4. Lecture-16

Welcome back to this last lecture of turbulent flow and laminar flows where we are going to talk about turbulent flow in smooth pipes. Last time in the last lecture we had seen what a smooth and rough bed is based on the Reynolds particle Reynolds number Re*.

In this introduction, the speaker sets the stage by summarizing the previous lecture's focus on Reynolds numbers, which categorize flows into laminar and turbulent types. Now, the attention shifts specifically to turbulent flow in smooth pipes, a key area of study in hydraulic engineering.

Think of driving on a smooth road versus a bumpy one. The smooth road allows for a constant speed and flow, much like turbulent flow in smooth pipes, where the fluid moves uniformly with less resistance compared to rough surfaces.

From the above equation, the velocity at the wall u at y is equal to 0 will be minus infinity, correct. If we put y is equal to 0. So, if we put ln 0, it will be minus infinity. u is positive at some distance far away from the wall.

This statement discusses the behavior of fluid velocity in relation to the position near the pipe wall. At the wall, the fluid velocity is theoretically zero. However, as we move away from the wall (to a point 'y'), the velocity increases. The logarithmic relationship is emphasized because it reveals how fluid velocity changes based on distance from the wall.

Imagine being at the edge of a swimming pool. When you are right at the edge (the wall), you aren’t moving at all. But as you swim away from the wall into the deeper part of the pool, your speed increases significantly.

Hence, from equation 18, we can say that at distance y prime C will be minus u star by Kappa ln y prime. Because if we put y is equal to 0 it is going to be infinity. So, this logarithmic profile does not fit this. Therefore, we assume that u is 0 at some finite distance y dash y prime from the wall.

The speaker explains a mathematical model that describes how velocity behaves in the turbulent flow near pipe walls. The value of 'C' is adjusted to accommodate the logarithmic profile of velocity distribution, indicating that there’s a distance from the wall (not just at the wall) where the velocity can effectively be considered zero.

It's like how the wind behaves around a building. Next to the wall of the building (pipe wall), there’s little to no wind (zero velocity), but a few meters away, the wind speeds up significantly. The logarithmic nature of this relationship helps engineers predict how fluid behaves in various situations.

From the Nikuradse’s experiment, y prime actually has been found out to be delta prime, where this is a thickness of the laminar sublayer viscous sublayer by hundred and seven.

Nikuradse's experiments led to the discovery of the thickness of the laminar sublayer, which is crucial for determining how fluid flows over surfaces. Understanding this thickness helps engineers design more efficient piping systems by enabling better predictions of resistance and turbulence.

Think of a river. Just like the water flows fast in the center but slows down as it brushes the riverbed, the findings from Nikuradse's experiments help us understand and predict how a fluid interacts with surfaces in pipes.

Now, if you take this 30 out, it is . Now, you see, this is the velocity distribution of turbulent flow in rough pipes.

The content discusses the velocity distribution for turbulent flow in rough pipes, which differs from smooth pipes. This difference can significantly affect calculations in hydraulic engineering applications as roughness impacts the friction and resistance experienced by the fluid.

Consider a scenario where you are riding a bike on a smooth road versus a gravel path. The smooth surface allows you to gain speed easily, while the rough surface slows you down. Similarly, the type of surface (rough or smooth) greatly influences the velocity of the fluid in pipes.

Now, we are going to talk about turbulent velocity distribution in terms of average velocity. So, there is a flow and there is an elementary circular ring here, as you can see, this is of radius R.

In this part, a practical example is introduced, focusing on how to determine average velocity in a pipe with turbulent flow. The speaker encourages applying learned equations to real-world problems, which is a critical skill in engineering. This encourages students to engage with the material hands-on.

Imagine measuring the flow of water in a hose. Just like you would calculate how much water passes through a certain length of the hose over time, engineers compute average flow velocity to understand and design piping systems efficiently.

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