22.4. Bernoulli Experiment

This is what the verification of Bernoulli equations in fluid mechanics lab in IIT, Guwahati. If you look at these ones, it has two tubes to maintaining the contents in supply heads. There is two tanks are there, which is maintaining the supply heads and here, you have a venture meters.

In this first chunk, we are introduced to the Bernoulli experiment conducted at IIT Guwahati. The purpose of this experiment is to verify the Bernoulli equations, which are fundamental in fluid mechanics. The setup involves two tubes that help maintain fluid in tanks, along with venturi meters, which are critical for measuring changes in fluid flow and pressure as the fluid moves through the apparatus.

Consider this experiment similar to a water slide in a water park. The slide starts wide and then narrows down before expanding again. As water flows down the slide, it speeds up when entering the narrow part. Similarly, in this experiment, fluid speeds up and slows down in different sections, just like the water on the slide.

So, there is a decreasing of the cross section area, then increasing. So, you have a converging zone, then it follows diversion gauge zone. So, if you conduct series of pressure meters which measure the pressures or the velocity head. If you look at that, this venture meters have a converging zones and the diverging zones.

This section discusses the functioning of the venturi meters used in the experiment to measure the pressure and velocity of fluid flow. A venturi meter has two main parts: a converging zone where the cross-sectional area decreases and a diverging zone where it increases again. According to the principle of continuity and Bernoulli's principle, the velocity of the fluid increases as it passes through the narrower part of the meter, leading to a decrease in pressure.

Think of drinking through a straw. When you put your thumb over the top of the straw, you create a narrow opening. The liquid inside the straw speeds up as it passes through that narrow section, just like the fluid in a venturi meter. Meanwhile, the pressure drops in that section, creating a situation where you can measure how fast the liquid is moving.

As we know, for a particular discharge, constant discharge, we can have a 11 pressure meters locations, where the radius are different, area of the flow is different, and the velocity will be different. That is what, so discharge is same since the area of the flow is varies.

This part elaborates on the concept of discharge, which is the volume of fluid that passes through a given surface per unit time. Despite variations in the flow area and velocity at different points along the venturi meter, the discharge remains constant. The experiment measures the pressure at multiple points (11 locations) to demonstrate how these different areas impact fluid velocity, aligning with Bernoulli’s equation.

It’s similar to a traffic situation: on a narrow road (smaller cross-section), more cars (higher velocity) pass through a point than on a broader road, where cars must slow down. Even though the number of cars (discharge) remains constant, the flow rate changes based on the width of the roadway.

This very simple thing, the discharge is equal to area into velocity. If area decreases velocity increases, that is what we got it. And we measure the velocity head, compute the velocity head, we have with a pressure head.

This section discusses the verification of Bernoulli's principle by demonstrating that the total mechanical energy (or total head) of the fluid remains the same along a streamline. By measuring the pressure head and velocity head at different points, the experiment shows how variations in area affect both velocity and pressure, which is consistent with the conservation of energy as described by Bernoulli’s equation.

Imagine a roller coaster: as the cart climbs to a high point (increased potential energy), it slows down (reduced velocity). As it descends, it speeds up (increased velocity) while losing potential energy. Just like in our experiment, where energy transforms between pressure and velocity, in the roller coaster, energy converts between potential and kinetic forms while conserving total energy.

Equating these, if you look it, more or less the total head is the same, that means we have verified it that the total head along a streamline when going through a venture meters, it has the same value.

In this chunk, it is emphasized that the computed total head (the sum of pressure head and velocity head) remains constant for the fluid moving through the venturi meter under steady conditions. This consistency serves as a practical verification of Bernoulli's equation, reinforcing the principle that energy is conserved within a fluid flow.

Imagine filling a balloon with air. As you squeeze it (similar to narrowing the tube), the air inside compresses and its pressure increases. Conversely, if you let go, the balloon expands (wider area) and the pressure decreases, demonstrating how similar concepts of energy conservation apply even in simple everyday examples.

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