Frictional loss in pipes refers to the energy lost as fluid flows through a length of the line. Several factors may contribute to this: the fluid’s viscosity, pipe diameter and roughness, pipe length, slope, and fittings. These all contribute to friction, which acts in the opposite direction of flow, leading to a loss in energy.
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Why is Frictional Loss in Pipes Important?
Frictional loss in pipes means a fluid loses energy to friction as it encounters resistance opposite the flow direction. This energy loss must be accounted for in designing a piping system, whether by increasing the output of pumps, or sizing pipes differently, which will cause costs to increase.
Significant Factors That Influence Frictional Loss in Pipes
In simple terms, viscosity is the “thickness” of a fluid. It is a measure of resistance to deformation at a given rate. A simple example is honey vs. water. Pouring honey from a cup takes longer than water. That’s because fluids with a higher viscosity, like honey in this example, experience greater friction.
Internal Pipe Diameter
The inner diameter of the pipe is essential to frictional loss because the more surface area a fluid has in contact with the pipe wall, the greater the friction loss will be. For example, with a small pipe, the fluid flowing through it fills up half of the line; friction loss occurs everywhere the fluid touches the pipe wall. However, in a larger pipe, the liquid is in contact with less surface area, resulting in less friction.
Pipe roughness is a simple concept. Every material has different properties and “roughness,” just like a piece of wood would feel rougher than a piece of glass. The rougher a pipe material is, the more friction it causes with the fluid leading to more significant head loss.
Type of Flow
When fluid flows through a pipe or enclosure, there are two types of flow, laminar and turbulent.
Laminar flow describes when fluid flow is smooth and predictable, while turbulent flow is irregular and chaotic. Again, think back to the river example. The sandy bottom with the smooth, calm flow would be like a laminar flow. At the same time, the rocky, choppy river would resemble a turbulent flow.
Calculating Frictional Loss in Pipes
Calculating the Reynolds number will determine whether the flow is laminar or turbulent. The critical Reynolds number is the limit where laminar flow transitions to turbulent flow. For Newtonian fluids, the commonly accepted critical Reynolds number is 2,100. Calculate Reynolds number by using the equation:
- ρ = the density of the fluid
- v = velocity of the flow
- D = diameter of the pipe
- µ = dynamic viscosity
Darcy Weisbach Formula
Frictional loss in pipes is usually measured in feet or meters of head of the fluid, so this is also known as calculating head loss due to friction. To determine this, use the Darcy Weisbach Formula:
- hL= head loss (ft or m)
- f = friction factor
- L = Length of pipe
- D = inner diameter of the pipe
- v = velocity of the fluid
- g = acceleration due to gravity
- Q = Volumetric flow rate
The friction factor is a function of velocity, roughness, viscosity, and diameter. The method for calculating friction loss depends on the type of flow determined by the Reynolds number. For example, for laminar flow, the friction factor is calculated using the following:
If the flow is turbulent, there are several ways to find the friction factor. The Moody diagram is the most common but is subject to a small margin of error.
This diagram plots the Reynolds number vs. relative pipe roughness, equal to ε/D. The material determines the absolute roughness, ε, as seen in the bottom left of the figure above. Knowing the relative pipe roughness and Reynolds number, the friction factor f can be calculated. Once known, the friction factor is substituted back into the Darcy Weisbach Equation to calculate friction loss, i.e., head loss.
Alternatively, use the Moody Chart calculator below to estimate the friction factor:
If the flow is turbulent, the Swamee-Jain equation is another way to solve for the friction factor. The equation is:
d = Pipe inner diameter
Re = Reynolds number
Friction Loss in a Pipe Example
Problem statement: Water flows through a 100m section of mortar-lined steel with a diameter of 100mm at a rate of 0.5 m/s. What is the friction loss or head loss for this section of pipe?
The first step for this problem would be to calculate the Reynolds number:
Re = 49.85
Since this value is less than the critical Reynolds number for water, the flow is laminar, and use the following equation for the friction factor:
The friction factor is then substituted into the Darcy Weisbach equation to calculate the total head loss:
The total head loss for this section of pipe is 16.3m.
Now, let’s do the same problem with a flow velocity of 25 m/s. First, find the Reynolds number:
Re = 2492.5 > 2100
Based on Reynold’s number, the flow is turbulent. Use the Moody diagram or the Swamee-Jain equation to find the friction factor.
f = 0.3143
Like before, substitute the friction factor back into the Darcy Weisbach equation:
When the flow is turbulent, there is a much higher loss due to friction. The example above is extreme but illustrates one of the main factors of friction loss.