,
2. ϵ/D is the relative roughness
3. Re is the Reynolds number.

offers a precise method to calculate f for smooth and moderately rough pipes, but it is implicit and requires iterative solutions. To avoid iteration, approximations like the Haaland equation:

Where:

1. f is the friction factor,
2. ϵ/D is the relative roughness
3. Re is the Reynolds number.

are commonly used in practice, providing reasonably accurate friction factor values without extensive calculation. Understanding these dynamics enables engineers to design pipe systems that manage flow efficiently, compensating for potential pressure losses over time as pipe roughness increases.