# Napkin Diagrams

Engineering, Technology, and DIY

## Pressure Drops In Pipes: Part 1, Basics

A a fluid flows through a pipe, it will experience a natural pressure drop due to several factors. Friction is a major player, which itself involves flow velocity, pipe dimensions, and possibly internal pipe roughness. Height changes across the length of a pipe also contribute to pressure drops. Any and all fittings, coupling, et cetera will account for a part of any drops as well, although less so than the former two. Pressure drop can be related to head loss, a way of measuring the energy drop, with Equation 1, where ΔP is pressure drop, ρ is fluid density, g is gravity, and Δh is height difference.

Equation 1. Relating pressure drop and height difference to head loss

Head loss can also be related to pipe geometry and flow characteristics, as shown in Equation 2. The first term are the major losses from friction, while the second is the minor losses from pipe fittings. L is the length of straight pipe, D is the internal diameter, ff is the friction factor, v is average pipe velocity, and K is a value obtained from literature for a given fitting.

Equation 2. Head loss in terms of major and minor losses

Average velocity can be rewritten in terms of flow rate and diameter (Equation 2a).

Equation 2a. Velocity in terms of flow rate and diameter

Friction factor can potentially be very complicated or very easy to calculate depending on the type of fluid flow involved, which can be found by finding the Reynolds Number (Equation 3). μ is fluid viscosity.

Equation 3. Reynolds Number.

If Re is less than 2100, it can safely be considered laminar flow, and Equation 4a can be used for friction factor. If it is much higher (>4000), however, it has to be treated as turbulent and friction factor will be implicitly defined with the Colebrook-White equation (Equation 4b), where ε is pipe roughness.

Equation 4a. Laminar friction factor

Equation 4b. Colebrook-White turbulent friction factor

Using these equations, it calculations become easy. One can, for example, predict pressure drops across a given length of pipe at various flow rates, which very useful to check whether pumps will be needed in a system to maintain proper end pressure. Conversely, one can use a pressure drop at a flow rate to back-solve for friction factor and pipe roughness.

Caution: Make sure to check your units! This can save you hours, even days of work and hair-pulling.

Read on with Part 2, Series and Parallel