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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.

### 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.

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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.

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 = \[\frac{F}{A(\frac{dv}{dx})}\]

FAQ (Frequently Asked Questions)

Q1. Give Some Limitations that Restrict the Application of Bernoulli’s Principle Practically.

The sum of the pressure energies, kinetic energies, and the potential energies upon mass gives Bernoulli's principle. However, we have ignored some amount of energy that is lost during the flow due to internal friction between the layers. The several layers in the fluid flow with different velocities which in turn causes friction to arise between the layers thus causing the loss of energy. This property is known as viscosity and some kinetic energy is lost due to viscous force.

Hence, Bernoulli’s principle is only valid for nonviscous fluids. In Bernoulli's equation, we do not consider elastic energies and hence we need incompressible fluids. Bernoulli's principle also fails to be applied for the turbulent flow of fluids because the velocity and pressure of the particles alter at different points of time.

Q2. How is Surface Tension Affected by the Nature of Liquid and Temperature?

Surface Tension refers to the work or energy needed to increase the surface area of a liquid by a unit area arising due to intermolecular forces. Since the property of surface tension occurs due to the intermolecular forces of attraction, there is a direct relationship between the intermolecular forces and surface tension. The larger the intermolecular force of attraction between the liquid molecules, the greater is the surface tension observed.

The lesser the attraction, the lesser is the surface tension. In general, the surface tension of liquid has an inverse relationship with temperature. An increase in the temperature of the liquid causes a decrease in the surface tension of the liquid. At the critical temperature, the surface tension reduces to zero. The inverse nature can be explained by the fact that with an increase in temperature, there is an increase in kinetic energy of the molecules which in turn results in lower intermolecular attraction.