1.1. Laminar and turbulent flow (Cond.)

So, the question here is, water is flowing between 2 large parallel plates which are 2 millimeters apart. So, that is, means t is 2 millimeter. Determine the maximum velocity, the pressure drop per unit length, that is, dp dx and the sheer stress at the wall of the plate if the average velocity is 0.4 meters per second. And viscosity of water is given as 0.01 poise.

This chunk presents a problem that involves calculating properties of laminar flow between two parallel plates. Given that the plates are 2 millimeters apart and the average velocity of water is 0.4 m/s, students will use these values to derive the maximum velocity, pressure drop per unit length, and shear stress at the wall. The viscosity of water, given as 0.01 poise, must be converted for calculations.

Imagine squeezing a thick liquid like honey between two flat surfaces. How fast can the honey flow? This problem helps us understand similar situations in engineering and nature, where properties like spacing and viscosity affect flow rates.

The given things are t is 2 millimeters or 2 into 10 to the power minus 3 meter, the average velocity is also given 0.4 meters per second, mu is given as 0.01 poise which will be divided by 10 to obtain into 10 to the power minus 3 Pascal second, and the density of water is assumed to be 1000 kilogram per meter cube.

In this section, the relevant parameters for the calculations are clarified. The conversion of viscosity from poise to Pascal seconds is emphasized. Understanding these conversions is crucial for solving fluid dynamic problems accurately.

Think of it like measuring the thickness of syrup. If someone uses the wrong unit (like teaspoons instead of cups), they will miscalculate how much syrup can fit on a pancake. In fluid dynamics, correctly using units is just as crucial.

Now, u is written as minus 1 / 2 mu dp dx into t y minus y square. u max is equal to 1.5 V average. This implies that u max is equal to 1.5 and this is 0.4 from here and that comes out to be 0.6 meters per second. So, that is, the first, the second u max is also written as minus 1 / 8 mu into dp dx t square.

This portion involves deriving equations for maximum flow velocity using known parameters. The connection between average and maximum velocity is established. Understanding the mathematical relationships is important for predicting how fluid will behave under various conditions.

Consider a narrow hose connected to a water faucet. The average water flow rate is smooth, but if you check at the narrowest point, you'd find the water shoots out faster. This is similar to what happens at certain points in laminar flow.

So, tau not is equal to mu du dy at y is equal to 0. So, tau not is mu du, we know u, so, we can differentiate that and obtain minus 1 / 2 mu dp dx into t.

The final calculations focus on determining shear stress at the wall of the plate. Here, differentiation of flow equations is applied to understand how forces act at the boundary of the fluid and solid surfaces. It's crucial for engineers to estimate how materials will withstand stresses.

When you rub your hands together, the force you apply creates friction. This friction is akin to shear stress in fluids where layers of fluid slide past each other and exert forces. It's easy to visualize how turbulence might increase this friction.

Now we are moving slowly to the phenomenon of turbulent flow. So, turbulent motion is an irregular motion which is associated with a random fluctuation of swirling regions of fluid called eddies.

Here, the concept of turbulent flow is introduced, contrasting it with laminar flow. Understanding how and why fluids can transition from a smooth to a chaotic state helps students relate to different real-world fluid dynamics scenarios.

Think of a calm river flowing smoothly (laminar) versus white water rapids (turbulent). The chaotic mixing and swirling in rapids illustrate how speed and obstacles can dramatically change fluid motion.

Osborne Reynolds verified the existence of laminar and turbulent flow regimes by injecting dye streaks into the flow in a glass pipe. He demonstrated that variations in fluid motion could be observed visually.

Reynolds’ experiment helps visualize the concepts of laminar and turbulent flow. It shows how behavior changes depending on flow velocity and viscosity. This foundational experiment is crucial for understanding fluid mechanics.

Imagine dropping food coloring into a glass of water. At low stirring speeds, the color spreads slowly and smoothly (laminar). As you stir faster, the color spirals and creates a mix (turbulent) – similar to what Reynolds observed in his experiments.

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