24.1.2. Applications of Bernoulli Equation

I will start with the applications, very interesting applications I will show to you, then I will go for orifice meter experiment in IIT, Guwahati, then I will talk about kinetic energy corrections factors. That means, for a non-uniform distribution of flow, when you apply this Bernoulli equations, we need to have a corrections factors if we are using average velocity.

In this introduction, the lecturer outlines the focus of the session on various applications of the Bernoulli equation. They will discuss how the equation can be utilized in practical situations, particularly when dealing with flow measurement devices like orifice and venturimeter. Additionally, the lecturer notes that corrections may be needed for kinetic energy calculations, especially with non-uniform flow distributions.

Imagine driving a car on a windy day. If the wind is pushing against your car from the side, the fuel consumption will increase even though you are driving at a constant speed. Similarly, in fluid mechanics, when flow conditions aren't uniform, we must adjust our calculations to get accurate results.

Fourth part, I will talk about how we can define the three different types of pressures; static, dynamic and stagnation pressures.

In this part of the lecture, the importance of distinguishing between three types of pressure in fluid dynamics is highlighted: static pressure, dynamic pressure, and stagnation pressure. Static pressure is the pressure exerted by a fluid at rest. Dynamic pressure measures the pressure due to the fluid's velocity, while stagnation pressure is the total pressure at a point where the fluid is brought to a complete stop.

Think of a garden hose with water flowing through it. The water hits a nozzle creating pressure as it comes to a stop. The pressure felt at the nozzle is the stagnation pressure, which combines both the static and dynamic pressures.

Now come back to where simple experimental setups, we generally do the measuring the flow in a pipe, either in a venturimeter or the orifice meter. The orifice meter is a small device...

This section explains the use of orifice meters and venturimeters in measuring flow rates. It's noted that these devices create areas of differing flow velocities, which leads to energy losses not accounted for in traditional Bernoulli calculations. The introduction of the coefficient of discharge (CD) helps adjust for these discrepancies, allowing us to relate the theoretical discharge predicted by Bernoulli's equation to the actual discharge observed in experiments.

Consider a water slide: when you enter, you're at rest (static pressure), but as you slide down, your speed increases (dynamic pressure). If the slide takes a sharp turn, some energy is lost due to friction, similar to how orifice meters work. The actual experience on the slide (like actual discharge) may differ from what a straight calculation would suggest.

Now, another interesting application of Bernoulli equations is that energy gradient line and the hydraulic gradient line. This is very great simplifications of the fluid flow problems.

The energy gradient line (EGL) and hydraulic gradient line (HGL) are vital concepts derived from Bernoulli's principle, useful for understanding how energy varies along a streamline in a flowing fluid. The EGL represents the total mechanical energy (pressure, kinetic, and potential energy), while the HGL considers only the static and potential energies, omitting the kinetic energy. Drawing these lines helps visualize how energy losses due to friction and other factors affect flow in pipes and channels.

Think of water flowing down a hill: the highest point represents a lot of energy. As it flows down, some energy is lost as the water tumbles over rocks and bends. The EGL is like the hill's slope, showing the total potential energy available, while the HGL shows where the water level would be had it not lost energy to those rocks.

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