22.6. Noncircular Conduits

Now coming to the other case, 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. 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.

Noncircular conduits are pipes that are not circular in shape, such as rectangular or triangular pipes. When dealing with these kinds of pipes, it’s important to introduce a new measurement called 'hydraulic diameter.' This hydraulic diameter helps us to analyze the flow characteristics much like how we would with a circular pipe. Hydraulic diameter is defined as a function of the pipe's cross-sectional area and the wetted perimeter, which is the part of the perimeter that is in contact with the fluid.

Think of it like measuring the size of a room using its area and the length of the walls that are touching the floor. Just as these dimensions help us understand how much space we have, hydraulic diameter gives us insight into how fluid will behave in a noncircular pipe.

which is a functions of area and wetted perimeter. The part of the perimeter which is under wetted conditions, wetted perimeters. Like for example, if I have the flow pipes, it is going through hole, so that way the total perimeter I can consider as wetted perimeter.

Hydraulic diameter is calculated by taking four times the cross-sectional area of the pipe and dividing it by the wetted perimeter. The wetted perimeter represents the surface of the pipe that is in contact with the fluid. If the pipe is half filled with water, then only half of the perimeter is wetted. This distinction is crucial because the characteristics of the fluid flow depend significantly on this wetted area.

Imagine a racetrack. If the track is circular, you can measure a simple diameter. But if the track is oval or another shape, you need to take into consideration the actual area where the racers can run (the part that touches the ground) as opposed to just the perimeter of the track. This analogy reflects how we define the hydraulics of noncircular conduits.

Now come back to the noncircular conduit like you may have a conditions where you have a only flow through this ones okay. That is called circular annulus diameter.

In scenarios where flow occurs in noncircular conduits, we often deal with specific shapes like a circular annulus—a ring-shaped type of conduit. The hydraulic diameter can be derived from the geometry of such shapes. Different cross-sections such as rectangular or triangular can behave differently regarding fluid flow, and by understanding these shapes, we can predict flow behavior like wall shear stress and velocity distributions.

Think of water flowing through a straw and a funnel. The straw is like a circular pipe, but a funnel can be seen as a noncircular conduit. Water flows differently through these shapes, with more turbulence in the funnel. Knowing the shape helps us predict how readily water will flow through.

Now let us come it with 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 laminar flow you will have a wall stress will be maximum near the mid points of the sides.

When analyzing fluid flow in a noncircular pipe, like a triangular pipe, the behavior of the fluid differs from circular pipes. In laminar flow, wall shear stress is highest at the midpoints of the sides and drops to zero at the vertex points of the triangle. This contrasts with circular pipes, where wall shear stress is distributed more evenly. Understanding where stress is highest helps in designing structures to resist these forces.

Imagine a slip-n-slide made from a triangular-shaped slide. Water flows fastest at the steepest middle part and not at the edges. Knowing this helps in figuring out how strong to make the sides to support the water flow without breaking.

If you look at 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.

In cases of turbulent flow within noncircular conduits, the distribution of velocity and wall shear stress become more complex. Unlike laminar flow, where the stress was at its maximum in specific points, turbulent flow creates swirling patterns, impacting how stress is spread throughout the pipe. Moody’s diagram is a tool employed to analyze these conditions and helps predict energy loss due to friction in various flow conditions.

Think of a crowded swimming pool. At times, the water is calm (laminar flow), and it's easy to predict the water's motion. But when everyone splashes around (turbulent flow), the water's movement becomes chaotic and harder to predict. In a similar way, knowing how to analyze turbulent flow in pipes helps us manage these chaotic movements effectively.

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