TOPIC 5: PRESSURE IN SOLIDS AND FLUIDS

PRESSURE IN SOLIDS AND FLUIDS

Pressure is defined as the force applied per unit area. It tells us how much force is exerted on a specific surface area. Pressure is a measure of how concentrated or spread out a force is over an area.

• Units of Pressure:
  The unit of pressure in the International System (SI) is the Pascal (Pa), where:

This means that 1 Pascal is the pressure exerted when 1 Newton of force is applied over an area of 1 square meter.

• Derivation of Units:
  • Force (F) is measured in Newtons (N).
  • Area (A) is measured in square meters (m²).

Minimum and Maximum Pressure

• Minimum Pressure:
  The lowest possible pressure is in a vacuum, where there are no gas molecules to exert force. This is known as absolute zero pressure, and it is theoretically the absence of pressure.
• Maximum Pressure:
  The highest pressure is the crushing pressure that can be exerted on a material. This varies depending on the material’s properties. For example, in the depths of the ocean, the pressure can become extremely high due to the weight of the water above.

Applications of Pressure:

• Minimum Pressure is useful in vacuum technology, where processes require a lack of air or gas (e.g., in vacuum pumps or space exploration).
• Maximum Pressure can be observed in deep-sea exploration, where the pressure is much higher due to the weight of water above.

Solving Numerical Problems Involving Pressure

The equation for pressure is:

Example Problem:
Calculate the pressure exerted when a force of 200 Newtons is applied to an area of 5 square meters.

Solution:

Thus, the pressure exerted is 40 Pascals.

Another Example:
A car has a weight of 1000 N and its tires have an area of 0.2 m² each. If there are four tires, calculate the pressure exerted by one tire on the ground.

Solution:

Total force per tire:

Effect of Depth on Fluid Pressure

Fluid Pressure increases with depth due to the weight of the fluid above. This means the deeper you go into a fluid (like water), the greater the pressure.

Experiment:

• Take a bottle of water and make small holes at different heights on the side of the bottle.
• When you fill the bottle with water and observe the water flowing out of each hole, you will see that:
  • The lower the hole, the stronger the pressure and the more water comes out.
  • The higher the hole, the weaker the pressure, and less water comes out.

Explanation:

Pressure Changes in Flowing Fluids

In flowing fluids (like water, air, or oil), pressure changes can be observed depending on the region.

• Shallow Regions:
  In regions where the fluid is shallow, the pressure is lower due to the smaller depth. As the fluid moves, it does not experience a large vertical column of fluid above it, resulting in less pressure.
• Deep Regions:
  In deeper regions, the fluid is subject to a higher pressure because the weight of the fluid above adds to the pressure at lower depths.
• Narrow Regions:
  In a pipe or conduit with a narrow region, fluid velocity increases. According to Bernoulli’s principle, as the velocity increases, the pressure decreases in that region. Hence, in narrow areas, the fluid moves faster but with lower pressure.
• Wide Regions:
  In wider regions of a pipe or conduit, the fluid velocity decreases, and the pressure increases.

Transmission of Fluid Pressure and Its Application in Hydraulic Machines

Transmission of Fluid Pressure:
Fluid pressure is transmitted equally in all directions in a confined fluid. This principle is described by Pascal’s Law, which states:

In hydraulic systems, this principle is applied to transmit force using an incompressible fluid (like oil). In a hydraulic press, for example, pressure applied on a small piston is transmitted through the fluid to a larger piston, which lifts a heavy object. The force is magnified due to the difference in area between the small and large pistons.

Applications:

• Hydraulic Brakes: The pressure applied to the brake fluid in the master cylinder is transmitted to the brake pads, applying pressure to the wheels and stopping the vehicle.
• Hydraulic Lifts: Used in garages and construction, where small input force applied to a small piston is transmitted through hydraulic fluid to lift heavy loads.
• Hydraulic Presses: Used in manufacturing to apply large amounts of force to materials, such as in metalworking and plastic molding.

Summary

Pressure is defined as the force exerted per unit area, and its units are derived from Newtons per square meter, known as Pascals. Pressure can vary depending on depth in a fluid, and it is higher at greater depths. In flowing fluids, pressure decreases in narrow regions and increases in wider regions. Hydraulic systems rely on the transmission of fluid pressure, which allows for the magnification of force to perform useful work, such as in brakes, lifts, and presses. Understanding how pressure works in solids and fluids is crucial in many scientific, engineering, and everyday applications.

What is Atmospheric Pressure?

Atmospheric Pressure is the force exerted by the weight of the air molecules that make up the Earth’s atmosphere. The Earth’s atmosphere is composed of gases such as nitrogen, oxygen, and other trace gases. These molecules are constantly in motion and collide with objects in their path, including the surface of the Earth, exerting pressure.

• Atmospheric Pressure at Sea Level: At sea level, atmospheric pressure is approximately 101,325 Pascals (Pa), or 1 atmosphere (atm), but this value can vary with altitude, weather, and other factors.
• Why Does Atmospheric Pressure Exist?
  Atmospheric pressure is caused by the Earth’s gravitational pull, which keeps the air molecules close to the surface. The air above us pushes down on us due to its weight. As altitude increases, there are fewer air molecules, and thus, atmospheric pressure decreases.

Constructing a Simple Mercury Barometer

A mercury barometer is a device used to measure atmospheric pressure by balancing the weight of a column of mercury against the atmospheric pressure.

How to Construct a Simple Mercury Barometer

1. Materials Needed:
   • A long, narrow glass tube (about 1 meter long).
   • Mercury (a liquid metal).
   • A container (bowl or dish) filled with mercury.
   • A solid, level surface.
2. Steps to Construct the Barometer:
   • Step 1: Fill the glass tube with mercury. To do this, first invert the tube and submerge it into the mercury-filled dish.
   • Step 2: Once the tube is filled, quickly seal the open end while still submerged to prevent mercury from spilling out. Then, invert the tube and place the open end in the mercury dish.
   • Step 3: The mercury in the tube will initially fall a bit and then stabilize at a certain height. This height of mercury in the tube is due to the atmospheric pressure pushing down on the mercury in the dish.
   • Step 4: The difference in height of mercury in the tube compared to the mercury in the dish reflects the atmospheric pressure. This height is usually measured in millimeters or inches.

How it Measures Atmospheric Pressure

• The height of the mercury column in the barometer tube is directly related to the atmospheric pressure.
• Atmospheric pressure is equal to the weight of the mercury column. A higher column of mercury indicates higher atmospheric pressure, while a lower column indicates lower atmospheric pressure.

Equation: The pressure of the atmosphere can be calculated using the formula:

Causes of Daily Variations in Atmospheric Pressure

Atmospheric pressure is not constant and changes throughout the day and night. These variations can be influenced by several factors, such as:

1. Temperature Changes:
   During the day, the sun heats the Earth’s surface, causing the air to warm up and expand. This expansion decreases the density of the air, leading to lower pressure. At night, the cooling air contracts, increasing air density, which leads to higher pressure.
2. Weather Systems:
   Low-pressure systems (like storms) are associated with cloudy, rainy weather and are characterized by descending air. High-pressure systems, on the other hand, are usually associated with clear skies and calm weather, as they involve ascending, cooler air.
3. Altitude:
   Atmospheric pressure decreases with altitude because the higher you go, the fewer air molecules are above you, thus reducing the weight of the air.
4. Air Movements:
   Winds and air currents can also cause fluctuations in local atmospheric pressure. These movements redistribute air masses, affecting pressure patterns.

Effect of Atmospheric Pressure on Weather and Climate:

• Low Pressure: Results in stormy, rainy weather and is typically found in regions where air is rising.
• High Pressure: Associated with clear, dry weather as air is descending and compressing.
• Climbers at High Altitude: At higher altitudes, atmospheric pressure is lower, which means less oxygen is available for breathing. This is why climbers may experience shortness of breath at high elevations (e.g., on mountains like Mount Everest).
• Divers: As divers descend into deeper water, the pressure from the water above them increases. The deeper they go, the higher the pressure they experience, which can affect their body and breathing.

Applications of Atmospheric Pressure

Atmospheric pressure is involved in many everyday applications. Here are a few examples:

1. Drinking Straw:
   When you drink from a straw, you reduce the pressure inside the straw by sucking air out of it. This creates a pressure difference between the inside of the straw (lower pressure) and the outside atmosphere (higher pressure). The atmospheric pressure on the surface of the liquid pushes the liquid up into the straw, allowing you to drink.
2. Syringe:
   In a syringe, when you pull the plunger, you create a low-pressure area inside the syringe. The higher atmospheric pressure on the outside forces the liquid (or air) into the syringe to fill the empty space. When you push the plunger, the liquid or air is expelled.
3. Siphon:
   A siphon works based on atmospheric pressure. When you fill a tube with liquid and place one end in a container and the other end lower than the container, the atmospheric pressure at the higher end pushes the liquid up and then down the siphon, causing the liquid to flow out.
4. Pumps:
   Many pumps operate based on the principle of atmospheric pressure. In a water pump, for example, as the pump creates a low-pressure area, the atmospheric pressure forces water into the pump, where it is then pushed through pipes to its destination.

Summary

Atmospheric pressure is the force exerted by the weight of the air molecules in the atmosphere, and it varies with altitude, temperature, and weather conditions. A mercury barometer can measure atmospheric pressure by balancing the weight of a column of mercury against atmospheric pressure. The causes of daily variations in atmospheric pressure include temperature fluctuations, weather systems, and altitude changes. Atmospheric pressure plays a significant role in various applications such as drinking through a straw, using syringes, operating siphons, and pumps. It is essential to understand the behavior of atmospheric pressure for both scientific and practical purposes.