Darcy Weisbach Calculator

The Darcy Weisbach Calculator estimates the change in pressure or the pressure drop due to the friction in a pipe during a fluid flow.

The roughness on the inner surface of a pipe can cause friction loss resulting in pressure drop, which is used to calculate the Darcy Weisbach friction factor. Pipes are used to transport fluids in a wide array of domains, such as pumping water supply. The pressure drop is crucial to estimate the actual pressure output and when selecting the material and pipe dimensions for construction.

Read on to understand the workings of the Darcy Weisbach equation and how to calculate pressure drop across a section of pipe.

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 $ΔP$ for a pipe having diameter $D$ and length $L$ is written as:

where:

• $\rho$ — The fluid density;
• $V$ — The flow velocity; and
• $f$ — Darcy friction factor.

The above equation is known as the Darcy Weisbach equation, which was named in honor of engineers Henry Darcy and Julius Weisbach. Alternatively, the pressure loss per unit length can be written as:

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 $k$ using the Colebrook equation:

where $\mathrm{Re}$ 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:

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

Follow the steps below to estimate the pressure drop using this Darcy Weisbach equation calculator:

• Step 1: Enter the pipe diameter, $D$.
• Step 2: Input the pipe length, $L$.
• Step 3: Insert the fluid flow velocity, $V$.
• Step 4: Enter the fluid density, $\rho$.
• Step 5: Fill in the value of Darcy friction factor, $f$.
• Step 6: The Darcy Weisbach calculator will return the value of pressure drop.

Determine the pressure drop per unit length in a $100\ \mathrm{m}$ long pipe having a diameter, $1\ \mathrm{m}$. Take the friction factor as $0.03$ and flow velocity as $100 \ \mathrm{m/s}$.

To find the pressure drop across the pipe:

1. Enter the pipe diameter, $\small D = 1\ \mathrm{m}$.
2. Input the pipe length, $\small L = 100\ \mathrm{m}$.
3. Insert the fluid flow velocity, $\small V = 100\ \mathrm{m/s}$.
4. Enter the fluid density, $\small \rho = 1000\ \mathrm{kg/m^3}$.
5. Fill in the value of Darcy friction factor, $\small f = 0.03$.
6. Using the Darcy Weisbach formula:

And:

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