1. Pressure Measurement and Hydrostatic Pressure

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For 4th Semester Polytechnic CE Students
Written by Garima Kanwar | Blog: Rajasthan Polytechnic

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Subject: Hydraulics (CE 4001 Same as CC/CV 4001)

Branch: Civil Engineering 🏗️
Semester: 4th Semester 📚

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Understanding Hydraulics: A Deep Dive into Unit 1 of CE 4001

Hydraulics is an essential branch of mechanical engineering that deals with the properties and behavior of fluids. It has wide-ranging applications in industries, from water supply systems to machinery in construction. In this blog, we’ll cover the first unit of the Hydraulics course for 4th-semester mechanical engineering students at Rajasthan Polytechnic. We’ll break down the key concepts in a simple and easy-to-understand manner.

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1. Pressure Measurement and Hydrostatic Pressure

This unit covers how fluids behave under pressure, how pressure is measured, and the importance of hydrostatic pressure in real-world applications.

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1.1. Technical Terms Used in Hydraulics

1.1.1. Fluid and Fluid Mechanics

• Fluid: A substance that flows and deforms continuously under the influence of applied forces. Fluids can be liquids (like water) or gases (like air).
• Fluid Mechanics: The study of fluids and their behavior, focusing on both fluids at rest (hydrostatics) and in motion (fluid dynamics). Fluid mechanics helps in designing systems that manage fluid flow efficiently.

Example: When water flows in a pipe, fluid mechanics helps us understand how the water moves and how forces affect the pipe.

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1.1.2. Hydraulics, Hydrostatics, and Hydrodynamics

• Hydraulics: The study of fluids in motion and their applications, such as in hydraulic machinery and systems.
• Hydrostatics: The study of fluids at rest, such as the pressure exerted by water in a dam or a submerged object.
• Hydrodynamics: The study of fluids in motion, focusing on the forces involved and how fluids flow, as in the design of ships or airplanes.

Example: Hydraulic systems in cranes use hydraulics, while the hydrostatics of a dam wall help engineers understand the pressure exerted by water at various depths.

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1.1.3. Ideal and Real Fluid

• Ideal Fluid: A hypothetical fluid with no viscosity (no resistance to flow) and incompressibility. It is used to simplify calculations and understand basic principles.
• Real Fluid: All fluids in real life are considered real fluids, as they have viscosity and are compressible to varying degrees.

Example: Water is often treated as an ideal fluid for basic calculations, but in practical scenarios, the viscosity of water (real fluid behavior) matters, like in the design of water pumps.

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1.1.4. Applications of Hydraulics

Hydraulic systems have a wide variety of applications:

• Excavators, cranes: Hydraulics is used to lift heavy loads.
• Hydraulic brakes in vehicles: Pressure applied to the brake fluid helps stop the vehicle.
• Water supply systems: Hydraulics help in pumping water efficiently.
• Turbines for power generation: Hydrodynamic principles are used in designing turbines in hydroelectric plants.

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1.2. Physical Properties of Fluid

This section dives into the physical characteristics of fluids, such as density, viscosity, and surface tension, which are crucial for understanding fluid behavior.

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1.2.1. Density and Specific Volume

• Density (ρ): The mass per unit volume of a fluid. It is expressed in kg/m³.

  $$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

  Example: The density of water is 1000 kg/m³.

• Specific Volume: The volume occupied by a unit mass of fluid, calculated as the inverse of density.

  $$\text{Specific Volume} = \frac{1}{\text{Density}}$$

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1.2.2. Specific Gravity

• Specific Gravity (SG): It is the ratio of the density of a fluid to the density of water at 4°C. $$SG = \frac{\rho_{\text{fluid}}}{\rho_{\text{water}}}$$Specific gravity is a dimensionless number. For example, the specific gravity of mercury is 13.6, meaning it is 13.6 times denser than water.

Example: For oil with a density of 850 kg/m³, its specific gravity would be:

$$SG = \frac{850}{1000} = 0.85$$

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1.2.3. Vapour Pressure, Surface Tension, and Capillarity

• Vapour Pressure: The pressure exerted by the vapor of a liquid when it is in equilibrium with its liquid form. It depends on temperature.
• Surface Tension: The force acting on the surface of a liquid, causing it to behave like a stretched elastic membrane. This is why water forms droplets.
• Capillarity: The ability of a liquid to flow in narrow spaces against gravity, such as water rising in a thin tube.

Example: A simple experiment to observe capillarity can be done by dipping a thin glass tube into water. The water will rise inside the tube due to surface tension.

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1.2.4. Viscosity and Newton’s Law of Viscosity

• Viscosity: A measure of a fluid’s resistance to flow. It is like the "thickness" of the fluid. Water has low viscosity, while honey has high viscosity.
  • Dynamic Viscosity (μ): Measures the internal friction of a fluid, in units of Pa·s.
  • Kinematic Viscosity (ν): The ratio of dynamic viscosity to the fluid’s density, in units of m²/s.

Newton’s Law of Viscosity: States that the shear stress is proportional to the rate of shear strain. This helps to understand how different fluids resist motion.

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1.3. Various Types of Pressure

Pressure is a fundamental concept in hydraulics. Let's look at the different types of pressure.

1.3.1 Atmospheric Pressure

• Definition: Atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere on any object within it.
• Measurement: It is usually measured using a barometer and is approximately 101.3 kPa (kilopascals) at sea level under standard conditions.
• Variation: Atmospheric pressure changes with altitude. It decreases as you move higher above sea level because there is less air above to exert force.
• Units: It is measured in pascals (Pa), atmospheres (atm), or millimeters of mercury (mmHg).

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1.3.2 Gauge Pressure

• Definition: Gauge pressure is the pressure measured relative to atmospheric pressure. It measures the difference between the absolute pressure of a system and the atmospheric pressure.
• Formula: $P_{gauge} = P_{absolute} - P_{atmospheric}$
• Measurement: Commonly used in tire pressure, blood pressure readings, and industrial applications.
• Note: Gauge pressure can never be negative (if it is negative, it is referred to as vacuum pressure).

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1.3.3 Absolute Pressure

• Definition: Absolute pressure is the total pressure exerted on a system, including both the atmospheric pressure and the gauge pressure.
• Formula: $P_{absolute} = P_{gauge} + P_{atmospheric}$
• Measurement: Absolute pressure is always positive and is used in scientific and engineering contexts, such as gas laws and thermodynamics.
• Example: A vacuum chamber, where the absolute pressure would be very close to zero.

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1.3.4 Vacuum Pressure

• Definition: Vacuum pressure refers to the pressure in a system that is below atmospheric pressure. It is a measure of how much lower the pressure in the system is compared to atmospheric pressure.
• Measurement: Vacuum pressure is typically measured using a vacuum gauge, and it is commonly expressed in terms of negative gauge pressure.
• Note: The term “vacuum” does not mean zero pressure; it indicates a condition where the pressure is lower than the atmospheric pressure.

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1.4. Concept of Pressure Head and its Unit

Pressure head refers to the height of a column of fluid that would exert a specific pressure at the bottom. It is used in fluid systems to simplify calculations.

$$\text{Pressure Head} = \frac{P}{\rho g}$$

Diagram:

     |--------|
     |  Fluid | 
     |--------|
        h
     Pressure Head

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1.5. Pascal’s Law of Fluid Pressure and its Uses

Pascal’s Law states that pressure applied to a confined fluid is transmitted equally in all directions. This principle is fundamental in hydraulic systems, like hydraulic lifts.

Example: In a hydraulic lift, a small force applied on a piston creates a large force that can lift heavy objects.

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1.6. Measurement of Differential Pressure

To measure the pressure difference between two points, several devices are used.

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1.6.1. Manometers

Manometers are instruments used to measure pressure. There are several types:

• Piezometer: A simple tube that measures fluid pressure at a specific point.
  • Limitation: It only works with fluids at rest and cannot measure atmospheric pressure.
• U-tube Manometer: A simple device to measure pressure differences using the difference in fluid height.
  • Simple U-tube: Measures the pressure at a point.
  • Differential U-tube: Measures the difference between two pressures.
  • Inverted U-tube: Measures small negative pressures.

Diagram:

    P1
     |         ________
     |        |        |
    / \       |________|
   |   |      |        |
   |---|      |        | P2
   |---|      |________|

• Micro-manometer: Measures very small pressure differences with high precision.

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1.7. Variation of Pressure with Depth

Pressure increases with depth in a fluid due to the weight of the fluid above.

1.7.1. Pressure Diagram

A pressure diagram shows how pressure increases with depth. The deeper you go in a fluid, the higher the pressure.

Diagram:

Pressure (P)
|
|              /
|             /
|            /
|___________/
            Depth (h)

1.7.2. Hydrostatic Pressure

Hydrostatic pressure is calculated using the formula:

$$P = \rho g h$$

Where:

• $P$ is the hydrostatic pressure,
• $ρ$ is the fluid density,
• $g$ is gravitational acceleration,
• $h$ is the depth.

1.7.3. Center of Pressure on Immersed Surfaces and Tank Walls

The center of pressure is the point where the total pressure force acts on a submerged surface. This helps in the design of structures like dams and tanks.

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Sample Questions for Practice

1. What is the difference between gauge pressure and absolute pressure?
2. A fluid has a density of 1200 kg/m³. Calculate the pressure at a depth of 5 meters in the fluid.
3. Explain Pascal’s Law and provide an example of its application in real life.
4. What is the importance of viscosity in fluid flow?
5. Draw a U-tube manometer and explain how it works to measure pressure differences.

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Conclusion

This first unit introduces the fundamental principles of hydraulics, such as pressure measurement, hydrostatic pressure, and the concept of fluid behavior. Understanding these concepts is essential for solving real-world engineering problems related to fluid systems. Practice with the given examples and questions will help reinforce your understanding and application of these principles.

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