Revision: Mechanical Properties of Fluids Physics HSC Science (General) 12th Standard Board Exam Maharashtra State Board

The force which produces compression is called thrust. Its S.I unit is the newton.

High pressure is an area of the atmosphere where the barometric pressure is higher than its surrounding areas. In this case, the wind from the center of high pressure blows towards the surrounding low-pressure areas.

A low-pressure area is an area in the atmosphere where the pressure is lower than its surrounding areas. In this situation, the wind from the surroundings blows towards the center of low pressure.

The pressure exerted by this mercury column is considered as the pressure of magnitude ‘one atmosphere’ (1 atm).

SI unit of pressure is the pascal (Pa) or Nm⁻²
One Pascal: When a force of one newton acts normally on an area of one square metre (1 m²) then the pressure acting on the surface acting on the surface is called one Pascal.

The angle between tangents drawn at the point of contact to the liquid surface and the solid surface inside the liquid is called the angle of contact for a pair of solid and liquid. It is denoted by θ.

Surface tension is defined as the force acting on a unit length of an imaginary line drawn on the free surface of the liquid, the direction of the force being perpendicular to the line so drawn and acting parallel to the surface.

When a liquid is in contact with a solid, the angle between the tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called the angle of contact.

Surface tension is defined as the force per unit length acting at right angles to an imaginary line drawn on the free surface of the liquid. 

A molecule's sphere of influence is described as an imaginary sphere with the molecule at its centre and the molecular range as its radius.

The maximum distance at which an appreciable intermolecular force of attraction exists between two molecules is known as the molecular range or range of molecular attraction.

The potential energy is greater for molecules at the surface film as compared to molecules well inside the liquid. This extra energy of the molecule on the surface layer of a liquid is called the surface energy of the liquid.

The coefficient of viscosity of a liquid is defined as the viscous force acting tangentially per unit area of a liquid layer having a unit velocity gradient in a direction perpendicular to the direction of flow of the liquid.

The maximum constant velocity acquired by a body while falling freely through a viscous medium is called the terminal velocity V_T.

The rate of change of velocity (dv) with distance (dx) measured from a stationary layer is called velocity gradient.

∴ Velocity gradient = `(dv)/dx`

Atmospheric pressure is the pressure exerted by the weight of the column of air above a unit area.

The maximum distance from a molecule up to which the molecular force is effective is called the range of molecular force.

Any two mo.lecules attract each other. This force between molecules is called intermolecular force.

The force of attraction between the molecules of the same substance is called cohesive force or force of cohesion.

The force of attraction between the molecules of different substances is called the adhesive force or force of adhesion.

Surface tension T is defined as the tangential force acting per unit length on both sides of an imaginary line drawn· on the free surface of liquid.

Mathematically. T = \[\frac {F}{L}\]
Sl unit: N/m
Dimension:  [L⁰M¹T^-2]

The extra energy of the molecules in the surface layer is called the surface energy of the liquid.

The angle of contact is the angle between the tangent drawn to the free surface of the liquid and the solid surface at the point of contact, measured within the liquid.

The surface layer of a liquid with thickness equal to the range of intermolecular force is called the surface film.

An imaginary sphere with a molecule at its center and radius equal to the molecular range is called the sphere of influence of the molecule.

The branch of Physics which deals with the study of properties of fluids in motion is called hydrodynamics.

The phenomenon of rise or fall of a liquid in a capillary tube when dipped in the liquid is called capillarity.

The velocity beyond which a streamline flow becomes turbulent is called the critical velocity.

The rote of change of veiocity (dv) with distance (dx) measured from a stationary layer is coiled velocity gradient (dv/dx).

Viscosity is that property of fluid, by virtue of which, the relative motion between different layers of a fluid experience a dragging force.
SI unit = N s /m²

The coefficient of viscosity can be defined as the viscous force per unit area per unit velocity gradient.

The continuity equation soys that the volume rote of flow of on incompressible fluid for a steady flow is the some throughout the flow.
A₁v₁ = A₂v₂ or, Av = constant

Any substance that can flow is a fluid.

The branch of physics which deals with the properties of fluids at rest is called hydrostatics.

The normal force (F) exerted by a fluid at rest per unit surface area (A) of contact is called the pressure (P) of the fluid.

P = \[\frac {F}{A}\]

SI unit: Pascal
Dimension: [L^-1M¹T²]

h = \[\frac {2T cosθ}{rρg}\]

\[\mathbf{v}_{\mathrm{c}}=\frac{R_{\mathrm{n}}\eta}{\rho d}\]

where,
v_c = critical velocity of the fluid
R_n= Reynolds number
η = coefficient of viscosity
ρ = density of fluid
d = diameter of tube 

\[\eta=\frac{2}{9}\frac{r^{2}\left(\rho-\sigma\right)g}{\mathrm{v}}\]

p = p₀ + pgh

Where:

• p_0​ = Atmospheric pressure
• ρ = Density of liquid
• g = Acceleration due to gravity
• h = Depth

T = `F/L`

where F = Force (N), L = Length (m)

= SI unit of T = `N/m`

Surface tension can also be written as

T = `W/A`

where W = Work (J), A = Area (m²)

= SI unit of T = `J/m^2`

We know

1J=1N×1m

So,

`J/m^2 = (N * m)/m^2 = N/m`

Both units are the same

`1N/m equiv 1J/m^2`

(b) There is no gravitational force acting downwards. However, when the starting velocity is 20 m/s, the viscous force, which is directly proportional to velocity, becomes maximum and tends to accelerate the ball upwards.

\[\text{ When the ball falls under gravity, }\]

\[\text{ neglecting the density of air: } \]

\[\text{ Mass of the sphere = m }\]

\[\text{ Radius = r }\]

\[\text{ Viscous drag coeff . }= \eta\]

\[\text{Terminal velocity is given by}: \]

\[\text{ mg  }= 6\pi\eta r v_T \]

\[ \Rightarrow \frac{6\pi\eta r v_T}{m} = g . . . (1)\]

\[\text{ Now, at terminal velocity, the acceleration of the ball due to the viscous force is given by: } \]

\[a = \frac{6\pi\eta r v_T}{m}\]

\[\text{ Comparing equations (1) and (2), we find that : } \]

\[ \text{ a = g }\]

Thus, we see that the initial acceleration of the ball will be 9.8 ms - 2  .

(c) The velocity of the ball will decrease with time because of the upward viscous drag. As the force of viscosity is directly proportional to the velocity of the ball, the acceleration due to the viscous force will also decrease.

(d) When all the kinetic energy of the ball is radiated as heat due to the viscous force, the ball comes to rest. 

The law states that, "The viscous force (F_v) acting on a small sphere falling through a viscous medium is directly proportional to the radius of the sphere (r), its velocity (v) through the fluid, and the coefficient of viscosity (η) of the fluid". 

This is Bernoulli's equation. It states that the work done per unit volume of a fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow.

Mathematically.
p + \[\frac {1}{2}\]ρv² + ρgh = constant

Pascal's law states that the pressure applied at any point of an enclosed fluid at rest is transmitted equally and undiminished to every point of the fluid and also on the walls of the container, provided the effect of gravity is neglected. 

• Pascal’s law states that pressure applied at any point of an enclosed fluid at rest is transmitted equally and undiminished to every part of the fluid and to the walls of the container.
• It applies only to fluids at rest (static conditions).
• The transmitted pressure acts equally in all directions.
• Mathematically, pressure remains constant throughout the fluid:
  \[\frac {F_1}{A_1}\] = \[\frac {F_2}{A_2}\]​​
• It is the working principle of hydraulic devices such as hydraulic lifts and hydraulic brakes.

• Soluble impurities, such as common salt, increase the surface tension of water, whereas detergents and phenol decrease it.
• Insoluble impurities reduce surface tension by decreasing cohesive forces, affecting droplet shape and meniscus formation.
• In most liquids, surface tension decreases with increasing temperature and vanishes at the critical temperature.

• For a plane surface, pressure just below the surface equals atmospheric pressure.
• For a convex surface, the pressure inside the liquid is greater than outside.
• For a concave surface, pressure inside the liquid is less than outside.

• Capillary rise occurs when liquid wets the tube (e.g., water in a glass).
• Capillary fall occurs when a liquid does not wet the tube (e.g., mercury in a glass tube).
• Rise or fall depends on surface tension and angle of contact.
• The narrower the tube, the greater the rise or fall.
• Capillarity plays an important role in natural processes like water rising in plants and oil rising in a lamp wick.

• In steady flow, properties such as pressure and velocity at a point remain constant over time.
• A flow line is the path followed by a particle in a moving fluid.
• A streamline is a curve whose tangent at any point gives the direction of fluid velocity.
• A flow tube is a bundle of streamlines; fluid does not cross its boundaries in steady flow.
• Laminar flow is smooth and orderly, while turbulent flow is irregular and chaotic.

• Speed of efflux: Liquid flowing out of a hole at depth hhh moves at the same speed as a body falling freely through a height hhh.
• Venturimeter: When a fluid passes through a narrow section, its speed increases and pressure decreases.
• Aeroplane lift: Faster airflow above the wings creates lower pressure, producing an upward lift force.
• Atomiser: High-speed air creates low pressure, causing liquid to rise and spray as fine droplets.
• Storm effect on roofs: Fast wind over a roof lowers pressure above it, and higher pressure below can lift the roof.

• They do not oppose deformation; they get permanently deformed.
• They have the ability to flow.
• They can take the shape of the container.