In this article we will discuss about fanning friction factor for laminar flow. Laminar flow is the simplest form of flow in which the layers of fluid do not intersect with each other.
The fluid layers flow very smoothly in a laminar flow, there two other types of flows too which we will discuss in detail in this article. We will first discuss about laminar flow, transient flow and turbulent flow. We will also discuss about their properties. Then we shall discuss about a dimensionless number called as Reynold’s number.
What is laminar flow?
A laminar flow is a type of flow in which the fluid moves in a very smooth manner and the layers of fluid do not intersect each other and rather flow in parallel lines.
To check whether a flow is laminar or not we take help of Reynold’s number. This is a dimensionless number which tells us about the type of flow, whether it is turbulent or transition or laminar flow. In later section of this article we shall study about Reynold’s number.
What is Reynold’s number?
Reynold’s number is a dimensionless number which helps us find the type of flow of fluid The flow maybe laminar, turbulent or transitional. It is very important to know the type of flow while dealing with fluid machinery.
To find the value of Laminar flow, we need the fluid’s kinematic viscosity, density of the fluid and the velocity of the fluid with which it is flowing. The Reynold’s number can also be used to find the frictional losses in the pipe. We shall study more about Laminar flow in this article.
What is Fanning factor?
Like Reynold’s number, Fanning factor is also a dimensionless number that is used while performing calculations in continuum mechanics’ calculations.
It can be defined as the ratio between the local shear stress to the local flow kinetic energy of the fluid. Mathematically, Fanning factor can be given by the following formula-
f is the Fanning factor
Tau is the local shear stress
u is the bulk flow velocity
Rho is the density of the fluid.
What is Fanning factor for laminar flow?
We have discussed in the above sections about both Fanning factor and Laminar flow. Now let us see what is the formula for Fanning factor for a laminar flow.
For a laminar flow, Fanning factor is given using the formula given below–
Re is the Reynold’s number
How do you calculate Fanning’s factor?
In simple terms, a quarter of Darcy’s friction factor gives us Fanning’s friction factor. The formula for Fanning’s friction factor is different for different types of flows.
We shall discuss about the formula used in laminar flow. For a fluid flowing in round tube with laminar flow, the Fanning factor will be given by the following-
Re is the Reynold’s number
Is Friction Factor higher with laminar flow?
Yes. The friction factor is higher with laminar flow. We can prove this by looking at the formula of friction factor. We have already discussed the formula for friction factor in the above section.
From the formula we can see that the friction factor is inversely proportional to Reynold’s number. Reynold’s number is least for a laminar flow hence resulting into higher value of friction factor.
Fanning friction factor use
The name itself suggests that the friction factor is related to friction. And we know how important it is to know the amount of frictional losses taking place in the flowing fluid.
It is also important to know a rough estimate of losses in kinetic energy taking place due to head loss and pressure loss. Fanning friction factor helps us to find the values of these quantities. By knowing these values we can design the pipes accordingly to avoid much loss due to friction.
Friction factor units
We have studied about the formula for finding the friction factor. If we work out the units of all the quantitites that have been used in the formula we will see that everything cancels out and the ratio comes out to be 1.
Hence we can conclude that the Fanning’s friction factor has no units. Just like Reynold’s number it is a dimensionless number. The factor in itself is a ratio between two similar quantities hence the friction factor has to be dimensionless.
Fanning friction factor formula
Fanning friction factor is the ratio between the local shear stress and the kinetic energy density of flow. We have already discussed the formula in the above sections but we shall study about it one more, this time for turbulent flow also.
The section below gives us the Fanning’s friction formula for both laminar and turbulent flow of a fluid flowing in a round pipe-
The Fanning friction formula for a fluid flowing in a laminar flow in a round pipe is given below-
f = 16/Re
The Fanning friction factor formula for a fluid flowing in a turbulent flow in a round pipe is given below-
Fanning friction factor pressure drop
Friction is the major reason for pressure drop to take place. The friction will decrease the velocity of the flow of the fluid and also decreases the pressure as the fluid flows in the pipe.
The pressure drop is directly proportional to the Fanning friction factor. Greater the value of Friction factor greater will be the pressure drop against the ends of pipe. Hence we can say that pressure reduces as the fluid flows through the pipe.
Factors affecting Reynold’s number
The formula of the Reynold’s number is given below-
From the above formula we can conclude that the value of the Reynold’s number depends on the density of the fluid flowing, its dynamic viscosity, velocity with which the fluid is flowing and the equivalent diameter of the cross section through which the fluid is flowing.
How are Darcy’s Friction Factor and Fanning’s friction factor related?
Both Darcy’s friction factor and Fanning’s friction factor represent the amount of friction taking place inside the fluid and tells us how much pressure drop is taking place inside the pipe.
Mathematically, Darcy’s friction factor is four times the Fanning’s friction factor. Both of these factors identical and represent the same quantity that is friction and are also used to find the same thing that is pressure drop. The only difference between them being the factor four that is multiplied by Fanning’s friction factor to find the value of Darcy’s factor.
Reasons for pressure drop inside a pipe
There can be many reasons for pressure drop to take place for a fluid flowing inside a pipe. Some of the reasons are given in the list below-
- Friction from the walls of pipe will decrease the pressure of the fluid. The pressure of the fluid exiting the pipe will be lesser than the pressure of the fluid entering the pipe.
- Bends in or narrowing of a pipe also contribute to the pressure drop inside the pipe.
- Obstructions inside a pipe
- Sensors attached inside the pipe that also acts as additional obstructions to the flowing stream of fluid.
- Leaks in side the walls of the pipe.
- Leaks fro the equipment installed on the pipe.
Hi ….I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.