22.2.2. Wall Shear Stress Computation

If you look at this any of the pipe flow we can have a laminar flow, the turbulent flow or the transitional in between the laminar and the turbulent flow. What the experiment is conducted by the Nikuradse is that with having very simple concept that the pipe put it with a roughness, this equivalent roughness is from the sand grains. This figure is shown it with a zoomed with a 20 times.

Wall shear stress refers to the frictional force acting on the wall of a conduit (like a pipe) due to the flow of fluid. When this fluid moves, it layers close to the wall experience different velocities, which can be laminar (smooth) or turbulent (chaotic) depending on factors like the pipe diameter and fluid speed. In 1930s, Nikuradse conducted crucial experiments to better understand how flow behaved in pipes with rough surfaces introduced by materials like sand grains. His work involved varying degrees of pipe roughness to observe how it affected wall shear stress.

Imagine rubbing your hand along a smooth wall versus a rough brick surface. The smooth wall feels different because there's less friction (lower shear stress), while the rough wall creates more resistance against your hand's motion (higher shear stress). This is similar to how fluids experience different shear stresses based on the surface they flow over.

The also we know very well the Reynolds numbers also control the flow behaviors. So that way to know it what is will be the wall stress the tau value, what could be the velocity distributions, what could be the energy losses when you have a pipe length of L with the informations about the roughness, informations about flow Reynolds numbers.

The Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is calculated based on medium speed, viscosity, and characteristic length (like diameter for pipes). When the Reynolds number is low, it indicates laminar flow, while a high value indicates turbulent flow. Understanding the Reynolds number helps in determining wall shear stress, velocity distribution within the pipe, and energy losses due to friction as fluid moves along a pipe of length L, factoring in roughness and flow characteristics.

Think of riding a bicycle in calm weather versus a windy day. On a still day (similar to low Reynolds number), your ride is smooth (laminar flow), but on a windy day (high Reynolds number), the bike feels more unstable and hard to control (turbulent flow). The conditions around you impact how smoothly you can ride, much like how fluid behaves differently in pipes based on its Reynolds number.

If you look at this any of the pipe flow we can have a laminar flow, the turbulent flow or the transitional in between the laminar and the turbulent flow. What the experiment is conducted by the Nikuradse is that with having very simple concept that the pipe put it with a roughness, this equivalent roughness is from the sand grains. This figure is shown it with a zoomed with a 20 times. That means you can see there is quite random the sand grains are roughened it or put it in here such a way that it can create a roughness on the wall of the pipe.

Nikuradse set up a series of experiments using pipes with controlled roughness by coating their interiors with sand grains. This method allowed him to examine different flow behaviors, specifically focusing on how pipe surface roughness impacted wall shear stress and energy loss. His findings provided crucial correlation between the friction factors of turbulent flow and parameters like roughness and Reynolds number, leading to the development of the Moody chart, which is still widely used today.

Consider how driving on a bumpy gravel road versus a smooth asphalt road affects your car's speed. On gravel, the car experiences more resistance due to the rough surface, similar to how flow experiences friction in a rough pipe. Nikuradse’s experiments showed us how this resistance can vary, helping engineers design better systems.

Now if you look it that by conducting a series of experiments, by Nikuradse finally bring a the friction factors relations with the Reynolds numbers which is Moody chart and we have been using that for designing all this pipe flow networks for the industry.

Through careful experimentation, Nikuradse established relationships between wall shear stress, velocity, and the pipe's roughness, resulting in what is known as the Moody chart. This chart illustrates how friction factors vary with different flow conditions, allowing engineers to design efficient pipe systems by anticipating energy losses based on known parameters like flow rate and pipe texture.

You can think of this like shopping. If you know the price and tax rate (similar to friction factors), you can better estimate your total expense before checkout. Similarly, engineers can use the Moody chart to predict how much energy will be lost in a piping system before it is built.

--