In this article the topic named “Darcy friction factor” and Darcy friction factor related facts will be discuss. In fluid mechanics the Darcy friction factor equation is play a very important role.

**The Darcy friction factor is a physical parameter which is related to head loss or loss of pressure for the reason of friction along the certain amount of length of a coil or pipe to the average velocity of the incompressible fluid. The Darcy friction factor is a dimensionless physical quantity.**

**What is Darcy friction factor?**

**What is Darcy friction factor?**

The Darcy friction factor is a physical parameter which is use to describe the loss for a coil or pipe due to friction. The Darcy friction factor is applicable for both open channel flow and close channel flow.

**The Darcy friction factor is a physical parameter which is describe as it is a physical quantity which is use for calculate the frictional energy loss. The Darcy friction factor is cased for resistance due to friction and velocity of the incompressible fluid inside a coil or pipe.**

The Darcy friction factor widely used in turbulent flow for calculating the amount of head loss during the friction in the pipe.

**Darcy friction factor formula:**

**Darcy friction factor formula:**

**The equation for Darcy friction factor is given below,**

**H _{f} = 4fLv^{2}/2gD**

**Where,**

**H _{f}**

**= Pressure loss or head loss**

**f = Coefficient of friction factor or Coefficient of friction factor**

**L = Length of the coil or pipe**

**v = Velocity of the incompressible fluid**

**g = Acceleration due to gravity (value of g is 9.8 meter per square second)**

**D = Diameter of the coil or pipe**

__Pressure loss equation:-__

__Pressure loss equation:-__

In a cylindrical coil or pipe where incompressible fluid is flow in a motion, the cylindrical coil or pipe which have a uniform diameter D, the pressure loss is appear during the viscous effect which is express as Δp is directly proportional to the length of the cylindrical coil or pipe can be express as with the help of Darcy – Weisbach equation,

Where,

Δp/L= The amount of pressure loss of per unit length is, which express as Pacals per meter

f_{D} = Coefficient of friction factor or Coefficient of friction factor

v = Velocity of the **incompressible fluid** which is express as meter per second

D_{H}= Hydraulic diameter which express as meter

ρ = The density of the fluid which is express as kg per cubic meter

__Head loss form:-__

__Head loss form:-__

The term of head loss which is express as Δh is the pressure loss appears for reason of friction in term of same length of a column of the incompressible fluid.

The mathematical form of the head loss is,

Δp =ρgΔh

Δh= The head loss appears for reason of friction in term of same length of a coil or pipe and unit is meter.

g = Acceleration due to gravity (value of g is 9.8 meter per square second)

It is beneficial the head loss appears for reason of friction in term of same length of a coil or pipe is,

Where,

L = Length of the coil or pipe and unit is meter

Darcy – Weisbach equation can be writing for head loss,

__In form of volumetric flow:-__

__In form of volumetric flow:-__

The relation between volumetric flow rate and mean flow velocity is,

Q = A * <v>

Where,

Q = Volumetric flow rate unit is cubic meter per second

A = Cross sectional area of the coil or pipe and unit is square meter

v = Velocity of the incompressible fluid which is express as meter per second

In a coil or pipe the fluid is flow with pipe diameter D_c,

Darcy – Weisbach equation can be written as,

__Shear stress form:-__

__Shear stress form:-__

Darcy – Weisbach equation can be in form of shear stress,

**How to calculate Darcy friction factor?**

**How to calculate Darcy friction factor?**

**The process of calculating friction factor for turbulent flow is given below,**

**At first we need to determine the value of Reynolds number for the turbulent flow using this formula,****ρ**x V x D x μ**In the next step relative roughness should be calculated using \frac{k}{D} formula which value to under 0.01****In the final step use the Moody formula for the roughness with the help of Reynolds number,****f = 0.0055 x [1 + (2 x 10^4 x k/D +10**^{6}/Re)^{1/3}

**Darcy friction factor for laminar flow:**

**Darcy friction factor for laminar flow:**

**Darcy friction factor for laminar flow can be written as,**

__Darcy friction factor for laminar flow in Circular pipes:-__

__Darcy friction factor for laminar flow in Circular pipes:-__

f_{D} = 64/Re

Where,

Re = Reynolds number

Where,

μ= Viscosity of the incompressible fluid

v = μ/ρ

__Darcy friction factor for laminar flow in Non Circular pipes:-__

__Darcy friction factor for laminar flow in Non Circular pipes:-__

f = K/Re

Range of the Darcy friction factor for laminar flow in Non Circular pipes is,

__Laminar flow:-__

__Laminar flow:-__

- When the value of Reynolds number is less than 2000 this type of flow called laminar flow.
- Mathematical analysis of the turbulent flow is easy.
- Velocity of the turbulent flow is too low.
- Regular movement is appearing in fluids which are flow in a motion in laminar flow.
- Laminar flow in general very rare type of flow.
- The velocities profile of the flow laminar the wall of the pipe or rod maximum.
- The velocity profile of the flow laminar in the center section of the rod or pipe is minimum.
- Average motion is appearing in which side fluid is flowing.

**Darcy friction factor for turbulent flow:**

**Darcy friction factor for turbulent flow:**

Maximum system of the fluid in the nuclear facilities is work with the flow type of turbulent flow. The resistance of this flow obey the equation of Darcy – Weisbach.

**The friction of the turbulent flow is measurement of the shear stress which is applied in the wall of a rod or pipe during the flow of turbulent. The flow of turbulent is obeying the equation of Darcy – Weisbach which is directly proportional to square of mean velocity of the flowing fluid in a certain area**.

__Turbulent flow:-__

__Turbulent flow:-__

- Reynolds number is more than 3500 .
- Velocity is too high.
- Irregular movement is appearing
- Average motion is appearing in which side fluid is flowing.
- The velocity profile of the flow turbulent in a certain area is quickly drops when it comes to the wall of the pipe or rod.
- The velocity profile of the flow turbulent in a certain area is clearly flat when it comes to the center section of the rod or pipe

__Friction factor for turbulent flow formula:__

__Friction factor for turbulent flow formula:__

The Colebrook–White equation is define as f for the Darcy friction factor, the function of for Reynolds number as R_{e}, pipe relative roughness express as, ε / Dh for both smooth pipes and rough pipes.

**The friction factor for turbulent flow formula is,**

or,

Where,

D_{h} (m , ft) = Hydraulic diameter for filling the fluid in circular conduits

D_{h} = D= Inside diameter of the area from where flow of turbulent is flowing

R_{h} (m , ft) = Hydraulic radius for filling the fluid in circular conduits

R_{h} = D/4= Inside diameter of the area from where flow of turbulent is flowing/4

The equation of Colebrook is solved by numerically for its implicit nature. Now a day Lambert W function is also use to obtain outspoken reformulation the equation of Colebrook.

a = 2.51/R_{e}

or,

10^{-1/2} = ax +b

p = 10^{-1/2}

We will get,

p^{x} = ax + b

__Expanded forms:-__

__Expanded forms:-__

Additional mathematical form of the equation of Colebrook is,

Where,

1.7384…. = 2 log (2 * 3.7) = 2 log (7.4)

18.574 = 2.51 * 3.7 * 2

And,

Or,

Where,

1.1364…. = 1.7384… = – 2 log (2) = 2 log

(7.4) – 2 log (2) = 2 log (3.7)

9.287 = 18.574/2 = 2.51 * 3.7

**Darcy friction factor chart:**

**Darcy friction factor chart:**

Darcy friction factor chart is combination of four physical parameters such as, pressure loss coefficient, Reynolds number, and **relative roughness** of the coil or pipe and diameter ratio of the coil or pipe.

**Darcy friction factor chart is dimensionless physical factor with the help of Darcy – Weisbach equation can be written as,**

Pressure drop can be calculate as,

Or,

**The expression for Darcy friction factor for laminar flow is,**

In the flow of turbulent the relation between Reynolds number represent as Re, friction factor represent as f_{D}, and relative roughness represent as ∈/D is complicated.

**The expression for Darcy friction factor for turbulent flow is,**

**Darcy friction factor for different materials:**

**Darcy friction factor for different materials:**

**The Darcy friction factor for different material is given below,**

Pipe material | Absolute roughness | |

Feet | Microns | |

Copper or drawn brass | 0.000005 | 1.5 |

Commercial steel | 0.000150 | 45 |

Concrete | 0.001 – .01 | 300 – 3000 |

Wood stave | 0.0006 – 0.003 | 200 – 900 |

Wrought iron | 0.000150 | 45 |

Riveted steel | 0.003 – 0.03 | 900 – 9000 |

**Darcy friction factor for pipe:**

**Darcy friction factor for pipe:**

**The moody chart or friction factor for pipe is plotted the relative roughness of a coil or pipe which is express as ∈/D** ** and Reynolds number.**

**Darcy friction factor for water:**

**Darcy friction factor for water:**

**The moody chart or friction factor is for water derives as the pressure loss of water n a coil or pipe for the reason of friction between the pipe and the water flow inside of it.**