22.6.4. Laminar Flow in Triangular Conduit

If you have 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. It will have a maximum at the midpoint of the side, wall shear stress. Becomes will be zero at this point, zero at this point, okay.

In a triangular conduit with laminar flow, the behavior of wall shear stress is not uniform. It reaches its highest value at the midpoints of the triangular sides and drops to zero at the vertices of the triangle. This distribution indicates how the fluid interacts with the walls of the conduit, with the most friction occurring in the middle where there is maximum contact area.

Imagine having a sliding piece of paper against the wall of a triangular box. If you push down in the middle, the friction is the highest because that’s where the force is applied directly against the wall. If you were to push at the corners, there would be less contact, and hence less friction, similar to how the wall shear stress behaves in a triangular conduit.

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. What we do it in any case of the turbulent flow we also use the Moody’s diagrams. Hydraulic diameters replacing with a D. That is what is used to quantify what could be the energy losses.

In turbulent flow conditions within a triangular conduit, the distribution of velocity and wall shear stress behaves differently compared to laminar flow. Here, the flow becomes chaotic, and the maximum wall shear stress does not occur at the midpoints. Instead, it becomes relatively uniform along the sides. Moody's diagrams, which relate friction factors to Reynolds numbers and pipe characteristics, help quantify energy losses experienced in such turbulent flows.

Think about a river with varying flow conditions. In calm sections (laminar flow), the water flows slowly and smoothly, while in turbulent sections, the water swirls rapidly with eddies forming. Similarly, when water flows through a triangular pipe, under turbulent conditions, it behaves like the chaotic currents observed in a stormy river.

So as you go from away from this circular pipes for this case like a triangular flow zones you have a more complicated the velocity distribution shear stress distribution as compared to the circular pipes as a symmetrical problems what we try to understand it.

When water flows in triangular conduits, the shape induces complex flow patterns, including vortex formations. These vortices lead to changes in both velocity distribution and shear stress compared to what we would find in circular pipes. The irregular geometry of triangular shapes results in different secondary flows that interact with the main current, causing variations in flow characteristics.

Imagine swirling a drink in a triangular glass versus a circular glass. The triangular edges create turbulence in the liquid, resulting in different swirling patterns compared to the smoother circular shape. This illustrates how triangular conduits cause more complex flow behaviors.

Now coming back to the turbulent flow again we can follow the same head loss equations. The head loss is a functions of the velocity head, which is related to energy losses during the flow.

In turbulent flow, head loss can be significant due to the energy lost as fluid flows through the conduit. This head loss relates directly to the velocity head, essentially the kinetic energy per unit weight of fluid. In this case, head loss contributes to determining how efficiently the fluid can be transported through the triangular conduit and is crucial for designing effective pipe systems.

Consider riding a bike uphill versus downhill. When you go uphill (analogous to high head loss), you use a lot more energy compared to when you race downhill (lower head loss). Just like energy is lost climbing, head loss impacts how smoothly and efficiently fluid can flow through a conduit.

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