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9.2.3 - Atmospheric Pressure and Gauge Pressure

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Understanding Atmospheric Pressure

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Teacher
Teacher

Today, we will start by discussing atmospheric pressure, which is the weight of air above us. Can anyone tell me how we detect this pressure?

Student 1
Student 1

Isn't it measured using a barometer?

Teacher
Teacher

Exactly! A barometer is a device that measures atmospheric pressure. Researcher Torricelli invented the mercury barometer by using a column of mercury to indicate air pressure. Can anyone tell me what height corresponds to 1 atm in a mercury barometer?

Student 2
Student 2

It’s about 76 cm, right?

Teacher
Teacher

Correct! This concept is significant in understanding how pressure works in fluids. Remember: **Height = Pressure**. A mnemonic to help you remember this is HAP — Height Affects Pressure.

Student 4
Student 4

So, higher altitudes mean lower pressure?

Teacher
Teacher

Yes, as we move higher up, atmospheric pressure decreases, which proves to be vital for things like weather predictions. Good thinking! Now let’s recap: atmospheric pressure is measured in mmHg or Pa, and Torricelli’s barometer is key in depicting this.

Concept of Gauge Pressure

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Teacher
Teacher

Moving on, let’s discuss gauge pressure. What does the term 'gauge pressure' mean?

Student 3
Student 3

It's the pressure relative to atmospheric pressure, isn’t it?

Teacher
Teacher

Exactly! Gauge pressure = Total pressure - Atmospheric pressure. Can anyone think of examples where gauge pressure applies?

Student 1
Student 1

Like in car tires or in medical tools like sphygmomanometers?

Teacher
Teacher

Yes! Both are great examples. The pressure in tires is often shown as gauge pressure and requires maintenance for proper function. Remember: **Gauge=Total-Atmospheric** to gauge your pressure!

Student 2
Student 2

What happens if gauge pressure is negative?

Teacher
Teacher

Good question! Negative gauge pressure means that the internal pressure is less than atmospheric pressure, possibly creating a vacuum. Always remember: gauge pressure emphasizes how the pressure we measure is relative to the environment around it.

Effects of Depth on Pressure

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Teacher
Teacher

Let’s dive into how pressure behaves in fluids at depth. What happens to pressure as you go deeper into water?

Student 4
Student 4

It increases, right? That’s what the equation P = Pa + ρgh is about.

Teacher
Teacher

Correct! This equation shows us that pressure not only depends on atmospheric pressure but also on the fluid’s density and the height of the fluid column. A memory trick is to think of **P=Pa + D x H**, where D is density and H is height.

Student 3
Student 3

So, does that mean at a certain depth, you can measure gauge pressure too?

Teacher
Teacher

Exactly! The gauge pressure at a certain depth in a fluid can be calculated as Pg = ρgh, which is the additional pressure exerted by the fluid column above a point.

Student 1
Student 1

That’s fascinating! So, deeper means greater pressure all around.

Teacher
Teacher

Precisely! The more we understand depth and pressure, the more effectively we can understand hydraulic systems, submarines, and even understand the ocean floor.

Introduction & Overview

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Quick Overview

This section discusses atmospheric pressure and gauge pressure, defining their significance in understanding fluid behavior.

Standard

The section explains atmospheric pressure as the weight of a column of air, introduces the concept of gauge pressure, and highlights methods for measuring pressure, including mercury barometers and manometers. It emphasizes the effects of pressure and variations with depth in a fluid.

Detailed

Atmospheric Pressure and Gauge Pressure

Atmospheric pressure is defined as the weight of a column of air above a point, measured typically at sea level as 1.013 × 10^5 Pa (or 1 atm). The historical method for measuring atmospheric pressure was pioneered by Torricelli through the mercury barometer.

In a barometer setup, a closed tube filled with mercury, inverted in a tray, illustrates how atmospheric pressure supports a mercury column of approximately 76 cm at sea level, equating to basic principles of pressure equilibrium. Following Torricelli's work, various pressure-measuring tools, like manometers (U-tube devices), help in determining gauge pressure, which is the pressure relative to atmospheric pressure. This is significant in many practical applications, from meteorology to engineering, where understanding fluid behaviors under varying pressures is essential.

Moreover, the section introduces the principle that at increased depths in a fluid, pressure increases linearly, governed by the equation P = Pa + ρgh, illustrating how pressure is influenced by height and density. The gauge pressure at depth is determined by P − Pa. This principle aids in comprehending the mechanical properties of fluids and has applications in various scientific fields.

Youtube Videos

Class 11th – Atmospheric and Gauge Pressure | Properties of Fluids | Tutorials Point
Class 11th – Atmospheric and Gauge Pressure | Properties of Fluids | Tutorials Point
ATMOSPHERIC PRESSURE | PHYSICS CLASS 11
ATMOSPHERIC PRESSURE | PHYSICS CLASS 11

Audio Book

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Definition of Atmospheric Pressure

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The pressure of the atmosphere at any point is equal to the weight of a column of air of unit cross-sectional area extending from that point to the top of the atmosphere. At sea level, it is 1.013 × 10^5 Pa (1 atm).

Detailed Explanation

Atmospheric pressure is the force exerted by the weight of air in the atmosphere on a given area. It is defined as the pressure due to a column of air extending from the point of measurement to the top of the atmosphere. At sea level, this pressure is measured to be approximately 1.013 × 10^5 Pascals, which is equivalent to 1 atmosphere (atm). This means that at sea level, 1 square meter area is pushed down by the weight of the air directly above it, creating pressure.

Examples & Analogies

Consider holding a balloon. The air inside the balloon exerts pressure on the inner walls, which is a result of the atmospheric pressure acting on the outside. If you take the balloon up a mountain, you'll notice it expands because the atmospheric pressure decreases with altitude. This shows how atmospheric pressure can change based on your location.

Measurement of Atmospheric Pressure

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Italian scientist Evangelista Torricelli (1608–1647) devised for the first time a method for measuring atmospheric pressure. A long glass tube closed at one end and filled with mercury is inverted into a trough of mercury as shown in Fig. 9.5 (a). This device is known as ‘mercury barometer’. The space above the mercury column in the tube contains only mercury vapour whose pressure P is so small that it may be neglected.

Detailed Explanation

Evangelista Torricelli created the mercury barometer, which is a device used to measure atmospheric pressure. In this design, a long glass tube that is sealed at one end is filled with mercury and then inverted into a container (or trough) of mercury. The mercury in the tube will drop to a certain height, and the weight of the mercury column is balanced by the atmospheric pressure pushing down on the mercury in the trough. This allows us to quantify the atmospheric pressure based on the height of the mercury column. The vapour pressure of mercury above the liquid in the tube is so negligible that it does not affect the reading significantly.

Examples & Analogies

Think of a soda can. When you open the can, the pressure inside is suddenly released, and the soda rushes out. Similarly, the mercury barometer works by measuring how much the atmospheric pressure pushes down on the column of mercury to maintain balance. Just as the pressure in the can is important to keep the soda inside, atmospheric pressure is crucial for understanding our environment.

Pressure Calculation in the Barometer

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Thus, the pressure at Point A=0. The pressure inside the column at Point B must be the same as the pressure at Point C, which is atmospheric pressure, P a. Pa = ρgh (9.8).

Detailed Explanation

In the barometer, when it is inverted, the pressure at the top of the mercury column (Point A) is considered to be zero because it is in a vacuum. The pressure at Point B (inside the mercury column) must equal the atmospheric pressure at Point C because they are at the same level. Therefore, using the equation Pa = ρgh, where ρ is the density of mercury, g is the acceleration due to gravity, and h is the height of the mercury column, we can derive the atmospheric pressure based on the height of mercury.

Examples & Analogies

Imagine filling a straw with juice, and when you put your finger over the top of the straw, the juice stays in the straw even when you pull it out. The atmospheric pressure on the juice in the glass is what holds the juice in the straw and allows you to drink. Similarly, in the barometer, it’s the atmospheric pressure holding up the column of mercury against gravity.

Common Pressure Units

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A common way of stating pressure is in terms of cm or mm of mercury (Hg). A pressure equivalent of 1 mm is called a torr (after Torricelli). 1 torr = 133 Pa.

Detailed Explanation

Pressure can be measured in various units, one of the most common being in terms of millimeters of mercury (mmHg). This unit dates back to the use of mercury barometers. One mmHg is also known as a torr, named after Evangelista Torricelli. Additionally, 1 torr is defined as equal to 133 Pascals (Pa), which is a unit in the International System of Units (SI) for measuring pressure.

Examples & Analogies

When you go for a medical check-up, the doctor often checks your blood pressure using a sphygmomanometer, which may give values in mmHg. For instance, a reading of 120/80 mmHg means your blood pressure is 120 mmHg during heartbeats and 80 mmHg in between beats, showcasing how pressure measurements are applied in everyday life.

Gauge Pressure Explanation

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What we normally measure is the gauge pressure, which is P − Pa, given by Eq. (9.8) and is proportional to manometer height.

Detailed Explanation

Gauge pressure is the pressure of a fluid measured above the atmospheric pressure. In simple terms, it indicates how much pressure is present over and above the surrounding atmospheric pressure. It is calculated using the equation P = P at the measuring point minus Pa, the atmospheric pressure. The height of the liquid in a manometer displays this gauge pressure; the higher the liquid column, the greater the gauge pressure.

Examples & Analogies

When you inflate a bicycle tire, you use a gauge to check the pressure. If it reads 30 psi, that means there is 30 pounds per square inch of air pressure inside the tire, but this doesn't account for the atmospheric pressure outside, which affects how the tire feels. If you were to measure absolute pressure, you would need to add atmospheric pressure to that reading.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Atmospheric Pressure: The weight of the air above a point.

  • Gauge Pressure: Pressure relative to atmospheric pressure.

  • Barometers: Devices used to measure atmospheric pressure.

  • Pressure Variation: Pressure increases with depth in fluids.

  • Hydrostatic Pressure: Pressure due to the weight of fluid above.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • A mercury barometer measuring atmospheric pressure where 76 cm of mercury indicates 1 atm.

  • Gauge pressure in a car tire indicating pressure above atmospheric pressure for efficiency.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • Pressure rises as you dive, deeper fluids come alive.

📖 Fascinating Stories

  • Imagine diving into the ocean; as you go deeper, the water pushes harder against you, feeling the force increase by the weight of the water above.

🧠 Other Memory Gems

  • Remember HAP for Hydrostatic pressure: Height Affects Pressure.

🎯 Super Acronyms

PAG - **Pressure = Atmospheric + Gauge**, relates to how we think about pressure.

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Atmospheric Pressure

    Definition:

    The weight of air above a point, typically at sea level about 1.013 × 10^5 Pa.

  • Term: Gauge Pressure

    Definition:

    The pressure relative to atmospheric pressure, calculated as the total pressure minus atmospheric pressure.

  • Term: Barometer

    Definition:

    A device used to measure atmospheric pressure, traditionally filled with mercury.

  • Term: Mercury Barometer

    Definition:

    A type of barometer using mercury to measure atmospheric pressure.

  • Term: Pressure Equation

    Definition:

    The formula P = Pa + ρgh, representing the total pressure at a point in a fluid.