22.5.2. Pressure Distribution

For nearly horizontal streamtube (blood vein) $\frac{p_1}{\rho} + \frac{v_1^2}{2g} + z_1 = \frac{p_2}{\rho} + \frac{v_2^2}{2g} + z_2$ We can look it, there is a relationship between the pressure and the velocity. So, wherever the pressure increases, the definite the velocity has to decrease or the velocity increases, the pressure decreases.

This equation illustrates the principle of conservation of energy along a streamline, specifically for fluids. When the pressure (p) in a fluid increases, the kinetic energy (related to its velocity, v) must decrease to conserve energy, and vice versa. This implies there’s a trade-off between pressure and velocity in a fluid flow. For example, in a blood vessel, when there’s a restriction, the blood pressure increases, and the velocity decreases, and vice versa when the vessel widens.

Think of a garden hose. When you cover part of the hose with your thumb, the pressure builds up at that point (you feel it push back), and the water shoots out faster at the end where it's free. This illustrates how a small area increases speed while the pressure in the narrower area goes up.

So, those relationships, you can look it from this relationship, which is observed many of the times, okay. Most often I can go back to the cyclonic disasters...

In times of cyclonic storms, the wind velocity increases significantly which can result in lower pressure on the roof. Since the pressure outside the house could be lower than the pressure inside (due to rapid air movement), this pressure difference can lift the roof off. This phenomenon occurs due to the varying velocities and resultant pressures acting on structures in storm conditions.

Imagine blowing across the top of a piece of paper. The paper rises because the air moving faster across its top decreases the pressure above it, while the pressure beneath the paper stays higher, creating lift. In a storm, a similar principle can lift much heavier structures!

If you look at the three mechanisms from a blot bend to the lifting of roof or lifting a wing of an aircraft, all are linked and we solved with a very simple concept of Bernoulli equations.

Bernoulli's principle has practical applications in various fields, including aviation and civil engineering. For aircraft, the wings are designed such that air flows faster over the top of the wing than underneath it, decreasing pressure above the wing and allowing lift. Similarly, in plumbing and fluid systems, Bernoulli’s principle helps in analyzing and predicting flow behavior.

Consider how a paper airplane flies. If designed correctly, the wings create varying air speeds above and below, producing lift and allowing it to fly. Just like this, aircraft wings utilize the same principles of fluid dynamics to achieve lift and fly effectively.

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...

In a laboratory, experiments can validate Bernoulli's equation by measuring pressures at different points along a fluid flow path. By using devices like venturi meters that change the diameter of the pipe, you can observe how pressure drops as velocity increases in a converging section of the tube. This lends practical evidence to the theoretical concepts of fluid mechanics.

Imagine running water through a garden hose that narrows at one point; you can feel it push back harder as it speeds up in the narrow part. This is the same principle we verify in experiments by measuring pressure and flow rates, confirming Bernoulli's equation in action.

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