Darcy Weisbach Calculator (2024)

The friction in the pipe due to surface roughness is related to the loss of pressure by means of an empirical equation. The equation also factors in the pipe dimensions, such as diameter and length, as well as fluid properties, such as density and flow velocity, and material properties, including friction factor. Mathematically, the pressure loss $ΔP$ΔP for a pipe having diameter $D$D and length $L$L is written as:

$$\footnotesize ΔP = \frac{f \cdot L\cdot V^2\cdot\rho}{2 \cdot D}$$ΔP=2⋅Df⋅L⋅V2⋅ρ​

$$\footnotesize\frac{ΔP }{L}=\frac{f\cdot V^2 \cdot \rho}{2\cdot D}$$LΔP​=2⋅Df⋅V2⋅ρ​

The Darcy friction factor is the key part of the equation that is based on the material's surface and is very difficult to calculate. One of the solutions presented uses a Moody diagram and the Colebrook-White equation. The Darcy Weisbach friction factor can be estimated for a pipe having surface roughness $k$k using the Colebrook equation:

$$\footnotesize \frac{1}{\sqrt{f}}=-2\cdot\log\left(\frac{k}{3.7\cdot D}+\frac{2.51}{\mathrm{Re}\cdot\sqrt{f}}\right)$$f​1​=−2⋅log(3.7⋅Dk​+Re⋅f​2.51​)

where $\mathrm{Re}$Re is the Reynold's number for the fluid flow. To solve the Colebrook-White equation, Lewis Moody presented an approximate solution known as Moody's approximation which is:

$$\!\footnotesize f=0.0055\!\cdot\!\!\Bigg(\!\!1+\!\!\bigg(\!2\cdot10^4\cdot \frac{k}{D}+\frac{10^6}{\mathrm{Re}}\bigg)^{\!\!\frac{1}{3}}\!\Bigg)$$f=0.0055⋅(1+(2⋅104⋅Dk​+Re106​)31​)

One can note that the friction factor depends on surface roughness, $k$k, and Reynold's number, which is estimated from fluid flow properties: you can learn more about this quantity at our Reynolds number calculator.

$$\footnotesize\begin{split}\frac{ΔP }{L}&=\frac{f\cdot V^2 \cdot \rho}{2\cdot D}\\[1em]&=\frac{0.03\cdot 100^2\cdot 1000}{2\cdot 1}\\[1em]&=15\cdot 10^4\ \mathrm{Pa}=0.15\ \mathrm{MPa}\end{split}$$LΔP​​=2⋅Df⋅V2⋅ρ​=2⋅10.03⋅1002⋅1000​=15⋅104Pa=0.15MPa​

And:

$$\footnotesize ΔP=15\cdot10^6\ \mathrm{Pa}=15\ \mathrm{MPa}$$ΔP=15⋅106Pa=15MPa

Therefore, the Darcy Weisbach equation calculator estimates a pressure drop of $0.15\ \mathrm{MPa}$0.15MPa per meter length of pipe whereas $15\ \mathrm{MPa}$15MPa is the pressure loss for a $100\ \mathrm{m}$100m long pipe.