PRESURE

Edwin Ogie Library

Pressure: Atmospheric Pressure & Pressure in Liquids

Introduction to Pressure

Pressure is defined as the force applied per unit area. It is a scalar quantity that plays a critical role in many areas of physics and engineering. Pressure is measured in pascals (Pa) in the S.I. system.

In this lesson, we will discuss atmospheric pressure and pressure in liquids. We will look at how pressure is measured with various instruments and understand the principles behind the operation of barometers and manometers. In addition, we will explore how pressure varies with height and its application as an altimeter.

Atmospheric Pressure

Definition

Atmospheric pressure is the force exerted by the weight of the air above a given point. It decreases with increasing altitude.

Units of Pressure

The S.I. unit for pressure is the pascal (Pa), where 1 Pa = 1 N/m². Other common units include the atmosphere (atm), torr, and bar.

Measurement of Pressure

Pressure can be measured using various instruments:

• Mercury Barometer: Measures atmospheric pressure by the height of a mercury column.
• Aneroid Barometer: Uses a small, flexible metal box (aneroid cell) that expands or contracts with pressure changes.
• Manometer: Consists of a U-shaped tube filled with a liquid (often mercury) that indicates pressure differences.

Variation of Pressure with Height

Atmospheric pressure decreases with an increase in altitude. This variation is used to estimate altitude.

Barometer as an Altimeter

A barometer can be used as an altimeter by correlating the atmospheric pressure with altitude. Lower pressure indicates a higher altitude.

Pressure in Liquids

Relationship between Pressure, Depth, and Density

In a liquid, the pressure increases with depth due to the weight of the liquid above. The relationship is given by:

P = ρgh

where P is the pressure at depth, ρ (rho) is the density of the liquid, g is the acceleration due to gravity, and h is the depth.

Transmission of Pressure in Liquids (Pascal’s Principle)

Pascal’s Principle states that when pressure is applied to a confined fluid, the pressure change is transmitted undiminished throughout the fluid. This principle is used in hydraulic systems.

Applications

Pressure in liquids is applied in various devices such as hydraulic lifts, braking systems, and presses.

Summary of Key Concepts

• Pressure: Force per unit area (Pa).
• Atmospheric Pressure: The pressure exerted by the weight of the air; measured using barometers and manometers.
• Variation with Height: Atmospheric pressure decreases as altitude increases.
• Pressure in Liquids: Increases with depth as given by P = ρgh.
• Pascal’s Principle: Pressure applied to a confined fluid is transmitted equally in all directions.

Extended Discussion and Applications

Atmospheric pressure affects weather patterns and is a key parameter in aviation and meteorology. The barometer, for example, not only measures pressure but also helps in predicting weather changes.

In liquids, understanding pressure is critical for designing hydraulic systems used in vehicles, machinery, and construction. The concept of pressure in liquids also underpins oceanography and the design of underwater structures.

Conclusion

Pressure is a fundamental concept in physics that governs the behavior of gases and liquids. Through various instruments and principles—such as barometers, manometers, the equation P = ρgh, and Pascal’s Principle—we can measure and apply pressure in both atmospheric and liquid contexts.

Mastery of these concepts is essential for solving real-world problems in engineering, meteorology, and many other fields.

10 Worked Examples on Pressure (Solutions Hidden)

Example 1: Defining Atmospheric Pressure

Question: Define atmospheric pressure and explain how it is measured.

Solution:

Atmospheric pressure is the force per unit area exerted by the weight of the air above a point. It is measured in pascals (Pa) using instruments such as mercury barometers, aneroid barometers, and manometers.

Example 2: Units of Pressure

Question: What is the SI unit of pressure and how is it defined?

Solution:

The SI unit of pressure is the pascal (Pa), defined as one newton per square meter (1 Pa = 1 N/m²).

Example 3: Mercury Barometer

Question: Explain how a simple mercury barometer measures atmospheric pressure.

Solution:

A mercury barometer consists of an inverted glass tube filled with mercury immersed in a mercury reservoir. Atmospheric pressure pushes mercury up into the tube; the height of the mercury column indicates the atmospheric pressure.

Example 4: Variation of Pressure with Height

Question: Describe how atmospheric pressure changes with altitude.

Solution:

Atmospheric pressure decreases as altitude increases because there is less air above the point of measurement. This relationship is approximately exponential.

Example 5: Barometer as an Altimeter

Question: How can a barometer be used as an altimeter?

Solution:

Since atmospheric pressure decreases with altitude, a barometer can measure pressure and, using a calibrated scale, determine the altitude. Lower pressure readings correspond to higher altitudes.

Example 6: Pressure in Liquids

Question: Explain the relationship between pressure, depth, and density in a liquid.

Solution:

In a liquid, pressure increases with depth due to the weight of the liquid above. This relationship is given by P = ρgh, where ρ is the density, g is the acceleration due to gravity, and h is the depth.

Example 7: Pascal’s Principle

Question: What is Pascal’s Principle and how is it applied in hydraulic systems?

Solution:

Pascal’s Principle states that any change in pressure applied to a confined fluid is transmitted equally throughout the fluid. This principle is applied in hydraulic systems to multiply force.

Example 8: Manometer

Question: Describe the working of a U-tube manometer.

Solution:

A U-tube manometer contains a liquid (often mercury or water). When there is a pressure difference between the two ends of the tube, the liquid levels will differ. The difference in height is proportional to the pressure difference.

Example 9: Hydraulic Lift Application

Question: Explain how the principle of pressure in liquids is used in a hydraulic lift.

Solution:

In a hydraulic lift, a small force applied to a small-area piston creates a pressure that is transmitted equally to a larger-area piston. This results in a much larger force that can lift heavy objects.

Example 10: Real-World Application of Barometers

Question: Discuss how barometers are used in weather forecasting.

Solution:

Barometers measure atmospheric pressure. In weather forecasting, falling pressure indicates an approaching storm, while rising pressure suggests fair weather.

30 CBT JAMB Quiz on Pressure

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