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Darcy Weisbach Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


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.

What is Darcy Weisbach equation?

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 ΔPΔP for a pipe having diameter DD and length LL is written as:

ΔP=fLV2ρ2D\footnotesize ΔP = \frac{f \cdot L\cdot V^2\cdot\rho}{2 \cdot D}

where:

  • ρ\rho — The fluid density;
  • VV — The flow velocity; and
  • ff — 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:

ΔPL=fV2ρ2D\footnotesize\frac{ΔP }{L}=\frac{f\cdot V^2 \cdot \rho}{2\cdot D}

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 kk using the Colebrook equation:

🙋 Friction is always hard to model: its consequences, however, are fairly simple, as you can see at our friction calculator and drag equation calculator!

1f=2log(k3.7D+2.51Ref)\footnotesize \frac{1}{\sqrt{f}}=-2\cdot\log\left(\frac{k}{3.7\cdot D}+\frac{2.51}{\mathrm{Re}\cdot\sqrt{f}}\right)

where Re\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:

 ⁣f=0.0055(1+(2104kD+106Re)13)\!\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)

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

How to calculate pressure drop?

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

  • Step 1: Enter the pipe diameter, DD.
  • Step 2: Input the pipe length, LL.
  • Step 3: Insert the fluid flow velocity, VV.
  • Step 4: Enter the fluid density, ρ\rho.
  • Step 5: Fill in the value of Darcy friction factor, ff.
  • Step 6: The Darcy Weisbach calculator will return the value of pressure drop.

Example — Using the Darcy Weisbach Calculator

Determine the pressure drop per unit length in a 100 m100\ \mathrm{m} long pipe having a diameter, 1 m1\ \mathrm{m}. Take the friction factor as 0.030.03 and flow velocity as 100 m/s100 \ \mathrm{m/s}.

To find the pressure drop across the pipe:

  1. Enter the pipe diameter, D=1 m\small D = 1\ \mathrm{m}.
  2. Input the pipe length, L=100 m\small L = 100\ \mathrm{m}.
  3. Insert the fluid flow velocity, V=100 m/s\small V = 100\ \mathrm{m/s}.
  4. Enter the fluid density, ρ=1000 kg/m3\small \rho = 1000\ \mathrm{kg/m^3}.
  5. Fill in the value of Darcy friction factor, f=0.03\small f = 0.03.
  6. Using the Darcy Weisbach formula:
ΔPL=fV2ρ2D=0.031002100021=15104 Pa=0.15 MPa\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}

And:

ΔP=15106 Pa=15 MPa\footnotesize ΔP=15\cdot10^6\ \mathrm{Pa}=15\ \mathrm{MPa}

Therefore, the Darcy Weisbach equation calculator estimates a pressure drop of 0.15 MPa0.15\ \mathrm{MPa} per meter length of pipe whereas 15 MPa15\ \mathrm{MPa} is the pressure loss for a 100 m100\ \mathrm{m} long pipe.

🙋 Not looking for the pressure drop? Maybe the differential pressure calculator is what you need!

FAQ

What is Darcy Weisbach equation?

The Darcy Weisbach equation is used to determine the pressure drop across a pipe for a fluid. Mathematically this is:

ΔP = (f × L × V² × ρ) / (2 × D)

where P is pressure, f is friction factor, L is pipe length, V is flow velocity, D is pipe diameter, and ρ is the fluid density.

How do I find pressure drop?

To find the pressure drop in a pipe using the Darcy Weisbach formula:

  1. Multiply the friction factor by pipe length and divide by pipe diameter.
  2. Multiply this product with the square of velocity.
  3. Divide the answer by 2.

What are the factors affecting pressure drop?

The pressure drop in the Darcy Weisbach formula is affected by three types of factors:

  1. Pipe dimensions — length and diameter.
  2. Material properties — Darcy friction factor.
  3. Fluid flow properties — density and velocity.

How do I calculate friction factor?

To calculate friction factor:

  1. Calculate the Reynold’s number for the flow (using ρ × V × D / μ).

  2. Check the relative roughness (k/D) to be under 0.01.

  3. Use the Reynold’s number, roughness in the Moody formula:

    f = 0.0055 × (1 + (2×100² × k/D + 100³/Re)^(1/3).

Rahul Dhari
Pipe with Length, L, diameter, D, and fluid pressures P1 and P2 on either ends.
Pipe length (L)
ft
Pipe diameter (D)
ft
Flow velocity (V)
ft/s
Density of fluid (ρ)
lb/cu ft
Darcy friction factor (f)
Pressure drop (ΔP)
psi
To calculate Darcy friction factor (f), try our dedicated friction factor calculator, that uses Moody approximation for Colebrook equation.
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