Key Principles: Pascal’s Law, Streamline Flow & Bernoulli’s Principle
Physics Mechanical Properties of Fluids
Fluids refer to substances that can flow, mainly denoting liquids and gases. The ability to flow is one of the fundamental characteristics of fluids which distinguishes between the solid and the liquid and gases collectively. While fluids do not have a shape and take the volume of the container they are kept in, solids have a definite shape and volume. The mechanical property of fluid Class 11 refers to the branch of Physics where we learn about the behaviour and properties of fluid material. The various sub-topics under this topic are pressure, Pascal’s law, streamline flow, Bernoulli’s principle, etc.
Notes of Mechanical Properties of Fluid
Pressure
The component of force acting normal to the area of the surface upon the area of the surface is termed as pressure.
P = \[\frac{F}{A}\]
It is a scalar quantity. Usually, to measure the pressure exerted by the fluid, a piston is used.
Pascal’s Law
Pascal’s law states that for an enclosed liquid if pressure is applied at any point in the liquid, it gets transmitted equally and undiminished to all parts of the liquid and the walls of the container enclosing the liquid.
P = \[\frac{F_{A}}{A_{A}}\] = \[\frac{F_{B}}{A_{B}}\] = \[\frac{F_{C}}{A_{C}}\]
(where A, B, and C are different points in the same enclosed liquid)
Pascal’s law has a wide range of applications like hydraulic machines. For constant pressure, if the area is small, the force will be higher and if the area is large, the force will be less.
Streamline Flow
The flow of liquids can be demonstrated in two types - streamline and turbulent. At all given points, if the velocity of all the particles in the fluid remains constant concerning time, the flow of fluid is said to be steady. The path followed by a steady fluid is called streamline flow. If the flow speed of the fluid reaches beyond a certain critical speed, the flow no longer remains steady but changes to turbulent flow.
For a steady incompressible fluid,
A\[_{1}\]v\[_{1}\] = A\[_{2}\]v\[_{2}\]
(where A represents the area of a cross-section of fluid and v is the velocity of fluid particles at the same point)
This equation is termed as the equation of continuity. It is based on the principle of conservation of mass in incompressible fluids. For a narrower pipe, the speed of flow of fluid is greater whereas, for a wider pipe, the speed of flow is less.
Bernoulli’s Principle
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Bernoulli’s principle is an expression which states the relationship between pressure changes with velocity and altitude changes. Basically for an incompressible fluid flowing in a streamline flow, the sum of pressure energy per unit mass, kinetic energy per unit mass (related to velocity change), and potential energy per unit mass (related to height change) is a constant.
P\[_{1}\] + \[\frac{1}{2}\]ρv\[_{1}^{2}\] + ρgh\[_{1}\] = P\[_{2}\] + \[\frac{1}{2}\]ρv\[_{2}^{2}\] + ρgh\[_{2}\]
(where 1 and 2 are different positions in the fluid)
Since the elastic energy is not considered here, the fluid must be incompressible to hold Bernoulli's equation true. For non-steady and turbulent flows, Bernoulli's principle does not hold because the pressure and the velocities do not remain constant over time.
Mechanical Properties of Fluids Class 11 Formulas
The different NCERT Mechanical properties of fluids formulae are:
P = \[\frac{F}{A}\]
P = \[\frac{F_{A}}{A_{A}}\] = \[\frac{F_{B}}{A_{B}}\] = \[\frac{F_{C}}{A_{C}}\]
A\[_{1}\]v\[_{1}\] = A\[_{2}\]v\[_{2}\]
P\[_{1}\] + \[\frac{1}{2}\]ρv\[_{1}^{2}\] + ρgh\[_{1}\] = P\[_{2}\] + \[\frac{1}{2}\]ρv\[_{2}^{2}\] + ρgh\[_{2}\]
η = \[\frac{F}{A(\frac{dv}{dx})}\]
FAQs on Mechanical Properties of Fluids Explained
1. What are the key mechanical properties of fluids we study in Class 11 Physics?
In Class 11, the study of the mechanical properties of fluids focuses on how they behave at rest and in motion. The main properties you will learn about are:
- Pressure: The force exerted by a fluid per unit area.
- Density: The mass of the fluid per unit volume.
- Buoyancy: The upward force exerted by a fluid that opposes the weight of an immersed object, as explained by Archimedes' principle.
- Viscosity: The measure of a fluid's resistance to flow, often described as its 'thickness'.
- Surface Tension: The tendency of a liquid's surface to shrink into the minimum possible surface area, allowing it to resist an external force.
- Fluid Dynamics: The study of fluids in motion, including concepts like streamline flow, turbulent flow, and Bernoulli's principle.
2. How does Pascal's Law explain the working of a hydraulic lift?
Pascal's Law is the core principle behind hydraulic systems. The law states that a pressure change at any point in a confined, incompressible fluid is transmitted equally to all points throughout the fluid. In a hydraulic lift, a small force is applied to a small piston. This creates pressure in the fluid. Because this pressure is transmitted equally everywhere, it acts on a much larger piston, generating a much larger force that is capable of lifting heavy objects like a car. This is how a small effort can be multiplied into a large force.
3. Why is it important to distinguish between streamline and turbulent flow?
Distinguishing between streamline (or laminar) and turbulent flow is crucial because the fundamental principles of fluid dynamics apply differently to each. Key reasons include:
- Predictability: In streamline flow, fluid particles move in smooth, predictable paths. This allows us to apply principles like Bernoulli’s equation to calculate pressure and velocity.
- Energy Loss: Turbulent flow is chaotic and characterised by eddies and swirls. This motion causes significant energy to be lost as heat and sound, making calculations more complex.
- Applicability of Laws: Many foundational concepts, such as Bernoulli's principle, are derived assuming ideal, streamline flow. They do not give accurate results for turbulent conditions.
Understanding the type of flow helps engineers and physicists model real-world situations correctly, from airflow over a plane's wing to water flow in a pipe.
4. Under what conditions does Bernoulli's principle not give accurate results?
Bernoulli's principle is a powerful tool, but it's based on an 'ideal fluid' and doesn't always apply perfectly in the real world. The principle becomes less accurate when:
- The fluid has significant viscosity (internal friction), as the principle assumes a non-viscous fluid. Viscosity causes energy loss that the equation doesn't account for.
- The flow is turbulent instead of streamline. The principle is only valid for smooth, layered flow.
- The fluid is compressible, like a gas under large pressure changes. The principle assumes the fluid's density is constant.
Essentially, any factor that causes energy loss or breaks the assumptions of ideal flow will limit the practical application of Bernoulli's principle.
5. How does a liquid like water rise in a thin tube against gravity?
This phenomenon is known as capillary action or capillarity. It happens because of two competing forces: cohesive forces (attraction between liquid molecules) and adhesive forces (attraction between liquid molecules and the tube's material). When the adhesive forces are stronger than the cohesive forces (like water in a glass tube), the water molecules are pulled towards the walls of the tube. This pull is strong enough to lift the column of liquid upwards against gravity until the weight of the lifted liquid balances the adhesive force.
6. What is viscosity, and how is it different from the friction we see in solids?
Viscosity is essentially friction inside a fluid. It is the property that describes a fluid's resistance to flowing. Think of it as the 'thickness' of a liquid; for example, honey has a much higher viscosity than water.
The key difference from solid friction is that viscosity depends on the relative motion between layers of the fluid. There is no viscosity if the fluid is not flowing. In contrast, static friction between solids can exist even when the objects are not moving. Viscosity is an internal property of the fluid itself, whereas solid friction occurs at the surface between two separate objects.
7. Why do small insects like water striders appear to walk on water?
Insects like water striders can walk on water due to a property called surface tension. The surface of the water acts like a very thin, stretched elastic membrane. This is because the water molecules at the surface are pulled inwards by cohesive forces from the molecules below them. The weight of the insect is distributed over its legs and is not enough to break this tension, allowing it to stand on the surface without sinking.
