9.1.2. Applications of Fluid at Rest

Welcome to this lecture on fluid mechanics. As we discussed in the last class fluid at rest and fluid statics we have derived basic equations of fluid statics. That is what the pressure equations with related to gravity field. So now, just we will have a two applications of the fluid at rest or hydrostatic pressure distributions that what I will address as a applications to two cases.

In this chunk, the introduction to the lecture on fluid mechanics highlights the previous discussion about fluid at rest, also known as fluid statics, where fundamental equations relating to pressure due to gravity were derived. This sets the stage for discussing two significant applications: the manometer and pressure distribution on an inclined surface. The lecturer emphasizes the importance of hydrostatic pressure distributions in understanding the behavior of fluids that are not in motion.

Consider how a still lake or a swimming pool demonstrates fluid at rest. The water at the bottom does not move but is still affected by the weight of the water above it. This pressure application is similar to how we will apply hydrostatic principles in practical scenarios like manometers and engineering structures.

Now let us come to the manometer. Very simple devices are used to measure the pressure like you have a, let have these type of conduit, the pipes the carrying any liquids and you want to measure it what could be the pressure on that pipe. So we can just insert the tubes like you can see can have the tube like this or can have a tube like this with inclined and all or you can have a inclined like this.

In this section, the lecturer introduces manometers, which are simple devices used for measuring the pressure of liquids in pipes. Manometers work by using a liquid column to measure pressure differences between two points. They can be designed in various shapes, such as vertical or inclined tubes. The flexibility in design allows for accurate pressure readings depending on the scenario, hence making them useful for various applications, including engineering and laboratory settings.

Imagine a clear plastic straw immersed in a glass of water. When you cover the top of the straw and pull it out of the water, the water remains in the straw due to atmospheric pressure pushing up against it. This basic principle is akin to how a manometer measures the pressure in a pipe system.

The simplest form is a piezometer. What is showing here is a piezometer and to find out the pressure. If you know it pressure at this point is P . P = P . If I taking a point P here and this dimension is atm atm very small as compared to the length of height of this piezometer column.

A piezometer is a specific type of manometer used for measuring static pressure in a fluid. It typically consists of a vertical tube connected to the liquid source. The height of the liquid column in the piezometer correlates with the pressure at that point in the system. If the pressure is atmospheric at the open end, the height of the liquid column measured gives the total pressure acting on the fluid in the pipe. This relationship allows for a straightforward calculation of pressure based on fluid height.

Think of a water well where the water level shows how deep the water source is. The height of the water in the well responds to the surrounding atmospheric pressure in the same way the liquid column in a piezometer responds to pressure changes.

Another case let we have an inclined manometer which is have a quite advantage in the sense that it amplifies the pressure reading as compared when you are talking about low pressure ranges. When you are measuring the low pressure ranges it being inclined so it is a give a easier for us to measure the low pressure as compared to the vertical one.

Inclined manometers are designed to measure low-pressure differences with greater accuracy than vertical manometers. The inclination of the tube allows for a longer liquid column to be measured, which enhances sensitivity to small changes in pressure. This means that even minor variations in pressure can be detected and quantified more easily, making inclined manometers valuable in various laboratory and field applications.

Consider trying to detect subtle changes in temperature with a thermometer. A thermometer with a long, thin tube will show changes more clearly compared to a stubby one. Similarly, an inclined manometer, with its longer measurement, can detect slight pressure changes efficiently.

Now there is another type of manometer which is called the differential manometers. As the name says that here, we do not measure a particular point pressure measurements where you consider two points. Because many of our applications, we are not worried about absolute pressure.

Differential manometers are utilized to measure the pressure difference between two points in a fluid system. Unlike traditional manometers that measure absolute pressure, these instruments focus on the variance in pressure that drives fluid flow. This allows engineers and scientists to understand how systems perform under different pressures, which is crucial for designing and optimizing fluid systems.

Think of differential manometers like a race between two runners. You care more about the difference in speed between them than their individual speeds. Similarly, in many fluid systems, understanding the pressure difference helps in evaluating performance more than knowing pressures at specific points.

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