# Rule-of-thumb to estimate pressure loss for differing pipe diameters A useful rule-of-thumb to estimate the frictional losses in a system for a different pipe diameter is to multiply your calculated frictional losses for a known diameter by the ratio of diameters to the fifth power. [[Darcy-Weisbach]] tells Us: $\Delta P=\frac{\rho fLv^2}{2D}$ At constant volumetric flow velocity changes with pipe area, so substitute $v=\frac{Q}{A}=\frac{4Q}{\pi D^2}$ $\Delta P=\frac{8\rho fLQ^2}{\pi^2D^5}$ Assuming density, Darcy friction factor, volumetric flowrate, and pipe length are constant we can simplify to: $\Delta P\propto\frac{1}{D^5}$ Applying this to states 1 and 2 with differing pipe diameter and constants as described above: $\Delta P_{2}=\Delta P_{1}\left ( \frac{D_{1}}{D_{2}} \right )^5$ > [!warning] > For incompressible flow only (i.e. liquids). May be used with caution for compressibles where $\Delta P<10\%\;P_{inlet}$. > [!warning] > This relation does not account for static head as it applies to frictional losses only.