WHAT IS RELATIVE AND ABSOLUTE ROUGHNESS? - PHYSICAL - 2025

Relative roughness and absolute roughness are two terms that are used to describe the set of irregularities existing inside commercial pipes that transport fluids. The absolute roughness is the mean or average value of these irregularities, translated into the mean variation of the internal radius of the pipe.

Absolute roughness is considered a property of the material used and is usually measured in meters, inches, or feet. For its part, the relative roughness is the quotient between the absolute roughness and the diameter of the pipe, being therefore a dimensionless quantity.

Figure 1. Copper pipes. Source: Pixabay.

Relative roughness is important since the same absolute roughness has a more marked effect on thin pipes than on large ones.

Obviously the roughness of the pipes collaborates with friction, which in turn reduces the speed with which the fluid moves inside them. In very long pipes, the fluid may even stop moving.

Therefore it is very important to evaluate the friction in the flow analysis, since to maintain the movement it is necessary to apply pressure by means of pumps. Compensating for losses makes it necessary to increase the power of the pumps, affecting costs.

Other sources of pressure loss are the viscosity of the fluid, the diameter of the tube, its length, possible constrictions and the presence of valves, taps and elbows.

Origin of roughness

The inside of the pipe is never completely smooth and smooth at the microscopic level. The walls have irregularities in the surface that depend largely on the material from which they are made.

Figure 2. Roughness inside a pipe. Source: self made.

Furthermore, after being in service, the roughness increases due to scale and corrosion caused by chemical reactions between the pipe material and the fluid. This increase can range between 5 and 10 times the value of the factory roughness.

Commercial pipes indicate the roughness value in meters or feet, although obviously they will be valid for new and clean pipes, because as soon as time passes, the roughness will change its factory value.

Roughness values ​​for some materials for commercial use

Below are the commonly accepted absolute roughness values ​​for commercial pipes:

- Copper, brass and lead: 1.5 x 10 ^-6 m (5 x 10 ^-6 ft).

- Uncoated Cast Iron: 2.4 x 10 ^-4 m (8 x 10 ^-4 ft).

- Wrought iron: 4.6 x 10 ^-5 m (1.5 x 10 ^-4 ft).

- Riveted steel: 1.8 x 10 ^-3 m (6 x 10 ^-3 ft).

- Commercial steel or welded steel: 4.6 x 10 ^-5 m (1.5 x 10 ^-4 ft).

- Asphalt Lined Cast Iron: 1.2 x 10 ^-4 m (4 x 10 ^-4 ft).

- Plastic and glass: 0.0 m (0.0 ft).

The relative roughness can be evaluated knowing the diameter of the pipe made with the material in question. If you denote the absolute roughness as e and the diameter as D, the relative roughness is expressed as:

The above equation assumes a cylindrical pipe, but if not, the magnitude called the hydraulic radius can be used, in which the diameter is replaced by four times this value.

Determination of absolute roughness

To find the roughness of the pipes, various empirical models have been proposed that take into account geometric factors such as the shape of the irregularities in the walls and their distribution.

Around 1933, the German engineer J. Nikuradse, a student of Ludwig Prandtl, coated pipes with grains of sand of different sizes, whose known diameters are precisely the absolute roughness e. Nikuradse handled pipes for which e / D values ​​ranged from 0.000985 to 0.0333,

In these well-controlled experiments, the roughnesses were uniformly distributed, which is not the case in practice. However, these values ​​of e are still a good approximation to estimate how roughness will influence friction losses.

The roughness indicated by the manufacturer of a pipe is actually equivalent to that created artificially, just as Nikuradse and other experimenters did. For this reason it is sometimes known as equivalent sand.

Laminar flow and turbulent flow

The roughness of the pipe is a very important factor to consider depending on the rate of movement of the fluid. The fluids in which the viscosity is relevant can move in a laminar regime or in a turbulent regime.

In laminar flow, in which the fluid moves orderly in layers, the irregularities in the surface of the pipe have less weight and therefore are usually not taken into account. In this case it is the viscosity of the fluid that creates shear stresses between the layers causing energy losses.

Examples of laminar flow are a stream of water coming out of the faucet at low speed, the smoke beginning to gush from a lit incense stick, or the beginning of an ink jet injected into a stream of water, as determined by Osborne Reynolds in 1883.

Instead, the turbulent flow is less orderly and more chaotic. It is a flow in which the movement is irregular and not very predictable. An example is the smoke from the incense stick when it stops moving smoothly and begins to form a series of irregular wisps called turbulence.

The dimensionless numerical parameter called Reynolds number N _R indicates whether the fluid has one or another regime, according to the following criteria:

If N _R <2000 the flow is laminar; If N _R > 4000 the flow is turbulent. For intermediate values, the regime is considered transitional and the movement is unstable.

The friction factor

This factor allows finding the energy loss due to friction and only depends on the Reynolds number for laminar flow, but in turbulent flow, the relative roughness is present.

If f is the friction factor, there is an empirical equation to find it, called the Colebrook equation. It depends on the relative roughness and the Reynolds number, but its resolution is not easy, since f is not given explicitly:

That is why curves such as the Moody diagram have been created, which make it easy to find the value of the friction factor for a given Reynolds number and relative roughness. Empirically, equations that do have f explicitly have been obtained, which are quite close to the Colebrook equation.

Aging pipes

There is an empirical formula to evaluate the increase in absolute roughness that occurs due to use, knowing the value of the factory absolute roughness e _o:

Where e is the roughness after t years elapsed and α is a coefficient with units of m / year, inches / year or foot / year called the rate of annual increase in roughness.

Originally deducted for cast iron pipes but works well with other types of pipe made from uncoated metal. In these, the pH of the fluid is important in terms of its durability, since alkaline waters greatly reduce the flow.

On the other hand, coated pipes or plastic, cement and smooth concrete do not experience notable increases in roughness with time.

References

1. Belyadi, Hoss. Hydraulic Fracturing Chemical Selection and Design. Recovered from: sciencedirect.com.
2. Cimbala, C. 2006. Fluid Mechanics, Fundamentals and Applications. Mc. Graw Hill. 335- 342.
3. Franzini, J. 1999. Fluid Mechanics with Application is in Engineering. Mc. Graw Hill. 176-177.
4. Mott, R. 2006. Fluid Mechanics. 4th. Edition. Pearson Education. 240-242.
5. Ratnayaka, D. Hydraulics. Recovered from: sciencedirect.com.