Unit 1 of ME 3003 (Mechanical/Automobile Engineering)

 Unit 1 of ME 3003 (Mechanical/Automobile Engineering). These are short notes for revision purpose. please refer you Reference book & College study materials for complete study.

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1. Introduction to Basic Properties of Fluids

Fluids are substances that can flow and do not have a fixed shape, such as liquids and gases. The study of fluids is essential in engineering, especially in mechanical and automobile fields.

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1.1 Surface Tension and Capillarity

Surface Tension:

• Surface tension is the force that acts at the surface of a liquid, making it behave like a stretched elastic membrane.
• It arises due to the cohesive forces between the molecules of the liquid.
• It is measured in N/m (Newtons per meter).

Capillarity:

• Capillarity refers to the ability of a liquid to flow in narrow spaces without the assistance of external forces (like gravity).
• It is caused by the adhesive force between the liquid and the walls of a tube and the cohesive force between the liquid molecules.
• In narrow tubes, liquids will either rise or fall depending on the adhesive forces (e.g., water rises in a glass tube, mercury falls in a glass tube).

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1.2 Fluid Pressure and Pressure Measurement

Fluid Pressure:

• Pressure in a fluid is defined as the force per unit area exerted by the fluid on the surfaces in contact with it.
• Pressure is a scalar quantity (it has magnitude but no direction).
• It is expressed in Pascals (Pa), where 1 Pa = 1 N/m².

1.2.1 Pressure Head and Pressure Intensity

• Pressure Head: The height of a fluid column that can exert a given pressure at its base.
  • Formula: $h = \frac{P}{\rho g}$
    • Where $h$ is the pressure head (m), $P$ is the pressure (Pa), $\rho$ is the fluid density (kg/m³), and $g$ is the acceleration due to gravity (9.81 m/s²).
• Pressure Intensity: It is the force per unit area exerted by the fluid on a surface.

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1.2.2 Concept of Vacuum and Gauge Pressures, Atmospheric Pressure, Absolute Pressure

• Atmospheric Pressure: The pressure exerted by the weight of the air in the atmosphere. At sea level, it is approximately 101.3 kPa.
• Absolute Pressure: The total pressure at a point, including atmospheric pressure.
  • Formula: $P_{\text{absolute}} = P_{\text{gauge}} + P_{\text{atm}}$
• Gauge Pressure: The pressure measured relative to atmospheric pressure. A vacuum gauge measures pressure below atmospheric pressure.
  • Gauge Pressure = Absolute Pressure - Atmospheric Pressure
  • If the gauge pressure is negative, it indicates a vacuum.

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1.2.3 Simple and Differential Manometers

• Simple Manometer: A device used to measure the pressure of a fluid in a container.
  • It typically consists of a U-tube filled with a liquid (like mercury or water).
  • The difference in fluid height gives the pressure difference.
• Differential Manometer: Used to measure the difference in pressure between two points in a fluid system.
  • It has two legs, one connected to each point, and the pressure difference is indicated by the height difference in the fluid.

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1.2.4 Bourdon Pressure Gauge

• A Bourdon Pressure Gauge is a mechanical device used to measure the pressure of a fluid (usually gas).
• It consists of a coiled tube that straightens as the pressure inside increases.
• The straightening motion moves a pointer over a dial, indicating the pressure.
• Commonly used for: Measuring the pressure of gases in industrial applications.

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1.2.5 Concept of Total Pressure on Immersed Bodies, Center of Pressure

• Total Pressure: The total force exerted by a fluid on an immersed body is the pressure at the surface multiplied by the area.
  • Formula: $F = P \cdot A$
    • Where $P$ is the pressure and $A$ is the area.
• Center of Pressure: The point at which the total pressure force can be considered to act. It is the centroid of the pressure distribution.
  • The center of pressure lies below the centroid of the object when it is immersed vertically in the fluid.
  • Formula for center of pressure: $h_{\text{cp}} = \frac{I_G + A \cdot h_c^2}{A \cdot h_c}$
    • Where $h_{\text{cp}}$ is the center of pressure, $I_G$ is the moment of inertia about the centroid, $h_c$ is the distance from the fluid surface to the centroid, and $A$ is the area.

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1.2.6 Simple Problems on Manometers

• Problem Example 1: A U-tube manometer is connected to a pipe carrying water. The height difference in the manometer is observed to be 0.2 meters. Calculate the pressure difference in the pipe.

  Solution:

  • The pressure difference $P = \rho \cdot g \cdot h$
  • Where $\rho$ is the density of water (1000 kg/m³), $g$ is gravity (9.81 m/s²), and $h$ is the height difference (0.2 m).
  • So, $P = 1000 \cdot 9.81 \cdot 0.2 = 1962 \, \text{Pa}$ or 1.96 kPa.

• Problem Example 2: A differential manometer is used to measure the pressure difference between two points in a pipe. The liquid in the manometer is mercury. If the height difference between the two arms of the manometer is 0.1 m, calculate the pressure difference between the two points.

  Solution:

  • The pressure difference $P = \rho \cdot g \cdot h$
  • Where $\rho$ for mercury is 13600 kg/m³, $g$ is gravity (9.81 m/s²), and $h$ is the height difference (0.1 m).
  • So, $P = 13600 \cdot 9.81 \cdot 0.1 = 1334.16 \, \text{Pa}$ or 1.33 kPa.

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Summary of Key Concepts

• Surface Tension: Force per unit length on the surface of a liquid.
• Capillarity: Movement of liquids in small spaces due to surface tension.
• Pressure: Force exerted by a fluid per unit area.
• Manometers: Devices for measuring pressure differences.
• Bourdon Gauge: Mechanical device for measuring pressure.
• Center of Pressure: The point where the total pressure force acts on an immersed body.

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