4.1. Laminar and turbulent flow (Contd.)

Welcome back to this last lecture of turbulent flow and laminar flows where we are going to talk about turbulent flow in smooth pipes.

In this introduction, the speaker sets the stage for discussing turbulent flow in smooth pipes, indicating that this will build on previous concepts introduced in earlier lectures, particularly focusing on the differences between laminar and turbulent flow.

Think of this as a coach's pre-game speech, where they review previous strategies and lay out the game plan for the upcoming match. Just as players must understand the basics before executing a play, students need to grasp the concepts of smooth and turbulent flow before diving into the details.

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.

Equation 18 discusses how the velocity of fluid flow behaves as it approaches the wall of a pipe. At the wall (y = 0), theoretically, the velocity approaches negative infinity due to the logarithmic nature of the equation. However, as we move away from the wall, the velocity becomes positive, which indicates a gradual increase in flow speed away from the surface.

Imagine a river flowing past a bank. Right at the edge of the river where it meets the bank, the water moves very slowly, almost stagnant, as it encounters friction. But as you move into the river, the water flows rapidly. This analogy can help students visualize how flow behaves near surfaces.

Hence, from equation 18, we can say that at distance y prime C will be minus u star by Kappa ln y prime.

This chunk explains how to derive the velocity profile for turbulent flow in smooth pipes using the logarithmic equation. The relationship shows that the velocity profile is dependent on a few factors including the friction velocity (u*) and a constant (Kappa), which explains how velocity decreases as we approach the wall, following a logarithmic scale.

Consider how the temperature of water decreases as it gets closer to ice in a glass. Right at the ice, the water is colder, but as you move away, the temperature starts to rise, similar to how the velocity changes in proximity to a pipe wall.

Now, again from the Nikuradse’s experiment, y prime actually has been found out to be delta prime.

This section highlights the importance of Nikuradse’s experiments, which provided empirical data to better understand turbulent flow. It defines y prime as delta prime, helping students to see how experimental findings validate theoretical equations, particularly focusing on the thickness of the laminar sublayer.

This can be compared to a scientist in a lab whose experiments either confirm or challenge established theories. For instance, a chemist may postulate that vinegar reacts with baking soda, and through experimentation finds conclusive evidence to support this claim.

Now, we are going to talk about turbulent velocity distribution in terms of average velocity.

The speaker introduces the concept of calculating average velocity in turbulent flow. This will include integrating velocity across a defined area (for example, a cross-section of a pipe) to understand overall flow behavior. The mathematical derivations lead to a comprehensive understanding of how turbulent fluid behaves in real-world pipes.

Imagine averaging the speeds of different cars on a busy highway. Some cars zip by quickly, while others may go slower; however, averaging out these speeds gives a clearer understanding of traffic flow as a whole.

Now, it is a good idea to solve one problem here, on this particular concept, and the solving the problem will give more understanding now.

An example problem is set up to calculate the roughness height of a pipe based on given velocities at different distances from the wall. This helps reinforce the concepts discussed and allows students to apply theoretical knowledge in practical scenarios.

This problem-solving approach is akin to studying math; working through problems helps students grasp concepts better than simply reading definitions. For instance, solving word problems in math helps illustrate how abstract concepts apply to real life.

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