22.6.5. Turbulent Flow in Noncircular Conduits

Now coming to the noncircular conduits, many of the times also we do not go for only the circular conduits or the circular pipes from one point to other points okay.

In fluid mechanics, flow is often considered through circular pipes. However, there are instances where we deal with noncircular conduits. These can include rectangular, triangular, or any other non-round shapes. Such conduits present unique challenges, and the principles used for circular pipes may need adaptation for noncircular configurations.

Think of water flowing through a garden hose, which is circular, versus water flowing through a ditch that's rectangular in shape. Both will allow water movement, but the way they handle flow is very different due to their shapes.

But when you go for a noncircular case you need to define as a equivalent flow okay. So that means we introduce a hydraulic diameters okay, it is called as hydraulic diameters, which is a functions of area and wetted perimeter.

To analyze the flow in noncircular conduits, we often use a concept called 'hydraulic diameter.' This is defined using the cross-sectional area of flow and the wetted perimeter (the part of the perimeter that is in contact with the liquid). The hydraulic diameter allows us to convert the noncircular shape parameters into something we can analyze similarly to circular pipes.

Imagine measuring the effectiveness of a straw versus a funnel. Both can hold and move liquid differently based on their shapes. The hydraulic diameter acts as a way of measuring how effectively a noncircular shape can move fluid in comparison to a circular one.

Now if you look it that when you have a noncircular pipe like if you have a pipe like a triangular shape okay. So in this case what will happen the if you have a laminar flow you will have a wall stress will be maximum near the mid points of the sides.

In noncircular pipes, like a triangular shape, the flow changes compared to a circular pipe. For laminar flow in triangular conduits, the wall shear stress (the frictional force exerted by fluid on the wall of the conduit) peaks at the midpoints of each side. This non-uniform distribution contrasts sharply with circular pipes, where the stress is distributed more evenly.

Consider how a flowing river behaves at the bends and curves of its banks. Similarly, water flows differently around the edges of a triangular pipe, causing varying pressures and stresses, just as it does around the contours of the land.

Now if you look it that if you have the turbulent flow same case you have a turbulent flow the velocity distributions as well as the wall shear stress distributions exchanges it.

In turbulent flow within noncircular conduits, the dynamics change significantly. Unlike laminar flow, turbulent flow has a more chaotic structure which leads to different velocity patterns and wall shear stress distributions. This means that the distribution of velocity is not uniform and changes interactively across the flow area.

Think of mixing paint with a brush. When you stir gently, the paint moves predictably (laminar), but when you vigorously mix it, the colors swirl erratically (turbulent). This chaos in turbulent flow leads to different frictional effects in noncircular shapes.

Now coming back to the velocity profile, or the shear stress at the boundary. Here we divide into two zones as suggested by Nikuradse by conducting a series of experiment, finding out velocity profiles for the turbulent flow where you have the flow Reynolds number less than three million.

Nikuradse's experiments helped identify two distinct flow zones within turbulent conditions based on the Reynolds number. For Reynolds numbers below three million, the flow shows a certain velocity profile that's somewhat predictable, breaking into layers due to the varying speed throughout the cross-section of the pipe.

Imagine layering different liquids in a jar. The lighter liquid floats on top, while the denser one settles at the bottom. Similarly, different flow velocities create distinct zones or layers in turbulent flow.

When you have the Reynolds numbers more than 3 millions, then there is certain zone of the velocity profile develops.

For Reynolds numbers exceeding three million, the behavior of the flow adjusts further, resulting in more complex layers, especially adjacent to the wall of the conduit. In this region, the flow acts more like laminar, showcasing high viscosity until further away from the wall, where turbulence reigns free.

Consider driving a car on a smooth highway versus off-roading through rough terrain. Close to the edges, it feels smooth, but in the middle of the chaos, it's a completely different experience of speed and pressure.

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