Key Principles: Pascal’s Law, Bernoulli’s Principle & Applications
Chapter 10 class 11 in physics is the mechanical properties of fluids. Students get to score higher scores in subjects like physics because the questions in competitive exams from the subject are based on basic concepts, formulas and problems related to the chapter. Theories are difficult to memorize and hence, there arises a chance of losing marks. In this chapter, our experts have tried to explain these concepts in detail so that students find it easy to understand and practice problems on the basis of understanding of the chapter.
In this chapter, students may learn in detail the mechanical properties of liquids and gases, pressure, streamline flow, viscosity, surface tension and so on.
Introduction
As we all know, a fluid is anything that has no fixed shape. Both liquids and gases are referred to as fluids because they have the tendency to flow. Fluids can yield to slightest external pressures. The study of mechanical properties of fluids is called Hydrostatics. The volume of liquid or gas depends on the pressure acting on it. Since liquids have a fixed volume, the change in volume due to the change in external pressure is less. It is not the same in the case of gases, as they do not have a fixed volume.
Let’s study more about the concepts of mechanical properties of fluids
Notes of Mechanical Properties of Fluids
Fluids are liquids and gases with the property to flow in a certain direction on the application of external force. Two major topics are studied when we talk about the mechanical properties of fluids. They are- hydrodynamics and hydrostatics.
Hydrodynamics
In physics, hydrodynamics is the study that concerns the forces acting on or exerted by fluids. It deals with the motion of fluids and the forces acting on solid bodies that are immersed in fluids. It also focuses on the motion relative to them. In short, it is the study of fluids in motion. Thus, it is a vast branch of science, which we will study more later.
In this chapter, we will focus more on Hydrostatics
Hydrostatics
This branch of physics is concerned with the fluids at rest.
Pascal’s Law
Pascal made an observation that the pressure in a fluid that is at rest is the same at all points, provided they are at the same height. He also inferred that the pressure difference depends upon the vertical distance between the two points. Thus, the pressure difference applied to the fluid which is enclosed can be transmitted undiminished to every point of the fluid and the container vessel’s walls as well.
It can thus be noted that when an incompressible fluid is passing between every second in a pipe of non-uniform cross-section, the volume will be the same as the steady flow.
Bernoulli’s Principle and Equation
Bernoulli’s principle states that the total energy of the water always remains constant, therefore when the flow of water in a system increases, the pressure necessarily decreases. When water starts to flow in a hydraulic system the pressure drops and when the flow of water stops, the pressure rises again.
Therefore, in a hydraulic system, the total energy head is equal to the sum of three individual energy heads.
This can be expressed as follows-
Total Head = [Elevation Head + Pressure Head + Velocity Head]
Where,
Elevation head- is the pressure due to the elevation of the water
Pressure head- is the height of a column of water that a given hydrostatic pressure in a system could support
Velocity head- is the energy present due to the velocity of the water.
Surface Tension
The amount of energy required to increase the surface of the liquid by unit area is defined as surface tension. It means it is the property of the surface of the liquid to resist force. Moreover, it is the force that holds the liquid molecules bound together. Therefore, surface tension is the amount of the extra energy which the molecules at the interface have when compared to the interior. Surface tension is denoted by the Greek letter ‘sigma’.
Viscosity
Viscosity is the measure of the resistance exerted by fluids to gradual deformation by shear or tensile stress. Thus, it can be considered as the fluid’s resistance to flow. When we say honey is thicker, milk is thinner, we intend to mean the viscosity of the liquid. Thus, the liquid that tends to flow less is more viscous.
It is measured in terms of a ratio of shearing stress to the velocity gradient in a fluid.
The equation to determine the viscosity of a fluid
When a sphere of radius a is dropped in a fluid of viscosity v, the viscosity is given by η=2ga2(Δρ)9v
Where,
∆ρ is the density difference between the fluid and the sphere
a is the radius of the sphere
g is the acceleration due to gravity
v is the velocity of the sphere
FAQs on Mechanical Properties of Fluids Explained
1. What are the main mechanical properties of fluids discussed in Class 11 Physics?
The main mechanical properties of fluids describe how they behave under force and in motion. For Class 11 students, the key properties to understand are:
- Pressure: The force a fluid exerts per unit area on a surface.
- Density: The mass of the fluid contained in a unit of volume.
- Viscosity: The fluid's internal resistance to flow, often described as its 'thickness'.
- Surface Tension: The tendency of a liquid's surface to shrink into the smallest possible area, acting like a thin elastic sheet.
- Capillarity: The ability of a liquid to rise or fall in a narrow tube due to surface tension and adhesive forces.
2. What is Pascal's Law and where can we see it in action?
Pascal's Law states that a pressure change applied to an enclosed, incompressible fluid is transmitted undiminished to every portion of the fluid and the walls of its container. A classic real-world example is a hydraulic lift in a car garage. A small force on a small piston creates pressure that is transferred through the hydraulic fluid to a larger piston, allowing it to lift a heavy car with ease.
3. Can you explain the concept of viscosity in simple terms?
Viscosity is a measure of a fluid's resistance to flow. Think of it as internal friction. A fluid with high viscosity, like honey, flows very slowly because its molecules create a lot of friction as they move past each other. A fluid with low viscosity, like water, flows easily because it has less internal friction.
4. What is the difference between streamline flow and turbulent flow?
The key difference lies in the fluid's movement pattern. In streamline flow (also called laminar flow), fluid particles move in smooth, orderly layers or paths. The velocity at any given point remains constant. In contrast, turbulent flow is chaotic and unpredictable, with particles moving in irregular paths, forming swirls and eddies. This usually happens at higher speeds or when an obstacle is present.
5. What is the main idea behind Bernoulli's principle?
Bernoulli's principle states that for a moving fluid, as the speed of the fluid increases, its pressure decreases. This inverse relationship between speed and pressure is fundamental to many applications. For example, it explains how the curved shape of an airplane's wing generates lift—air travels faster over the top surface, creating lower pressure there compared to the bottom surface.
6. Why are raindrops spherical in shape?
Raindrops are spherical due to a property called surface tension. A liquid naturally tries to minimise its surface area because of the cohesive forces between its molecules. For a given volume, a sphere has the smallest possible surface area. This is why falling raindrops, free from other forces, pull themselves into a nearly perfect spherical shape.
7. How is surface tension different from viscosity?
While both are properties of fluids, they describe different things. Surface tension is a property of the liquid's surface, causing it to behave like a stretched membrane. It's why insects can stand on water. Viscosity, on the other hand, is a bulk property that relates to the entire fluid's resistance to flow or internal motion. In short, surface tension is a 'surface' phenomenon, while viscosity is an 'internal' phenomenon.
8. What is meant by an 'ideal fluid' and why is this concept useful in physics?
An 'ideal fluid' is a theoretical concept used to simplify complex fluid dynamics problems. It is a fluid that is assumed to have two key characteristics:
- It is incompressible (its density is constant).
- It has zero viscosity (it flows without any internal friction).
Although no real fluid is perfectly ideal, this model helps us understand and derive fundamental principles like Bernoulli's theorem in a much simpler way.
